Development of probabilistic thinking-oriented learning tools for probability materials at junior high school students

NASA Astrophysics Data System (ADS)

Sari, Dwi Ivayana; Hermanto, Didik

2017-08-01

This research is a developmental research of probabilistic thinking-oriented learning tools for probability materials at ninth grade students. This study is aimed to produce a good probabilistic thinking-oriented learning tools. The subjects were IX-A students of MTs Model Bangkalan. The stages of this development research used 4-D development model which has been modified into define, design and develop. Teaching learning tools consist of lesson plan, students' worksheet, learning teaching media and students' achievement test. The research instrument used was a sheet of learning tools validation, a sheet of teachers' activities, a sheet of students' activities, students' response questionnaire and students' achievement test. The result of those instruments were analyzed descriptively to answer research objectives. The result was teaching learning tools in which oriented to probabilistic thinking of probability at ninth grade students which has been valid. Since teaching and learning tools have been revised based on validation, and after experiment in class produced that teachers' ability in managing class was effective, students' activities were good, students' responses to the learning tools were positive and the validity, sensitivity and reliability category toward achievement test. In summary, this teaching learning tools can be used by teacher to teach probability for develop students' probabilistic thinking.

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

PubMed

Hudson Kam, Carla L

2009-04-01

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.

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

PubMed

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

2016-02-02

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.

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

ERIC Educational Resources Information Center

Clinton, Virginia; Alibali, Martha Wagner; Nathan, Mitchel 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…

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…

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…

Understanding Bilingual Word Learning: The Role of Phonotactic Probability and Phonological Neighborhood Density

ERIC Educational Resources Information Center

Nair, Vishnu K. K.; Biedermann, Britta; Nickels, Lyndsey

2017-01-01

Purpose: Previous research has shown that the language-learning mechanism is affected by bilingualism resulting in a novel word learning advantage for bilingual speakers. However, less is known about the factors that might influence this advantage. This article reports an investigation of 2 factors: phonotactic probability and phonological…

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. (c) 2015 APA, all rights reserved).

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. Copyright © 2014 Elsevier Ltd. All rights reserved.

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.

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…

Supervised learning of probability distributions by neural networks

NASA Technical Reports Server (NTRS)

Baum, Eric B.; Wilczek, Frank

1988-01-01

Supervised learning algorithms for feedforward neural networks are investigated analytically. The back-propagation algorithm described by Werbos (1974), Parker (1985), and Rumelhart et al. (1986) is generalized by redefining the values of the input and output neurons as probabilities. The synaptic weights are then varied to follow gradients in the logarithm of likelihood rather than in the error. This modification is shown to provide a more rigorous theoretical basis for the algorithm and to permit more accurate predictions. A typical application involving a medical-diagnosis expert system is discussed.

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…

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…

Probability cueing of distractor locations: both intertrial facilitation and statistical learning mediate interference reduction.

PubMed

Goschy, Harriet; Bakos, Sarolta; Müller, Hermann J; Zehetleitner, Michael

2014-01-01

Targets in a visual search task are detected faster if they appear in a probable target region as compared to a less probable target region, an effect which has been termed "probability cueing." The present study investigated whether probability cueing cannot only speed up target detection, but also minimize distraction by distractors in probable distractor regions as compared to distractors in less probable distractor regions. To this end, three visual search experiments with a salient, but task-irrelevant, distractor ("additional singleton") were conducted. Experiment 1 demonstrated that observers can utilize uneven spatial distractor distributions to selectively reduce interference by distractors in frequent distractor regions as compared to distractors in rare distractor regions. Experiments 2 and 3 showed that intertrial facilitation, i.e., distractor position repetitions, and statistical learning (independent of distractor position repetitions) both contribute to the probability cueing effect for distractor locations. Taken together, the present results demonstrate that probability cueing of distractor locations has the potential to serve as a strong attentional cue for the shielding of likely distractor locations.

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…

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. Copyright © 2014 John Wiley & Sons, Ltd.

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

PubMed Central

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

2014-01-01

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. PMID:25316152

Teaching Probability to Pre-Service Teachers with Argumentation Based Science Learning Approach

ERIC Educational Resources Information Center

Can, Ömer Sinan; Isleyen, Tevfik

2016-01-01

The aim of this study is to explore the effects of the argumentation based science learning (ABSL) approach on the teaching probability to pre-service teachers. The sample of the study included 41 students studying at the Department of Elementary School Mathematics Education in a public university during the 2014-2015 academic years. The study is…

The Probable Prevalence and Sociodemographic Characteristics of Specific Learning Disorder in Primary School Children in Edirne.

PubMed

Görker, Işık; Bozatli, Leyla; Korkmazlar, Ümran; Yücel Karadağ, Meltem; Ceylan, Cansın; Söğüt, Ceren; Aykutlu, Hasan Cem; Subay, Büşra; Turan, Nesrin

2017-12-01

The aim of this study was to research the probable prevalence of Specific Learning Disorder (SLD) in primary school children in Edirne City and the relationships with their sociodemographic characteristics. The sample of our study was composed of 2,174 children who were educated in primary schools in second, third, and fourth grades in the academic year 2013-2014 in Edirne City. The teachers and parents of these children were given Specific Learning Difficulties Symptom Scale, Learning Disabilities Symptoms Checklist (teacher and parent forms), and sociodemographic data forms to fill in. Binary logistic regression analysis was used to assess the risk factors for SLD. Our study revealed that the probable prevalence of SLD was 13.6%; 17% for boys and 10.4% for girls. Reading impairment was 3.6%, writing impairment was 6.9%, and mathematic impairment was 6.5%. We determined that consanguineous marriages, low income, history of neonatal jaundice were found as risks for SLD; born by caesarean, developmental delay of walking, and history of neonatal jaundice were found as risks for mathematic impairment. A history of learning difficulties of parents was a risk factor for forming SLD and subtypes. Our findings were consistent with other study results about the prevalence of SLD. The relationships between the probable prevalence rates and sociodemographic data were discussed.

The Probable Prevalence and Sociodemographic Characteristics of Specific Learning Disorder in Primary School Children in Edirne

PubMed Central

GÖRKER, Işık; BOZATLI, Leyla; KORKMAZLAR, Ümran; YÜCEL KARADAĞ, Meltem; CEYLAN, Cansın; SÖĞÜT, Ceren; AYKUTLU, Hasan Cem; SUBAY, Büşra; TURAN, Nesrin

2017-01-01

Introduction The aim of this study was to research the probable prevalence of Specific Learning Disorder (SLD) in primary school children in Edirne City and the relationships with their sociodemographic characteristics. Methods The sample of our study was composed of 2,174 children who were educated in primary schools in second, third, and fourth grades in the academic year 2013–2014 in Edirne City. The teachers and parents of these children were given Specific Learning Difficulties Symptom Scale, Learning Disabilities Symptoms Checklist (teacher and parent forms), and sociodemographic data forms to fill in. Binary logistic regression analysis was used to assess the risk factors for SLD. Results Our study revealed that the probable prevalence of SLD was 13.6%; 17% for boys and 10.4% for girls. Reading impairment was 3.6%, writing impairment was 6.9%, and mathematic impairment was 6.5%. We determined that consanguineous marriages, low income, history of neonatal jaundice were found as risks for SLD; born by caesarean, developmental delay of walking, and history of neonatal jaundice were found as risks for mathematic impairment. A history of learning difficulties of parents was a risk factor for forming SLD and subtypes. Conclusion Our findings were consistent with other study results about the prevalence of SLD. The relationships between the probable prevalence rates and sociodemographic data were discussed. PMID:29321709

Implementing Inquiry-Based Learning and Examining the Effects in Junior College Probability Lessons

ERIC Educational Resources Information Center

Chong, Jessie Siew Yin; Chong, Maureen Siew Fang; Shahrill, Masitah; Abdullah, Nor Azura

2017-01-01

This study examined how Year 12 students use their inquiry skills in solving conditional probability questions by means of Inquiry-Based Learning application. The participants consisted of 66 students of similar academic abilities in Mathematics, selected from three classes, along with their respective teachers. Observational rubric and lesson…

What subject matter questions motivate the use of machine learning approaches compared to statistical models for probability prediction?

PubMed

Binder, Harald

2014-07-01

This is a discussion of the following papers: "Probability estimation with machine learning methods for dichotomous and multicategory outcome: Theory" by Jochen Kruppa, Yufeng Liu, Gérard Biau, Michael Kohler, Inke R. König, James D. Malley, and Andreas Ziegler; and "Probability estimation with machine learning methods for dichotomous and multicategory outcome: Applications" by Jochen Kruppa, Yufeng Liu, Hans-Christian Diener, Theresa Holste, Christian Weimar, Inke R. König, and Andreas Ziegler. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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…

Modulation of Complex-Spike Duration and Probability during Cerebellar Motor Learning in Visually Guided Smooth-Pursuit Eye Movements of Monkeys

PubMed Central

2017-01-01

Abstract Activation of an inferior olivary neuron powerfully excites Purkinje cells via its climbing fiber input and triggers a characteristic high-frequency burst, known as the complex spike (CS). The theory of cerebellar learning postulates that the CS induces long-lasting depression of the strength of synapses from active parallel fibers onto Purkinje cells, and that synaptic depression leads to changes in behavior. Prior reports showed that a CS on one learning trial is linked to a properly timed depression of simple spikes on the subsequent trial, as well as a learned change in pursuit eye movement. Further, the duration of a CS is a graded instruction for single-trial plasticity and behavioral learning. We now show across multiple learning paradigms that both the probability and duration of CS responses are correlated with the magnitudes of neural and behavioral learning in awake behaving monkeys. When the direction of the instruction for learning repeatedly was in the same direction or alternated directions, the duration and probability of CS responses decreased over a learning block along with the magnitude of trial-over-trial neural learning. When the direction of the instruction was randomized, CS duration, CS probability, and neural and behavioral learning remained stable across time. In contrast to depression, potentiation of simple-spike firing rate for ON-direction learning instructions follows a longer time course and plays a larger role as depression wanes. Computational analysis provides a model that accounts fully for the detailed statistics of a complex set of data. PMID:28698888

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.

Online Reinforcement Learning Using a Probability Density Estimation.

PubMed

Agostini, Alejandro; Celaya, Enric

2017-01-01

Function approximation in online, incremental, reinforcement learning needs to deal with two fundamental problems: biased sampling and nonstationarity. In this kind of task, biased sampling occurs because samples are obtained from specific trajectories dictated by the dynamics of the environment and are usually concentrated in particular convergence regions, which in the long term tend to dominate the approximation in the less sampled regions. The nonstationarity comes from the recursive nature of the estimations typical of temporal difference methods. This nonstationarity has a local profile, varying not only along the learning process but also along different regions of the state space. We propose to deal with these problems using an estimation of the probability density of samples represented with a gaussian mixture model. To deal with the nonstationarity problem, we use the common approach of introducing a forgetting factor in the updating formula. However, instead of using the same forgetting factor for the whole domain, we make it dependent on the local density of samples, which we use to estimate the nonstationarity of the function at any given input point. To address the biased sampling problem, the forgetting factor applied to each mixture component is modulated according to the new information provided in the updating, rather than forgetting depending only on time, thus avoiding undesired distortions of the approximation in less sampled regions.

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.

Obtaining Accurate Probabilities Using Classifier Calibration

ERIC Educational Resources Information Center

Pakdaman Naeini, Mahdi

2016-01-01

Learning probabilistic classification and prediction models that generate accurate probabilities is essential in many prediction and decision-making tasks in machine learning and data mining. One way to achieve this goal is to post-process the output of classification models to obtain more accurate probabilities. These post-processing methods are…

A Model-Free Machine Learning Method for Risk Classification and Survival Probability Prediction.

PubMed

Geng, Yuan; Lu, Wenbin; Zhang, Hao Helen

2014-01-01

Risk classification and survival probability prediction are two major goals in survival data analysis since they play an important role in patients' risk stratification, long-term diagnosis, and treatment selection. In this article, we propose a new model-free machine learning framework for risk classification and survival probability prediction based on weighted support vector machines. The new procedure does not require any specific parametric or semiparametric model assumption on data, and is therefore capable of capturing nonlinear covariate effects. We use numerous simulation examples to demonstrate finite sample performance of the proposed method under various settings. Applications to a glioma tumor data and a breast cancer gene expression survival data are shown to illustrate the new methodology in real data analysis.

Psychomotor development and learning difficulties in preschool children with probable attention deficit hyperactivity disorder: An epidemiological study in Navarre and La Rioja.

PubMed

Marín-Méndez, J J; Borra-Ruiz, M C; Álvarez-Gómez, M J; Soutullo Esperón, C

2017-10-01

ADHD symptoms begin to appear at preschool age. ADHD may have a significant negative impact on academic performance. In Spain, there are no standardized tools for detecting ADHD at preschool age, nor is there data about the incidence of this disorder. To evaluate developmental factors and learning difficulties associated with probable ADHD and to assess the impact of ADHD in school performance. We conducted a population-based study with a stratified multistage proportional cluster sample design. We found significant differences between probable ADHD and parents' perception of difficulties in expressive language, comprehension, and fine motor skills, as well as in emotions, concentration, behaviour, and relationships. Around 34% of preschool children with probable ADHD showed global learning difficulties, mainly in patients with the inattentive type. According to the multivariate analysis, learning difficulties were significantly associated with both delayed psychomotor development during the first 3 years of life (OR: 5.57) as assessed by parents, and probable ADHD (OR: 2.34) CONCLUSIONS: There is a connection between probable ADHD in preschool children and parents' perception of difficulties in several dimensions of development and learning. Early detection of ADHD at preschool ages is necessary to start prompt and effective clinical and educational interventions. Copyright © 2016 Sociedad Española de Neurología. Publicado por Elsevier España, S.L.U. All rights reserved.

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…

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…

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…

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…

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…

Risk estimation using probability machines

PubMed Central

2014-01-01

Background Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. Results We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. Conclusions The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from. PMID:24581306

Risk estimation using probability machines.

PubMed

Dasgupta, Abhijit; Szymczak, Silke; Moore, Jason H; Bailey-Wilson, Joan E; Malley, James D

2014-03-01

Logistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios. We show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented. The models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a "risk machine", will share properties from the statistical machine that it is derived from.

Improved Membership Probability for Moving Groups: Bayesian and Machine Learning Approaches

NASA Astrophysics Data System (ADS)

Lee, Jinhee; Song, Inseok

2018-01-01

Gravitationally unbound loose stellar associations (i.e., young nearby moving groups: moving groups hereafter) have been intensively explored because they are important in planet and disk formation studies, exoplanet imaging, and age calibration. Among the many efforts devoted to the search for moving group members, a Bayesian approach (e.g.,using the code BANYAN) has become popular recently because of the many advantages it offers. However, the resultant membership probability needs to be carefully adopted because of its sensitive dependence on input models. In this study, we have developed an improved membership calculation tool focusing on the beta-Pic moving group. We made three improvements for building models used in BANYAN II: (1) updating a list of accepted members by re-assessing memberships in terms of position, motion, and age, (2) investigating member distribution functions in XYZ, and (3) exploring field star distribution functions in XYZUVW. Our improved tool can change membership probability up to 70%. Membership probability is critical and must be better defined. For example, our code identifies only one third of the candidate members in SIMBAD that are believed to be kinematically associated with beta-Pic moving group.Additionally, we performed cluster analysis of young nearby stars using an unsupervised machine learning approach. As more moving groups and their members are identified, the complexity and ambiguity in moving group configuration has been increased. To clarify this issue, we analyzed ~4,000 X-ray bright young stellar candidates. Here, we present the preliminary results. By re-identifying moving groups with the least human intervention, we expect to understand the composition of the solar neighborhood. Moreover better defined moving group membership will help us understand star formation and evolution in relatively low density environments; especially for the low-mass stars which will be identified in the coming Gaia release.

Are baboons learning "orthographic" representations? Probably not

PubMed Central

Bröker, Franziska; Ramscar, Michael; Baayen, Harald

2017-01-01

The ability of Baboons (papio papio) to distinguish between English words and nonwords has been modeled using a deep learning convolutional network model that simulates a ventral pathway in which lexical representations of different granularity develop. However, given that pigeons (columba livia), whose brain morphology is drastically different, can also be trained to distinguish between English words and nonwords, it appears that a less species-specific learning algorithm may be required to explain this behavior. Accordingly, we examined whether the learning model of Rescorla and Wagner, which has proved to be amazingly fruitful in understanding animal and human learning could account for these data. We show that a discrimination learning network using gradient orientation features as input units and word and nonword units as outputs succeeds in predicting baboon lexical decision behavior—including key lexical similarity effects and the ups and downs in accuracy as learning unfolds—with surprising precision. The models performance, in which words are not explicitly represented, is remarkable because it is usually assumed that lexicality decisions, including the decisions made by baboons and pigeons, are mediated by explicit lexical representations. By contrast, our results suggest that in learning to perform lexical decision tasks, baboons and pigeons do not construct a hierarchy of lexical units. Rather, they make optimal use of low-level information obtained through the massively parallel processing of gradient orientation features. Accordingly, we suggest that reading in humans first involves initially learning a high-level system building on letter representations acquired from explicit instruction in literacy, which is then integrated into a conventionalized oral communication system, and that like the latter, fluent reading involves the massively parallel processing of the low-level features encoding semantic contrasts. PMID:28859134

Are baboons learning "orthographic" representations? Probably not.

PubMed

Linke, Maja; Bröker, Franziska; Ramscar, Michael; Baayen, Harald

2017-01-01

The ability of Baboons (papio papio) to distinguish between English words and nonwords has been modeled using a deep learning convolutional network model that simulates a ventral pathway in which lexical representations of different granularity develop. However, given that pigeons (columba livia), whose brain morphology is drastically different, can also be trained to distinguish between English words and nonwords, it appears that a less species-specific learning algorithm may be required to explain this behavior. Accordingly, we examined whether the learning model of Rescorla and Wagner, which has proved to be amazingly fruitful in understanding animal and human learning could account for these data. We show that a discrimination learning network using gradient orientation features as input units and word and nonword units as outputs succeeds in predicting baboon lexical decision behavior-including key lexical similarity effects and the ups and downs in accuracy as learning unfolds-with surprising precision. The models performance, in which words are not explicitly represented, is remarkable because it is usually assumed that lexicality decisions, including the decisions made by baboons and pigeons, are mediated by explicit lexical representations. By contrast, our results suggest that in learning to perform lexical decision tasks, baboons and pigeons do not construct a hierarchy of lexical units. Rather, they make optimal use of low-level information obtained through the massively parallel processing of gradient orientation features. Accordingly, we suggest that reading in humans first involves initially learning a high-level system building on letter representations acquired from explicit instruction in literacy, which is then integrated into a conventionalized oral communication system, and that like the latter, fluent reading involves the massively parallel processing of the low-level features encoding semantic contrasts.

Impact of statistical learning methods on the predictive power of multivariate normal tissue complication probability models.

PubMed

Xu, Cheng-Jian; van der Schaaf, Arjen; Schilstra, Cornelis; Langendijk, Johannes A; van't Veld, Aart A

2012-03-15

To study the impact of different statistical learning methods on the prediction performance of multivariate normal tissue complication probability (NTCP) models. 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. 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. The commonly used stepwise selection method, which is simple to execute, may be insufficient for NTCP modeling. The LASSO method is recommended. Copyright © 2012 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Cocco, Simona; Monasson, Rémi

2015-11-01

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

The Effect of Phonotactic Probability and Neighbourhood Density on Pseudoword Learning in 6- and 7-Year-Old Children

ERIC Educational Resources Information Center

van der Kleij, Sanne W.; Rispens, Judith E.; Scheper, Annette R.

2016-01-01

The aim of this study was to examine the influence of phonotactic probability (PP) and neighbourhood density (ND) on pseudoword learning in 17 Dutch-speaking typically developing children (mean age 7;2). They were familiarized with 16 one-syllable pseudowords varying in PP (high vs low) and ND (high vs low) via a storytelling procedure. The…

Spatial Probability Cuing and Right Hemisphere Damage

ERIC Educational Resources Information Center

Shaqiri, Albulena; Anderson, Britt

2012-01-01

In this experiment we studied statistical learning, inter-trial priming, and visual attention. We assessed healthy controls and right brain damaged (RBD) patients with and without neglect, on a simple visual discrimination task designed to measure priming effects and probability learning. All participants showed a preserved priming effect for item…

Probability matching in perceptrons: Effects of conditional dependence and linear nonseparability.

PubMed

Dawson, Michael R W; Gupta, Maya

2017-01-01

Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent's environment. For instance, when artificial neural networks match probability, the activity in their output unit equals the past probability of reward in the presence of a stimulus. Our previous research demonstrated that simple artificial neural networks (perceptrons, which consist of a set of input units directly connected to a single output unit) learn to match probability when presented different cues in isolation. The current paper extends this research by showing that perceptrons can match probabilities when presented simultaneous cues, with each cue signaling different reward likelihoods. In our first simulation, we presented up to four different cues simultaneously; the likelihood of reward signaled by the presence of one cue was independent of the likelihood of reward signaled by other cues. Perceptrons learned to match reward probabilities by treating each cue as an independent source of information about the likelihood of reward. In a second simulation, we violated the independence between cues by making some reward probabilities depend upon cue interactions. We did so by basing reward probabilities on a logical combination (AND or XOR) of two of the four possible cues. We also varied the size of the reward associated with the logical combination. We discovered that this latter manipulation was a much better predictor of perceptron performance than was the logical structure of the interaction between cues. This indicates that when perceptrons learn to match probabilities, they do so by assuming that each signal of a reward is independent of any other; the best predictor of perceptron performance is a quantitative measure of the independence of these input signals, and not the logical structure of the problem being learned.

Probability matching in perceptrons: Effects of conditional dependence and linear nonseparability

PubMed Central

2017-01-01

Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent’s environment. For instance, when artificial neural networks match probability, the activity in their output unit equals the past probability of reward in the presence of a stimulus. Our previous research demonstrated that simple artificial neural networks (perceptrons, which consist of a set of input units directly connected to a single output unit) learn to match probability when presented different cues in isolation. The current paper extends this research by showing that perceptrons can match probabilities when presented simultaneous cues, with each cue signaling different reward likelihoods. In our first simulation, we presented up to four different cues simultaneously; the likelihood of reward signaled by the presence of one cue was independent of the likelihood of reward signaled by other cues. Perceptrons learned to match reward probabilities by treating each cue as an independent source of information about the likelihood of reward. In a second simulation, we violated the independence between cues by making some reward probabilities depend upon cue interactions. We did so by basing reward probabilities on a logical combination (AND or XOR) of two of the four possible cues. We also varied the size of the reward associated with the logical combination. We discovered that this latter manipulation was a much better predictor of perceptron performance than was the logical structure of the interaction between cues. This indicates that when perceptrons learn to match probabilities, they do so by assuming that each signal of a reward is independent of any other; the best predictor of perceptron performance is a quantitative measure of the independence of these input signals, and not the logical structure of the problem being learned. PMID:28212422

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…

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…

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.

Saccade selection when reward probability is dynamically manipulated using Markov chains

PubMed Central

Lovejoy, Lee P.; Krauzlis, Richard J.

2012-01-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200–600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection. PMID:18330552

Saccade selection when reward probability is dynamically manipulated using Markov chains.

PubMed

Nummela, Samuel U; Lovejoy, Lee P; Krauzlis, Richard J

2008-05-01

Markov chains (stochastic processes where probabilities are assigned based on the previous outcome) are commonly used to examine the transitions between behavioral states, such as those that occur during foraging or social interactions. However, relatively little is known about how well primates can incorporate knowledge about Markov chains into their behavior. Saccadic eye movements are an example of a simple behavior influenced by information about probability, and thus are good candidates for testing whether subjects can learn Markov chains. In addition, when investigating the influence of probability on saccade target selection, the use of Markov chains could provide an alternative method that avoids confounds present in other task designs. To investigate these possibilities, we evaluated human behavior on a task in which stimulus reward probabilities were assigned using a Markov chain. On each trial, the subject selected one of four identical stimuli by saccade; after selection, feedback indicated the rewarded stimulus. Each session consisted of 200-600 trials, and on some sessions, the reward magnitude varied. On sessions with a uniform reward, subjects (n = 6) learned to select stimuli at a frequency close to reward probability, which is similar to human behavior on matching or probability classification tasks. When informed that a Markov chain assigned reward probabilities, subjects (n = 3) learned to select the greatest reward probability more often, bringing them close to behavior that maximizes reward. On sessions where reward magnitude varied across stimuli, subjects (n = 6) demonstrated preferences for both greater reward probability and greater reward magnitude, resulting in a preference for greater expected value (the product of reward probability and magnitude). These results demonstrate that Markov chains can be used to dynamically assign probabilities that are rapidly exploited by human subjects during saccade target selection.

Identification of probabilities.

PubMed

Vitányi, Paul M B; Chater, Nick

2017-02-01

Within psychology, neuroscience and artificial intelligence, there has been increasing interest in the proposal that the brain builds probabilistic models of sensory and linguistic input: that is, to infer a probabilistic model from a sample. The practical problems of such inference are substantial: the brain has limited data and restricted computational resources. But there is a more fundamental question: is the problem of inferring a probabilistic model from a sample possible even in principle? We explore this question and find some surprisingly positive and general results. First, for a broad class of probability distributions characterized by computability restrictions, we specify a learning algorithm that will almost surely identify a probability distribution in the limit given a finite i.i.d. sample of sufficient but unknown length. This is similarly shown to hold for sequences generated by a broad class of Markov chains, subject to computability assumptions. The technical tool is the strong law of large numbers. Second, for a large class of dependent sequences, we specify an algorithm which identifies in the limit a computable measure for which the sequence is typical, in the sense of Martin-Löf (there may be more than one such measure). The technical tool is the theory of Kolmogorov complexity. We analyze the associated predictions in both cases. We also briefly consider special cases, including language learning, and wider theoretical implications for psychology.

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 (c) 2016 APA, all rights reserved).

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…

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…

Task specificity of attention training: the case of probability cuing

PubMed Central

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

2014-01-01

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

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…

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

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.

Calibrating random forests for probability estimation.

PubMed

Dankowski, Theresa; Ziegler, Andreas

2016-09-30

Probabilities can be consistently estimated using random forests. It is, however, unclear how random forests should be updated to make predictions for other centers or at different time points. In this work, we present two approaches for updating random forests for probability estimation. The first method has been proposed by Elkan and may be used for updating any machine learning approach yielding consistent probabilities, so-called probability machines. The second approach is a new strategy specifically developed for random forests. Using the terminal nodes, which represent conditional probabilities, the random forest is first translated to logistic regression models. These are, in turn, used for re-calibration. The two updating strategies were compared in a simulation study and are illustrated with data from the German Stroke Study Collaboration. In most simulation scenarios, both methods led to similar improvements. In the simulation scenario in which the stricter assumptions of Elkan's method were not met, the logistic regression-based re-calibration approach for random forests outperformed Elkan's method. It also performed better on the stroke data than Elkan's method. The strength of Elkan's method is its general applicability to any probability machine. However, if the strict assumptions underlying this approach are not met, the logistic regression-based approach is preferable for updating random forests for probability estimation. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

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…

Neural dynamics of reward probability coding: a Magnetoencephalographic study in humans

PubMed Central

Thomas, Julie; Vanni-Mercier, Giovanna; Dreher, Jean-Claude

2013-01-01

Prediction of future rewards and discrepancy between actual and expected outcomes (prediction error) are crucial signals for adaptive behavior. In humans, a number of fMRI studies demonstrated that reward probability modulates these two signals in a large brain network. Yet, the spatio-temporal dynamics underlying the neural coding of reward probability remains unknown. Here, using magnetoencephalography, we investigated the neural dynamics of prediction and reward prediction error computations while subjects learned to associate cues of slot machines with monetary rewards with different probabilities. We showed that event-related magnetic fields (ERFs) arising from the visual cortex coded the expected reward value 155 ms after the cue, demonstrating that reward value signals emerge early in the visual stream. Moreover, a prediction error was reflected in ERF peaking 300 ms after the rewarded outcome and showing decreasing amplitude with higher reward probability. This prediction error signal was generated in a network including the anterior and posterior cingulate cortex. These findings pinpoint the spatio-temporal characteristics underlying reward probability coding. Together, our results provide insights into the neural dynamics underlying the ability to learn probabilistic stimuli-reward contingencies. PMID:24302894

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…

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

PubMed

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

2016-06-01

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

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

PubMed Central

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

2015-01-01

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

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®…

The analysis of probability task completion; Taxonomy of probabilistic thinking-based across gender in elementary school students

NASA Astrophysics Data System (ADS)

Sari, Dwi Ivayana; Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

Formulation of mathematical learning goals now is not only oriented on cognitive product, but also leads to cognitive process, which is probabilistic thinking. Probabilistic thinking is needed by students to make a decision. Elementary school students are required to develop probabilistic thinking as foundation to learn probability at higher level. A framework of probabilistic thinking of students had been developed by using SOLO taxonomy, which consists of prestructural probabilistic thinking, unistructural probabilistic thinking, multistructural probabilistic thinking and relational probabilistic thinking. This study aimed to analyze of probability task completion based on taxonomy of probabilistic thinking. The subjects were two students of fifth grade; boy and girl. Subjects were selected by giving test of mathematical ability and then based on high math ability. Subjects were given probability tasks consisting of sample space, probability of an event and probability comparison. The data analysis consisted of categorization, reduction, interpretation and conclusion. Credibility of data used time triangulation. The results was level of boy's probabilistic thinking in completing probability tasks indicated multistructural probabilistic thinking, while level of girl's probabilistic thinking in completing probability tasks indicated unistructural probabilistic thinking. The results indicated that level of boy's probabilistic thinking was higher than level of girl's probabilistic thinking. The results could contribute to curriculum developer in developing probability learning goals for elementary school students. Indeed, teachers could teach probability with regarding gender difference.

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.

Pointwise probability reinforcements for robust statistical inference.

PubMed

Frénay, Benoît; Verleysen, Michel

2014-02-01

Statistical inference using machine learning techniques may be difficult with small datasets because of abnormally frequent data (AFDs). AFDs are observations that are much more frequent in the training sample that they should be, with respect to their theoretical probability, and include e.g. outliers. Estimates of parameters tend to be biased towards models which support such data. This paper proposes to introduce pointwise probability reinforcements (PPRs): the probability of each observation is reinforced by a PPR and a regularisation allows controlling the amount of reinforcement which compensates for AFDs. The proposed solution is very generic, since it can be used to robustify any statistical inference method which can be formulated as a likelihood maximisation. Experiments show that PPRs can be easily used to tackle regression, classification and projection: models are freed from the influence of outliers. Moreover, outliers can be filtered manually since an abnormality degree is obtained for each observation. Copyright © 2013 Elsevier Ltd. All rights reserved.

Storm-based Cloud-to-Ground Lightning Probabilities and Warnings

NASA Astrophysics Data System (ADS)

Calhoun, K. M.; Meyer, T.; Kingfield, D.

2017-12-01

A new cloud-to-ground (CG) lightning probability algorithm has been developed using machine-learning methods. With storm-based inputs of Earth Networks' in-cloud lightning, Vaisala's CG lightning, multi-radar/multi-sensor (MRMS) radar derived products including the Maximum Expected Size of Hail (MESH) and Vertically Integrated Liquid (VIL), and near storm environmental data including lapse rate and CAPE, a random forest algorithm was trained to produce probabilities of CG lightning up to one-hour in advance. As part of the Prototype Probabilistic Hazard Information experiment in the Hazardous Weather Testbed in 2016 and 2017, National Weather Service forecasters were asked to use this CG lightning probability guidance to create rapidly updating probability grids and warnings for the threat of CG lightning for 0-60 minutes. The output from forecasters was shared with end-users, including emergency managers and broadcast meteorologists, as part of an integrated warning team.

Tuned by experience: How orientation probability modulates early perceptual processing.

PubMed

Jabar, Syaheed B; Filipowicz, Alex; Anderson, Britt

2017-09-01

Probable stimuli are more often and more quickly detected. While stimulus probability is known to affect decision-making, it can also be explained as a perceptual phenomenon. Using spatial gratings, we have previously shown that probable orientations are also more precisely estimated, even while participants remained naive to the manipulation. We conducted an electrophysiological study to investigate the effect that probability has on perception and visual-evoked potentials. In line with previous studies on oddballs and stimulus prevalence, low-probability orientations were associated with a greater late positive 'P300' component which might be related to either surprise or decision-making. However, the early 'C1' component, thought to reflect V1 processing, was dampened for high-probability orientations while later P1 and N1 components were unaffected. Exploratory analyses revealed a participant-level correlation between C1 and P300 amplitudes, suggesting a link between perceptual processing and decision-making. We discuss how these probability effects could be indicative of sharpening of neurons preferring the probable orientations, due either to perceptual learning, or to feature-based attention. Copyright © 2017 Elsevier Ltd. All rights reserved.

Dynamic Encoding of Speech Sequence Probability in Human Temporal Cortex

PubMed Central

Leonard, Matthew K.; Bouchard, Kristofer E.; Tang, Claire

2015-01-01

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. PMID:25948269

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.

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.

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. Copyright © 2015 the American Physiological Society.

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.

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

PubMed Central

Christou, Nicolas; Dinov, Ivo D.

2011-01-01

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. PMID:21603097

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.

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…

Implicit chaining in cotton-top tamarins (Saguinus oedipus) with elements equated for probability of reinforcement

PubMed Central

Dillon, Laura; Collins, Meaghan; Conway, Maura; Cunningham, Kate

2013-01-01

Three experiments examined the implicit learning of sequences under conditions in which the elements comprising a sequence were equated in terms of reinforcement probability. In Experiment 1 cotton-top tamarins (Saguinus oedipus) experienced a five-element sequence displayed serially on a touch screen in which reinforcement probability was equated across elements at .16 per element. Tamarins demonstrated learning of this sequence with higher latencies during a random test as compared to baseline sequence training. In Experiments 2 and 3, manipulations of the procedure used in the first experiment were undertaken to rule out a confound owing to the fact that the elements in Experiment 1 bore different temporal relations to the intertrial interval (ITI), an inhibitory period. The results of Experiments 2 and 3 indicated that the implicit learning observed in Experiment 1 was not due to temporal proximity between some elements and the inhibitory ITI. The results taken together support two conclusion: First that tamarins engaged in sequence learning whether or not there was contingent reinforcement for learning the sequence, and second that this learning was not due to subtle differences in associative strength between the elements of the sequence. PMID:23344718

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

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 show improvement…

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

PubMed

Song, Yanlong; Smiley-Oyen, Ann L

2017-12-01

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

Evaluation of the probability of arrester failure in a high-voltage transmission line using a Q learning artificial neural network model

NASA Astrophysics Data System (ADS)

Ekonomou, L.; Karampelas, P.; Vita, V.; Chatzarakis, G. E.

2011-04-01

One of the most popular methods of protecting high voltage transmission lines against lightning strikes and internal overvoltages is the use of arresters. The installation of arresters in high voltage transmission lines can prevent or even reduce the lines' failure rate. Several studies based on simulation tools have been presented in order to estimate the critical currents that exceed the arresters' rated energy stress and to specify the arresters' installation interval. In this work artificial intelligence, and more specifically a Q-learning artificial neural network (ANN) model, is addressed for evaluating the arresters' failure probability. The aims of the paper are to describe in detail the developed Q-learning ANN model and to compare the results obtained by its application in operating 150 kV Greek transmission lines with those produced using a simulation tool. The satisfactory and accurate results of the proposed ANN model can make it a valuable tool for designers of electrical power systems seeking more effective lightning protection, reducing operational costs and better continuity of service.

The first cycle of the reflective pedagogical paradigm implementation in the introduction probability theory course

NASA Astrophysics Data System (ADS)

Julie, Hongki

2017-08-01

One of purposes of this study was describing the steps of the teaching and learning process if the teacher in the Introduction Probability Theory course wanted to teach about the event probability by using the reflective pedagogical paradigm (RPP) and describing the results achieved by the students. The study consisted of three cycles, but the results would be presented in this paper was limited to the results obtained in the first cycle. Stages conducted by the researcher in the first cycle could be divided into five stages, namely (1) to know the students' context, (2) to plan and provide student learning experiences, (3) to facilitate students in actions, (4) to ask students to make a reflection and (5) to evaluate. The type of research used in this research was descriptive qualitative and quantitative research. The students' learning experience, the students' action, and the students' reflection would be described qualitatively. The student evaluation results would be described quantitatively. The research subject in this study was 38 students taking the introduction probability theory course in class C. From the students' reflection, still quite a lot of students were not complete in writing concepts that they have learned and / or have not been precise in describing the relationships between concepts that they have learned. From the students' evaluation, 85.29% students got score under 7. If examined more deeply, the most difficulty of students were in the mathematical horizontal process. As a result, they had difficulty in performing the mathematical vertical process.

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…

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

PubMed Central

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

2014-01-01

Summary Data analysis requires subtle probability reasoning to answer questions like What is the chance of event A occurring, given that event B was observed? This generic question arises in discussions of many intriguing scientific questions such as What is the probability that an adolescent weighs between 120 and 140 pounds given that they are of average height? and What is the probability of (monetary) inflation exceeding 4% and housing price index below 110? To address such problems, learning some applied, theoretical or cross-disciplinary probability concepts is necessary. Teaching such courses can be improved by utilizing modern information technology resources. Students’ understanding of multivariate distributions, conditional probabilities, correlation and causation can be significantly strengthened by employing interactive web-based science educational resources. Independent of the type of a probability course (e.g. majors, minors or service probability course, rigorous measure-theoretic, applied or statistics course) student motivation, learning experiences and knowledge retention may be enhanced by blending modern technological tools within the classical conceptual pedagogical models. We have designed, implemented and disseminated a portable open-source web-application for teaching multivariate distributions, marginal, joint and conditional probabilities using the special case of bivariate Normal distribution. A real adolescent height and weight dataset is used to demonstrate the classroom utilization of the new web-application to address problems of parameter estimation, univariate and multivariate inference. PMID:25419016

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

PubMed

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

2013-01-01

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

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…

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.

Predicting Robust Learning with the Visual Form of the Moment-by-Moment Learning Curve

ERIC Educational Resources Information Center

Baker, Ryan S.; Hershkovitz, Arnon; Rossi, Lisa M.; Goldstein, Adam B.; Gowda, Sujith M.

2013-01-01

We present a new method for analyzing a student's learning over time for a specific skill: analysis of the graph of the student's moment-by-moment learning over time. Moment-by-moment learning is calculated using a data-mined model that assesses the probability that a student learned a skill or concept at a specific time during learning (Baker,…

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.

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. Copyright © 2016 Elsevier Inc. All rights reserved.

Stimulus discriminability may bias value-based probabilistic learning.

PubMed

Schutte, Iris; Slagter, Heleen A; Collins, Anne G E; Frank, Michael J; Kenemans, J Leon

2017-01-01

Reinforcement learning tasks are often used to assess participants' tendency to learn more from the positive or more from the negative consequences of one's action. However, this assessment often requires comparison in learning performance across different task conditions, which may differ in the relative salience or discriminability of the stimuli associated with more and less rewarding outcomes, respectively. To address this issue, in a first set of studies, participants were subjected to two versions of a common probabilistic learning task. The two versions differed with respect to the stimulus (Hiragana) characters associated with reward probability. The assignment of character to reward probability was fixed within version but reversed between versions. We found that performance was highly influenced by task version, which could be explained by the relative perceptual discriminability of characters assigned to high or low reward probabilities, as assessed by a separate discrimination experiment. Participants were more reliable in selecting rewarding characters that were more discriminable, leading to differences in learning curves and their sensitivity to reward probability. This difference in experienced reinforcement history was accompanied by performance biases in a test phase assessing ability to learn from positive vs. negative outcomes. In a subsequent large-scale web-based experiment, this impact of task version on learning and test measures was replicated and extended. Collectively, these findings imply a key role for perceptual factors in guiding reward learning and underscore the need to control stimulus discriminability when making inferences about individual differences in reinforcement learning.

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...

PROBABILITY SURVEYS , CONDITIONAL PROBABILITIES AND ECOLOGICAL RISK ASSESSMENT

EPA Science Inventory

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

Probability Surveys, Conditional 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 ...

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

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

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 subspacesmore » 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.« less

The Estimation of Tree Posterior Probabilities Using Conditional Clade Probability Distributions

PubMed Central

Larget, Bret

2013-01-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample. [Bayesian phylogenetics; conditional clade distributions; improved accuracy; posterior probabilities of trees.] PMID:23479066

The Influence of Phonotactic Probability on Nonword Repetition and Fast Mapping in 3-Year-Olds With a History of Expressive Language Delay.

PubMed

MacRoy-Higgins, Michelle; Dalton, Kevin Patrick

2015-12-01

The purpose of this study was to examine the influence of phonotactic probability on sublexical (phonological) and lexical representations in 3-year-olds who had a history of being late talkers in comparison with their peers with typical language development. Ten 3-year-olds who were late talkers and 10 age-matched typically developing controls completed nonword repetition and fast mapping tasks; stimuli for both experimental procedures differed in phonotactic probability. Both participant groups repeated nonwords containing high phonotactic probability sequences more accurately than nonwords containing low phonotactic probability sequences. Participants with typical language showed an early advantage for fast mapping high phonotactic probability words; children who were late talkers required more exposures to the novel words to show the same advantage for fast mapping high phonotactic probability words. Children who were late talkers showed similar sensitivities to phonotactic probability in nonword repetition and word learning when compared with their peers with no history of language delay. However, word learning in children who were late talkers appeared to be slower when compared with their peers.

Modulation of spatial attention by goals, statistical learning, and monetary reward.

PubMed

Jiang, Yuhong V; Sha, Li Z; Remington, Roger W

2015-10-01

This study documented the relative strength of task goals, visual statistical learning, and monetary reward in guiding spatial attention. Using a difficult T-among-L search task, we cued spatial attention to one visual quadrant by (i) instructing people to prioritize it (goal-driven attention), (ii) placing the target frequently there (location probability learning), or (iii) associating that quadrant with greater monetary gain (reward-based attention). Results showed that successful goal-driven attention exerted the strongest influence on search RT. Incidental location probability learning yielded a smaller though still robust effect. Incidental reward learning produced negligible guidance for spatial attention. The 95 % confidence intervals of the three effects were largely nonoverlapping. To understand these results, we simulated the role of location repetition priming in probability cuing and reward learning. Repetition priming underestimated the strength of location probability cuing, suggesting that probability cuing involved long-term statistical learning of how to shift attention. Repetition priming provided a reasonable account for the negligible effect of reward on spatial attention. We propose a multiple-systems view of spatial attention that includes task goals, search habit, and priming as primary drivers of top-down attention.

Modulation of spatial attention by goals, statistical learning, and monetary reward

PubMed Central

Sha, Li Z.; Remington, Roger W.

2015-01-01

This study documented the relative strength of task goals, visual statistical learning, and monetary reward in guiding spatial attention. Using a difficult T-among-L search task, we cued spatial attention to one visual quadrant by (i) instructing people to prioritize it (goal-driven attention), (ii) placing the target frequently there (location probability learning), or (iii) associating that quadrant with greater monetary gain (reward-based attention). Results showed that successful goal-driven attention exerted the strongest influence on search RT. Incidental location probability learning yielded a smaller though still robust effect. Incidental reward learning produced negligible guidance for spatial attention. The 95 % confidence intervals of the three effects were largely nonoverlapping. To understand these results, we simulated the role of location repetition priming in probability cuing and reward learning. Repetition priming underestimated the strength of location probability cuing, suggesting that probability cuing involved long-term statistical learning of how to shift attention. Repetition priming provided a reasonable account for the negligible effect of reward on spatial attention. We propose a multiple-systems view of spatial attention that includes task goals, search habit, and priming as primary drivers of top-down attention. PMID:26105657

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.

Learning in a Changing Environment

ERIC Educational Resources Information Center

Speekenbrink, Maarten; Shanks, David R.

2010-01-01

Multiple cue probability learning studies have typically focused on stationary environments. We present 3 experiments investigating learning in changing environments. A fine-grained analysis of the learning dynamics shows that participants were responsive to both abrupt and gradual changes in cue-outcome relations. We found no evidence that…

Prior probability modulates anticipatory activity in category-specific areas.

PubMed

Trapp, Sabrina; Lepsien, Jöran; Kotz, Sonja A; Bar, Moshe

2016-02-01

Bayesian models are currently a dominant framework for describing human information processing. However, it is not clear yet how major tenets of this framework can be translated to brain processes. In this study, we addressed the neural underpinning of prior probability and its effect on anticipatory activity in category-specific areas. Before fMRI scanning, participants were trained in two behavioral sessions to learn the prior probability and correct order of visual events within a sequence. The events of each sequence included two different presentations of a geometric shape and one picture of either a house or a face, which appeared with either a high or a low likelihood. Each sequence was preceded by a cue that gave participants probabilistic information about which items to expect next. This allowed examining cue-related anticipatory modulation of activity as a function of prior probability in category-specific areas (fusiform face area and parahippocampal place area). Our findings show that activity in the fusiform face area was higher when faces had a higher prior probability. The finding of a difference between levels of expectations is consistent with graded, probabilistically modulated activity, but the data do not rule out the alternative explanation of a categorical neural response. Importantly, these differences were only visible during anticipation, and vanished at the time of stimulus presentation, calling for a functional distinction when considering the effects of prior probability. Finally, there were no anticipatory effects for houses in the parahippocampal place area, suggesting sensitivity to stimulus material when looking at effects of prediction.

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.

The estimation of tree posterior probabilities using conditional clade probability distributions.

PubMed

Larget, Bret

2013-07-01

In this article I introduce the idea of conditional independence of separated subtrees as a principle by which to estimate the posterior probability of trees using conditional clade probability distributions rather than simple sample relative frequencies. I describe an algorithm for these calculations and software which implements these ideas. I show that these alternative calculations are very similar to simple sample relative frequencies for high probability trees but are substantially more accurate for relatively low probability trees. The method allows the posterior probability of unsampled trees to be calculated when these trees contain only clades that are in other sampled trees. Furthermore, the method can be used to estimate the total probability of the set of sampled trees which provides a measure of the thoroughness of a posterior sample.

Elastic K-means using posterior probability

PubMed Central

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model. PMID:29240756

Elastic K-means using posterior probability.

PubMed

Zheng, Aihua; Jiang, Bo; Li, Yan; Zhang, Xuehan; Ding, Chris

2017-01-01

The widely used K-means clustering is a hard clustering algorithm. Here we propose a Elastic K-means clustering model (EKM) using posterior probability with soft capability where each data point can belong to multiple clusters fractionally and show the benefit of proposed Elastic K-means. Furthermore, in many applications, besides vector attributes information, pairwise relations (graph information) are also available. Thus we integrate EKM with Normalized Cut graph clustering into a single clustering formulation. Finally, we provide several useful matrix inequalities which are useful for matrix formulations of learning models. Based on these results, we prove the correctness and the convergence of EKM algorithms. Experimental results on six benchmark datasets demonstrate the effectiveness of proposed EKM and its integrated model.

Comparison of Content Structure and Cognitive Structure in the Learning of Probability.

ERIC Educational Resources Information Center

Geeslin, William E.

Digraphs, graphs, and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability. Mathematical structure was defined as the relationship between concepts within a set of abstract systems. The word association technique was used to measure the existing relations (cognitive structure) in S's memory…

Nash Equilibrium of Social-Learning Agents in a Restless Multiarmed Bandit Game.

PubMed

Nakayama, Kazuaki; Hisakado, Masato; Mori, Shintaro

2017-05-16

We study a simple model for social-learning agents in a restless multiarmed bandit (rMAB). The bandit has one good arm that changes to a bad one with a certain probability. Each agent stochastically selects one of the two methods, random search (individual learning) or copying information from other agents (social learning), using which he/she seeks the good arm. Fitness of an agent is the probability to know the good arm in the steady state of the agent system. In this model, we explicitly construct the unique Nash equilibrium state and show that the corresponding strategy for each agent is an evolutionarily stable strategy (ESS) in the sense of Thomas. It is shown that the fitness of an agent with ESS is superior to that of an asocial learner when the success probability of social learning is greater than a threshold determined from the probability of success of individual learning, the probability of change of state of the rMAB, and the number of agents. The ESS Nash equilibrium is a solution to Rogers' paradox.

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.

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.

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

NASA Astrophysics Data System (ADS)

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.

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.

Guidance of spatial attention by incidental learning and endogenous cuing

PubMed Central

Jiang, Yuhong V.; Swallow, Khena M.; Rosenbaum, Gail M.

2012-01-01

Our visual system is highly sensitive to regularities in the environment. Locations that were important in one’s previous experience are often prioritized during search, even though observers may not be aware of the learning. In this study we characterized the guidance of spatial attention by incidental learning of a target’s spatial probability, and examined the interaction between endogenous cuing and probability cuing. Participants searched for a target (T) among distractors (L’s). The target was more often located in one region of the screen than in others. We found that search RT was faster when the target appeared in the high-frequency region rather than the low-frequency regions. This difference increased when there were more items on the display, suggesting that probability cuing guides spatial attention. Additional data indicated that on their own, probability cuing and endogenous cuing (e.g., a central arrow that predicted a target’s location) were similarly effective at guiding attention. However, when both cues were presented at once, probability cuing was largely eliminated. Thus, although both incidental learning and endogenous cuing can effectively guide attention, endogenous cuing takes precedence over incidental learning. PMID:22506784

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

On Probability Domains IV

NASA Astrophysics Data System (ADS)

Frič, Roman; Papčo, Martin

2017-12-01

Stressing a categorical approach, we continue our study of fuzzified domains of probability, in which classical random events are replaced by measurable fuzzy random events. In operational probability theory (S. Bugajski) classical random variables are replaced by statistical maps (generalized distribution maps induced by random variables) and in fuzzy probability theory (S. Gudder) the central role is played by observables (maps between probability domains). We show that to each of the two generalized probability theories there corresponds a suitable category and the two resulting categories are dually equivalent. Statistical maps and observables become morphisms. A statistical map can send a degenerated (pure) state to a non-degenerated one —a quantum phenomenon and, dually, an observable can map a crisp random event to a genuine fuzzy random event —a fuzzy phenomenon. The dual equivalence means that the operational probability theory and the fuzzy probability theory coincide and the resulting generalized probability theory has two dual aspects: quantum and fuzzy. We close with some notes on products and coproducts in the dual categories.

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

PubMed Central

Tosun, Tuğçe; Gür, Ezgi; Balcı, Fuat

2016-01-01

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

Q-Learning-Based Adjustable Fixed-Phase Quantum Grover Search Algorithm

NASA Astrophysics Data System (ADS)

Guo, Ying; Shi, Wensha; Wang, Yijun; Hu, Jiankun

2017-02-01

We demonstrate that the rotation phase can be suitably chosen to increase the efficiency of the phase-based quantum search algorithm, leading to a dynamic balance between iterations and success probabilities of the fixed-phase quantum Grover search algorithm with Q-learning for a given number of solutions. In this search algorithm, the proposed Q-learning algorithm, which is a model-free reinforcement learning strategy in essence, is used for performing a matching algorithm based on the fraction of marked items λ and the rotation phase α. After establishing the policy function α = π(λ), we complete the fixed-phase Grover algorithm, where the phase parameter is selected via the learned policy. Simulation results show that the Q-learning-based Grover search algorithm (QLGA) enables fewer iterations and gives birth to higher success probabilities. Compared with the conventional Grover algorithms, it avoids the optimal local situations, thereby enabling success probabilities to approach one.

Optimizing one-shot learning with binary synapses.

PubMed

Romani, Sandro; Amit, Daniel J; Amit, Yali

2008-08-01

A network of excitatory synapses trained with a conservative version of Hebbian learning is used as a model for recognizing the familiarity of thousands of once-seen stimuli from those never seen before. Such networks were initially proposed for modeling memory retrieval (selective delay activity). We show that the same framework allows the incorporation of both familiarity recognition and memory retrieval, and estimate the network's capacity. In the case of binary neurons, we extend the analysis of Amit and Fusi (1994) to obtain capacity limits based on computations of signal-to-noise ratio of the field difference between selective and non-selective neurons of learned signals. We show that with fast learning (potentiation probability approximately 1), the most recently learned patterns can be retrieved in working memory (selective delay activity). A much higher number of once-seen learned patterns elicit a realistic familiarity signal in the presence of an external field. With potentiation probability much less than 1 (slow learning), memory retrieval disappears, whereas familiarity recognition capacity is maintained at a similarly high level. This analysis is corroborated in simulations. For analog neurons, where such analysis is more difficult, we simplify the capacity analysis by studying the excess number of potentiated synapses above the steady-state distribution. In this framework, we derive the optimal constraint between potentiation and depression probabilities that maximizes the capacity.

The Relationship between Socio-Economic Status, General Language Learning Outcome, and Beliefs about Language Learning

ERIC Educational Resources Information Center

Ariani, Mohsen Ghasemi; Ghafournia, Narjes

2016-01-01

The objective of this study is to explore the probable relationship between Iranian students' socioeconomic status, general language learning outcome, and their beliefs about language learning. To this end, 350 postgraduate students, doing English for specific courses at Islamic Azad University of Neyshabur participated in this study. They were…

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…

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…

Risks and probabilities of breast cancer: short-term versus lifetime probabilities.

PubMed Central

Bryant, H E; Brasher, P M

1994-01-01

OBJECTIVE: To calculate age-specific short-term and lifetime probabilities of breast cancer among a cohort of Canadian women. DESIGN: Double decrement life table. SETTING: Alberta. SUBJECTS: Women with first invasive breast cancers registered with the Alberta Cancer Registry between 1985 and 1987. MAIN OUTCOME MEASURES: Lifetime probability of breast cancer from birth and for women at various ages; short-term (up to 10 years) probability of breast cancer for women at various ages. RESULTS: The lifetime probability of breast cancer is 10.17% at birth and peaks at 10.34% at age 25 years, after which it decreases owing to a decline in the number of years over which breast cancer risk will be experienced. However, the probability of manifesting breast cancer in the next year increases steadily from the age of 30 onward, reaching 0.36% at 85 years. The probability of manifesting the disease within the next 10 years peaks at 2.97% at age 70 and decreases thereafter, again owing to declining probabilities of surviving the interval. CONCLUSIONS: Given that the incidence of breast cancer among Albertan women during the study period was similar to the national average, we conclude that currently more than 1 in 10 women in Canada can expect to have breast cancer at some point during their life. However, risk varies considerably over a woman's lifetime, with most risk concentrated after age 49. On the basis of the shorter-term age-specific risks that we present, the clinician can put breast cancer risk into perspective for younger women and heighten awareness among women aged 50 years or more. PMID:8287343

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.

Guide star probabilities

NASA Technical Reports Server (NTRS)

Soneira, R. M.; Bahcall, J. N.

1981-01-01

Probabilities are calculated for acquiring suitable guide stars (GS) with the fine guidance system (FGS) of the space telescope. A number of the considerations and techniques described are also relevant for other space astronomy missions. The constraints of the FGS are reviewed. The available data on bright star densities are summarized and a previous error in the literature is corrected. Separate analytic and Monte Carlo calculations of the probabilities are described. A simulation of space telescope pointing is carried out using the Weistrop north galactic pole catalog of bright stars. Sufficient information is presented so that the probabilities of acquisition can be estimated as a function of position in the sky. The probability of acquiring suitable guide stars is greatly increased if the FGS can allow an appreciable difference between the (bright) primary GS limiting magnitude and the (fainter) secondary GS limiting magnitude.

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…

The Classicist and the Frequentist Approach to Probability within a "TinkerPlots2" Combinatorial Problem

ERIC Educational Resources Information Center

Prodromou, Theodosia

2012-01-01

This article seeks to address a pedagogical theory of introducing the classicist and the frequentist approach to probability, by investigating important elements in 9th grade students' learning process while working with a "TinkerPlots2" combinatorial problem. Results from this research study indicate that, after the students had seen…

Chances Are...Making Probability and Statistics Fun To Learn and Easy To Teach.

ERIC Educational Resources Information Center

Pfenning, Nancy

Probability and statistics may be the horror of many college students, but if these subjects are trimmed to include only the essential symbols, they are easily within the grasp of interested middle school or even elementary school students. This book can serve as an introduction for any beginner, from gifted students who would like to broaden…

Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

PubMed

Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li

2018-02-01

In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.

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…

A brief introduction to probability.

PubMed

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

2018-02-01

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

Language experience changes subsequent learning

PubMed Central

Onnis, Luca; Thiessen, Erik

2013-01-01

What are the effects of experience on subsequent learning? We explored the effects of language-specific word order knowledge on the acquisition of sequential conditional information. Korean and English adults were engaged in a sequence learning task involving three different sets of stimuli: auditory linguistic (nonsense syllables), visual non-linguistic (nonsense shapes), and auditory non-linguistic (pure tones). The forward and backward probabilities between adjacent elements generated two equally probable and orthogonal perceptual parses of the elements, such that any significant preference at test must be due to either general cognitive biases, or prior language-induced biases. We found that language modulated parsing preferences with the linguistic stimuli only. Intriguingly, these preferences are congruent with the dominant word order patterns of each language, as corroborated by corpus analyses, and are driven by probabilistic preferences. Furthermore, although the Korean individuals had received extensive formal explicit training in English and lived in an English-speaking environment, they exhibited statistical learning biases congruent with their native language. Our findings suggest that mechanisms of statistical sequential learning are implicated in language across the lifespan, and experience with language may affect cognitive processes and later learning. PMID:23200510

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.

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.

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…

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.

ERP Correlates of Verbal and Numerical Probabilities in Risky Choices: A Two-Stage Probability Processing View

PubMed Central

Li, Shu; Du, Xue-Lei; Li, Qi; Xuan, Yan-Hua; Wang, Yun; Rao, Li-Lin

2016-01-01

Two kinds of probability expressions, verbal and numerical, have been used to characterize the uncertainty that people face. However, the question of whether verbal and numerical probabilities are cognitively processed in a similar manner remains unresolved. From a levels-of-processing perspective, verbal and numerical probabilities may be processed differently during early sensory processing but similarly in later semantic-associated operations. This event-related potential (ERP) study investigated the neural processing of verbal and numerical probabilities in risky choices. The results showed that verbal probability and numerical probability elicited different N1 amplitudes but that verbal and numerical probabilities elicited similar N2 and P3 waveforms in response to different levels of probability (high to low). These results were consistent with a levels-of-processing framework and suggest some internal consistency between the cognitive processing of verbal and numerical probabilities in risky choices. Our findings shed light on possible mechanism underlying probability expression and may provide the neural evidence to support the translation of verbal to numerical probabilities (or vice versa). PMID:26834612

Math Academy: Are You Game? Explorations in Probability. Supplemental Math Materials for Grades 3-6

ERIC Educational Resources Information Center

Rimbey, Kimberly

2007-01-01

Created by teachers for teachers, the Math Academy tools and activities included in this booklet were designed to create hands-on activities and a fun learning environment for the teaching of mathematics to the students. This booklet contains the themed program "Are You Game? Math Academy--Explorations in Probability," which teachers can use to…

Last-position elimination-based learning automata.

PubMed

Zhang, Junqi; Wang, Cheng; Zhou, MengChu

2014-12-01

An update scheme of the state probability vector of actions is critical for learning automata (LA). The most popular is the pursuit scheme that pursues the estimated optimal action and penalizes others. This paper proposes a reverse philosophy that leads to last-position elimination-based learning automata (LELA). The action graded last in terms of the estimated performance is penalized by decreasing its state probability and is eliminated when its state probability becomes zero. All active actions, that is, actions with nonzero state probability, equally share the penalized state probability from the last-position action at each iteration. The proposed LELA is characterized by the relaxed convergence condition for the optimal action, the accelerated step size of the state probability update scheme for the estimated optimal action, and the enriched sampling for the estimated nonoptimal actions. The proof of the ϵ-optimal property for the proposed algorithm is presented. Last-position elimination is a widespread philosophy in the real world and has proved to be also helpful for the update scheme of the learning automaton via the simulations of well-known benchmark environments. In the simulations, two versions of the LELA, using different selection strategies of the last action, are compared with the classical pursuit algorithms Discretized Pursuit Reward-Inaction (DP(RI)) and Discretized Generalized Pursuit Algorithm (DGPA). Simulation results show that the proposed schemes achieve significantly faster convergence and higher accuracy than the classical ones. Specifically, the proposed schemes reduce the interval to find the best parameter for a specific environment in the classical pursuit algorithms. Thus, they can have their parameter tuning easier to perform and can save much more time when applied to a practical case. Furthermore, the convergence curves and the corresponding variance coefficient curves of the contenders are illustrated to characterize their

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.

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…

Decision analysis with approximate probabilities

NASA Technical Reports Server (NTRS)

Whalen, Thomas

1992-01-01

This paper concerns decisions under uncertainty in which the probabilities of the states of nature are only approximately known. Decision problems involving three states of nature are studied. This is due to the fact that some key issues do not arise in two-state problems, while probability spaces with more than three states of nature are essentially impossible to graph. The primary focus is on two levels of probabilistic information. In one level, the three probabilities are separately rounded to the nearest tenth. This can lead to sets of rounded probabilities which add up to 0.9, 1.0, or 1.1. In the other level, probabilities are rounded to the nearest tenth in such a way that the rounded probabilities are forced to sum to 1.0. For comparison, six additional levels of probabilistic information, previously analyzed, were also included in the present analysis. A simulation experiment compared four criteria for decisionmaking using linearly constrained probabilities (Maximin, Midpoint, Standard Laplace, and Extended Laplace) under the eight different levels of information about probability. The Extended Laplace criterion, which uses a second order maximum entropy principle, performed best overall.

Feedback-Driven Trial-by-Trial Learning in Autism Spectrum Disorders

PubMed Central

Solomon, Marjorie; Frank, Michael J.; Ragland, J. Daniel; Smith, Anne C.; Niendam, Tara A.; Lesh, Tyler A.; Grayson, David S.; Beck, Jonathan S.; Matter, John C.; Carter, Cameron S.

2017-01-01

Objective Impairments in learning are central to autism spectrum disorders. The authors investigated the cognitive and neural basis of these deficits in young adults with autism spectrum disorders using a well-characterized probabilistic reinforcement learning paradigm. Method The probabilistic selection task was implemented among matched participants with autism spectrum disorders (N=22) and with typical development (N=25), aged 18–40 years, using rapid event-related functional MRI. Participants were trained to choose the correct stimulus in high-probability (AB), medium-probability (CD), and low-probability (EF) pairs, presented with valid feedback 80%, 70%, and 60% of the time, respectively. Whole-brain voxel-wise and parametric modulator analyses examined early and late learning during the stimulus and feedback epochs of the task. Results The groups exhibited comparable performance on medium- and low-probability pairs. Typically developing persons showed higher accuracy on the high-probability pair, better win-stay performance (selection of the previously rewarded stimulus on the next trial of that type), and more robust recruitment of the anterior and medial prefrontal cortex during the stimulus epoch, suggesting development of an intact reward-based working memory for recent stimulus values. Throughout the feedback epoch, individuals with autism spectrum disorders exhibited greater recruitment of the anterior cingulate and orbito-frontal cortices compared with individuals with typical development, indicating continuing trial-by-trial activity related to feedback processing. Conclusions Individuals with autism spectrum disorders exhibit learning deficits reflecting impaired ability to develop an effective reward-based working memory to guide stimulus selection. Instead, they continue to rely on trial-by-trial feedback processing to support learning dependent upon engagement of the anterior cingulate and orbito-frontal cortices. PMID:25158242

Heart sounds analysis using probability assessment.

PubMed

Plesinger, F; Viscor, I; Halamek, J; Jurco, J; Jurak, P

2017-07-31

This paper describes a method for automated discrimination of heart sounds recordings according to the Physionet Challenge 2016. The goal was to decide if the recording refers to normal or abnormal heart sounds or if it is not possible to decide (i.e. 'unsure' recordings). Heart sounds S1 and S2 are detected using amplitude envelopes in the band 15-90 Hz. The averaged shape of the S1/S2 pair is computed from amplitude envelopes in five different bands (15-90 Hz; 55-150 Hz; 100-250 Hz; 200-450 Hz; 400-800 Hz). A total of 53 features are extracted from the data. The largest group of features is extracted from the statistical properties of the averaged shapes; other features are extracted from the symmetry of averaged shapes, and the last group of features is independent of S1 and S2 detection. Generated features are processed using logical rules and probability assessment, a prototype of a new machine-learning method. The method was trained using 3155 records and tested on 1277 hidden records. It resulted in a training score of 0.903 (sensitivity 0.869, specificity 0.937) and a testing score of 0.841 (sensitivity 0.770, specificity 0.913). The revised method led to a test score of 0.853 in the follow-up phase of the challenge. The presented solution achieved 7th place out of 48 competing entries in the Physionet Challenge 2016 (official phase). In addition, the PROBAfind software for probability assessment was introduced.

Language experience changes subsequent learning.

PubMed

Onnis, Luca; Thiessen, Erik

2013-02-01

What are the effects of experience on subsequent learning? We explored the effects of language-specific word order knowledge on the acquisition of sequential conditional information. Korean and English adults were engaged in a sequence learning task involving three different sets of stimuli: auditory linguistic (nonsense syllables), visual non-linguistic (nonsense shapes), and auditory non-linguistic (pure tones). The forward and backward probabilities between adjacent elements generated two equally probable and orthogonal perceptual parses of the elements, such that any significant preference at test must be due to either general cognitive biases, or prior language-induced biases. We found that language modulated parsing preferences with the linguistic stimuli only. Intriguingly, these preferences are congruent with the dominant word order patterns of each language, as corroborated by corpus analyses, and are driven by probabilistic preferences. Furthermore, although the Korean individuals had received extensive formal explicit training in English and lived in an English-speaking environment, they exhibited statistical learning biases congruent with their native language. Our findings suggest that mechanisms of statistical sequential learning are implicated in language across the lifespan, and experience with language may affect cognitive processes and later learning. Copyright © 2012 Elsevier B.V. All rights reserved.

Statistical Learning in a Natural Language by 8-Month-Old Infants

PubMed Central

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

2013-01-01

Numerous studies over the past decade support the claim that infants are equipped with powerful statistical language learning mechanisms. The primary evidence for statistical language learning in word segmentation comes from studies using artificial languages, continuous streams of synthesized syllables that are highly simplified relative to real speech. To what extent can these conclusions be scaled up to natural language learning? In the current experiments, English-learning 8-month-old infants’ ability to track transitional probabilities in fluent infant-directed Italian speech was tested (N = 72). The results suggest that infants are sensitive to transitional probability cues in unfamiliar natural language stimuli, and support the claim that statistical learning is sufficiently robust to support aspects of real-world language acquisition. PMID:19489896

Statistical learning in a natural language by 8-month-old infants.

PubMed

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

2009-01-01

Numerous studies over the past decade support the claim that infants are equipped with powerful statistical language learning mechanisms. The primary evidence for statistical language learning in word segmentation comes from studies using artificial languages, continuous streams of synthesized syllables that are highly simplified relative to real speech. To what extent can these conclusions be scaled up to natural language learning? In the current experiments, English-learning 8-month-old infants' ability to track transitional probabilities in fluent infant-directed Italian speech was tested (N = 72). The results suggest that infants are sensitive to transitional probability cues in unfamiliar natural language stimuli, and support the claim that statistical learning is sufficiently robust to support aspects of real-world language acquisition.

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

PubMed

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

2014-08-01

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

Promoting Active Learning When Teaching Introductory Statistics and Probability Using a Portfolio Curriculum Approach

ERIC Educational Resources Information Center

Adair, Desmond; Jaeger, Martin; Price, Owen M.

2018-01-01

The use of a portfolio curriculum approach, when teaching a university introductory statistics and probability course to engineering students, is developed and evaluated. The portfolio curriculum approach, so called, as the students need to keep extensive records both as hard copies and digitally of reading materials, interactions with faculty,…

Learning Probabilistic Logic Models from Probabilistic Examples

PubMed Central

Chen, Jianzhong; Muggleton, Stephen; Santos, José

2009-01-01

Abstract We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) time-trace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches - abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from non-probabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from non-probabilistic examples. PMID:19888348

Learning Probabilistic Logic Models from Probabilistic Examples.

PubMed

Chen, Jianzhong; Muggleton, Stephen; Santos, José

2008-10-01

We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) time-trace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches - abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from non-probabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from non-probabilistic examples.

Learning predictive statistics from temporal sequences: Dynamics and strategies

PubMed Central

Wang, Rui; Shen, Yuan; Tino, Peter; Welchman, Andrew E.; Kourtzi, Zoe

2017-01-01

Human behavior is guided by our expectations about the future. Often, we make predictions by monitoring how event sequences unfold, even though such sequences may appear incomprehensible. Event structures in the natural environment typically vary in complexity, from simple repetition to complex probabilistic combinations. How do we learn these structures? Here we investigate the dynamics of structure learning by tracking human responses to temporal sequences that change in structure unbeknownst to the participants. Participants were asked to predict the upcoming item following a probabilistic sequence of symbols. Using a Markov process, we created a family of sequences, from simple frequency statistics (e.g., some symbols are more probable than others) to context-based statistics (e.g., symbol probability is contingent on preceding symbols). We demonstrate the dynamics with which individuals adapt to changes in the environment's statistics—that is, they extract the behaviorally relevant structures to make predictions about upcoming events. Further, we show that this structure learning relates to individual decision strategy; faster learning of complex structures relates to selection of the most probable outcome in a given context (maximizing) rather than matching of the exact sequence statistics. Our findings provide evidence for alternate routes to learning of behaviorally relevant statistics that facilitate our ability to predict future events in variable environments. PMID:28973111

Learning predictive statistics from temporal sequences: Dynamics and strategies.

PubMed

Wang, Rui; Shen, Yuan; Tino, Peter; Welchman, Andrew E; Kourtzi, Zoe

2017-10-01

Human behavior is guided by our expectations about the future. Often, we make predictions by monitoring how event sequences unfold, even though such sequences may appear incomprehensible. Event structures in the natural environment typically vary in complexity, from simple repetition to complex probabilistic combinations. How do we learn these structures? Here we investigate the dynamics of structure learning by tracking human responses to temporal sequences that change in structure unbeknownst to the participants. Participants were asked to predict the upcoming item following a probabilistic sequence of symbols. Using a Markov process, we created a family of sequences, from simple frequency statistics (e.g., some symbols are more probable than others) to context-based statistics (e.g., symbol probability is contingent on preceding symbols). We demonstrate the dynamics with which individuals adapt to changes in the environment's statistics-that is, they extract the behaviorally relevant structures to make predictions about upcoming events. Further, we show that this structure learning relates to individual decision strategy; faster learning of complex structures relates to selection of the most probable outcome in a given context (maximizing) rather than matching of the exact sequence statistics. Our findings provide evidence for alternate routes to learning of behaviorally relevant statistics that facilitate our ability to predict future events in variable environments.

Brain networks for confidence weighting and hierarchical inference during probabilistic learning.

PubMed

Meyniel, Florent; Dehaene, Stanislas

2017-05-09

Learning is difficult when the world fluctuates randomly and ceaselessly. Classical learning algorithms, such as the delta rule with constant learning rate, are not optimal. Mathematically, the optimal learning rule requires weighting prior knowledge and incoming evidence according to their respective reliabilities. This "confidence weighting" implies the maintenance of an accurate estimate of the reliability of what has been learned. Here, using fMRI and an ideal-observer analysis, we demonstrate that the brain's learning algorithm relies on confidence weighting. While in the fMRI scanner, human adults attempted to learn the transition probabilities underlying an auditory or visual sequence, and reported their confidence in those estimates. They knew that these transition probabilities could change simultaneously at unpredicted moments, and therefore that the learning problem was inherently hierarchical. Subjective confidence reports tightly followed the predictions derived from the ideal observer. In particular, subjects managed to attach distinct levels of confidence to each learned transition probability, as required by Bayes-optimal inference. Distinct brain areas tracked the likelihood of new observations given current predictions, and the confidence in those predictions. Both signals were combined in the right inferior frontal gyrus, where they operated in agreement with the confidence-weighting model. This brain region also presented signatures of a hierarchical process that disentangles distinct sources of uncertainty. Together, our results provide evidence that the sense of confidence is an essential ingredient of probabilistic learning in the human brain, and that the right inferior frontal gyrus hosts a confidence-based statistical learning algorithm for auditory and visual sequences.

Brain networks for confidence weighting and hierarchical inference during probabilistic learning

PubMed Central

Meyniel, Florent; Dehaene, Stanislas

2017-01-01

Learning is difficult when the world fluctuates randomly and ceaselessly. Classical learning algorithms, such as the delta rule with constant learning rate, are not optimal. Mathematically, the optimal learning rule requires weighting prior knowledge and incoming evidence according to their respective reliabilities. This “confidence weighting” implies the maintenance of an accurate estimate of the reliability of what has been learned. Here, using fMRI and an ideal-observer analysis, we demonstrate that the brain’s learning algorithm relies on confidence weighting. While in the fMRI scanner, human adults attempted to learn the transition probabilities underlying an auditory or visual sequence, and reported their confidence in those estimates. They knew that these transition probabilities could change simultaneously at unpredicted moments, and therefore that the learning problem was inherently hierarchical. Subjective confidence reports tightly followed the predictions derived from the ideal observer. In particular, subjects managed to attach distinct levels of confidence to each learned transition probability, as required by Bayes-optimal inference. Distinct brain areas tracked the likelihood of new observations given current predictions, and the confidence in those predictions. Both signals were combined in the right inferior frontal gyrus, where they operated in agreement with the confidence-weighting model. This brain region also presented signatures of a hierarchical process that disentangles distinct sources of uncertainty. Together, our results provide evidence that the sense of confidence is an essential ingredient of probabilistic learning in the human brain, and that the right inferior frontal gyrus hosts a confidence-based statistical learning algorithm for auditory and visual sequences. PMID:28439014

METAPHOR: Probability density estimation for machine learning based photometric redshifts

NASA Astrophysics Data System (ADS)

Amaro, V.; Cavuoti, S.; Brescia, M.; Vellucci, C.; Tortora, C.; Longo, G.

2017-06-01

We present METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts), a method able to provide a reliable PDF for photometric galaxy redshifts estimated through empirical techniques. METAPHOR is a modular workflow, mainly based on the MLPQNA neural network as internal engine to derive photometric galaxy redshifts, but giving the possibility to easily replace MLPQNA with any other method to predict photo-z's and their PDF. We present here the results about a validation test of the workflow on the galaxies from SDSS-DR9, showing also the universality of the method by replacing MLPQNA with KNN and Random Forest models. The validation test include also a comparison with the PDF's derived from a traditional SED template fitting method (Le Phare).

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…

Excluding joint probabilities from quantum theory

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Danageozian, Arshag

2018-03-01

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

Subjective Probabilities in Household Surveys

PubMed Central

Hurd, Michael D.

2011-01-01

Subjective probabilities are now collected on a number of large household surveys with the objective of providing data to better understand inter-temporal decision making. Comparison of subjective probabilities with actual outcomes shows that the probabilities have considerable predictive power in situations where individuals have considerable private information such as survival and retirement. In contrast the subjective probability of a stock market gain varies greatly across individuals even though no one has private information and the outcome is the same for everyone. An explanation is that there is considerable variation in accessing and processing information. Further, the subjective probability of a stock market gain is considerably lower than historical averages, providing an explanation for the relatively low frequency of stock holding. An important research objective will be to understand how individuals form their subjective probabilities. PMID:21643535

Learn-as-you-go acceleration of cosmological parameter estimates

NASA Astrophysics Data System (ADS)

Aslanyan, Grigor; Easther, Richard; Price, Layne C.

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

Probability concepts in quality risk management.

PubMed

Claycamp, H Gregg

2012-01-01

Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although risk is generally a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management tools are relatively silent on the meaning and uses of "probability." The probability concept is typically applied by risk managers as a combination of frequency-based calculation and a "degree of belief" meaning of probability. Probability as a concept that is crucial for understanding and managing risk is discussed through examples from the most general, scenario-defining and ranking tools that use probability implicitly to more specific probabilistic tools in risk management. A rich history of probability in risk management applied to other fields suggests that high-quality risk management decisions benefit from the implementation of more thoughtful probability concepts in both risk modeling and risk management. Essentially any concept of risk is built on fundamental concepts of chance, likelihood, or probability. Although "risk" generally describes a probability of loss of something of value, given that a risk-generating event will occur or has occurred, it is ironic that the quality risk management literature and guidelines on quality risk management methodologies and respective tools focus on managing severity but are relatively silent on the in-depth meaning and uses of "probability." Pharmaceutical manufacturers are expanding their use of quality risk management to identify and manage risks to the patient that might occur in phases of the pharmaceutical life cycle from drug development to manufacture, marketing to product discontinuation. A probability concept is typically applied by risk managers as a combination of data-based measures of probability and a subjective "degree of belief" meaning of probability. Probability as

The perception of probability.

PubMed

Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E

2014-01-01

We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

Protein-Protein Interaction Site Predictions with Three-Dimensional Probability Distributions of Interacting Atoms on Protein Surfaces

PubMed Central

Chen, Ching-Tai; Peng, Hung-Pin; Jian, Jhih-Wei; Tsai, Keng-Chang; Chang, Jeng-Yih; Yang, Ei-Wen; Chen, Jun-Bo; Ho, Shinn-Ying; Hsu, Wen-Lian; Yang, An-Suei

2012-01-01

Protein-protein interactions are key to many biological processes. Computational methodologies devised to predict protein-protein interaction (PPI) sites on protein surfaces are important tools in providing insights into the biological functions of proteins and in developing therapeutics targeting the protein-protein interaction sites. One of the general features of PPI sites is that the core regions from the two interacting protein surfaces are complementary to each other, similar to the interior of proteins in packing density and in the physicochemical nature of the amino acid composition. In this work, we simulated the physicochemical complementarities by constructing three-dimensional probability density maps of non-covalent interacting atoms on the protein surfaces. The interacting probabilities were derived from the interior of known structures. Machine learning algorithms were applied to learn the characteristic patterns of the probability density maps specific to the PPI sites. The trained predictors for PPI sites were cross-validated with the training cases (consisting of 432 proteins) and were tested on an independent dataset (consisting of 142 proteins). The residue-based Matthews correlation coefficient for the independent test set was 0.423; the accuracy, precision, sensitivity, specificity were 0.753, 0.519, 0.677, and 0.779 respectively. The benchmark results indicate that the optimized machine learning models are among the best predictors in identifying PPI sites on protein surfaces. In particular, the PPI site prediction accuracy increases with increasing size of the PPI site and with increasing hydrophobicity in amino acid composition of the PPI interface; the core interface regions are more likely to be recognized with high prediction confidence. The results indicate that the physicochemical complementarity patterns on protein surfaces are important determinants in PPIs, and a substantial portion of the PPI sites can be predicted correctly with

Dopamine neurons learn relative chosen value from probabilistic rewards

PubMed Central

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

2016-01-01

Economic theories posit reward probability as one of the factors defining reward value. Individuals learn the value of cues that predict probabilistic rewards from experienced reward frequencies. Building on the notion that responses of dopamine neurons increase with reward probability and expected value, we asked how dopamine neurons in monkeys acquire this value signal that may represent an economic decision variable. We found in a Pavlovian learning task that reward probability-dependent value signals arose from experienced reward frequencies. We then assessed neuronal response acquisition during choices among probabilistic rewards. Here, dopamine responses became sensitive to the value of both chosen and unchosen options. Both experiments showed also the novelty responses of dopamine neurones that decreased as learning advanced. These results show that dopamine neurons acquire predictive value signals from the frequency of experienced rewards. This flexible and fast signal reflects a specific decision variable and could update neuronal decision mechanisms. DOI: http://dx.doi.org/10.7554/eLife.18044.001 PMID:27787196

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…

The probability of reinforcement per trial affects posttrial responding and subsequent extinction but not within-trial responding.

PubMed

Harris, Justin A; Kwok, Dorothy W S

2018-01-01

During magazine approach conditioning, rats do not discriminate between a conditional stimulus (CS) that is consistently reinforced with food and a CS that is occasionally (partially) reinforced, as long as the CSs have the same overall reinforcement rate per second. This implies that rats are indifferent to the probability of reinforcement per trial. However, in the same rats, the per-trial reinforcement rate will affect subsequent extinction-responding extinguishes more rapidly for a CS that was consistently reinforced than for a partially reinforced CS. Here, we trained rats with consistently and partially reinforced CSs that were matched for overall reinforcement rate per second. We measured conditioned responding both during and immediately after the CSs. Differences in the per-trial probability of reinforcement did not affect the acquisition of responding during the CS but did affect subsequent extinction of that responding, and also affected the post-CS response rates during conditioning. Indeed, CSs with the same probability of reinforcement per trial evoked the same amount of post-CS responding even when they differed in overall reinforcement rate and thus evoked different amounts of responding during the CS. We conclude that reinforcement rate per second controls rats' acquisition of responding during the CS, but at the same time, rats also learn specifically about the probability of reinforcement per trial. The latter learning affects the rats' expectation of reinforcement as an outcome of the trial, which influences their ability to detect retrospectively that an opportunity for reinforcement was missed, and, in turn, drives extinction. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

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.

BIODEGRADATION PROBABILITY PROGRAM (BIODEG)

EPA Science Inventory

The Biodegradation Probability Program (BIODEG) calculates the probability that a chemical under aerobic conditions with mixed cultures of microorganisms will biodegrade rapidly or slowly. It uses fragment constants developed using multiple linear and non-linear regressions and d...

Identifying Chinese Microblog Users With High Suicide Probability Using Internet-Based Profile and Linguistic Features: Classification Model.

PubMed

Guan, Li; Hao, Bibo; Cheng, Qijin; Yip, Paul Sf; Zhu, Tingshao

2015-01-01

Traditional offline assessment of suicide probability is time consuming and difficult in convincing at-risk individuals to participate. Identifying individuals with high suicide probability through online social media has an advantage in its efficiency and potential to reach out to hidden individuals, yet little research has been focused on this specific field. The objective of this study was to apply two classification models, Simple Logistic Regression (SLR) and Random Forest (RF), to examine the feasibility and effectiveness of identifying high suicide possibility microblog users in China through profile and linguistic features extracted from Internet-based data. There were nine hundred and nine Chinese microblog users that completed an Internet survey, and those scoring one SD above the mean of the total Suicide Probability Scale (SPS) score, as well as one SD above the mean in each of the four subscale scores in the participant sample were labeled as high-risk individuals, respectively. Profile and linguistic features were fed into two machine learning algorithms (SLR and RF) to train the model that aims to identify high-risk individuals in general suicide probability and in its four dimensions. Models were trained and then tested by 5-fold cross validation; in which both training set and test set were generated under the stratified random sampling rule from the whole sample. There were three classic performance metrics (Precision, Recall, F1 measure) and a specifically defined metric "Screening Efficiency" that were adopted to evaluate model effectiveness. Classification performance was generally matched between SLR and RF. Given the best performance of the classification models, we were able to retrieve over 70% of the labeled high-risk individuals in overall suicide probability as well as in the four dimensions. Screening Efficiency of most models varied from 1/4 to 1/2. Precision of the models was generally below 30%. Individuals in China with high suicide

An investigation of the role of some person and situation variables in multiple cue probability learning.

PubMed

Bayindir, Mustafa; Bolger, Fergus; Say, Bilge

2016-07-19

Making decisions using judgements of multiple non-deterministic indicators is an important task, both in everyday and professional life. Learning of such decision making has often been studied as the mapping of stimuli (cues) to an environmental variable (criterion); however, little attention has been paid to the effects of situation-by-person interactions on this learning. Accordingly, we manipulated cue and feedback presentation mode (graphic or numeric) and task difficulty, and measured individual differences in working memory capacity (WMC). We predicted that graphic presentation, fewer cues, and elevated WMC would facilitate learning, and that person and task characteristics would interact such that presentation mode compatible with the decision maker's cognitive capability (enhanced visual or verbal WMC) would assist learning, particularly for more difficult tasks. We found our predicted main effects, but no significant interactions, except that those with greater WMC benefited to a larger extent with graphic than with numeric presentation, regardless of which type of working memory was enhanced or number of cues. Our findings suggest that the conclusions of past research based predominantly on tasks using numeric presentation need to be reevaluated and cast light on how working memory helps us learn multiple cue-criterion relationships, with implications for dual-process theories of cognition.

Definition of the Neutrosophic Probability

NASA Astrophysics Data System (ADS)

Smarandache, Florentin

2014-03-01

Neutrosophic probability (or likelihood) [1995] is a particular case of the neutrosophic measure. It is an estimation of an event (different from indeterminacy) to occur, together with an estimation that some indeterminacy may occur, and the estimation that the event does not occur. The classical probability deals with fair dice, coins, roulettes, spinners, decks of cards, random works, while neutrosophic probability deals with unfair, imperfect such objects and processes. For example, if we toss a regular die on an irregular surface which has cracks, then it is possible to get the die stuck on one of its edges or vertices in a crack (indeterminate outcome). The sample space is in this case: {1, 2, 3, 4, 5, 6, indeterminacy}. So, the probability of getting, for example 1, is less than 1/6. Since there are seven outcomes. The neutrosophic probability is a generalization of the classical probability because, when the chance of determinacy of a stochastic process is zero, these two probabilities coincide. The Neutrosophic Probability that of an event A occurs is NP (A) = (ch (A) , ch (indetA) , ch (A ̲)) = (T , I , F) , where T , I , F are subsets of [0,1], and T is the chance that A occurs, denoted ch(A); I is the indeterminate chance related to A, ch(indetermA) ; and F is the chance that A does not occur, ch (A ̲) . So, NP is a generalization of the Imprecise Probability as well. If T, I, and F are crisp numbers then: - 0 <= T + I + F <=3+ . We used the same notations (T,I,F) as in neutrosophic logic and set.

Failure probability under parameter uncertainty.

PubMed

Gerrard, R; Tsanakas, A

2011-05-01

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

Sparse Learning with Stochastic Composite Optimization.

PubMed

Zhang, Weizhong; Zhang, Lijun; Jin, Zhongming; Jin, Rong; Cai, Deng; Li, Xuelong; Liang, Ronghua; He, Xiaofei

2017-06-01

In this paper, we study Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution from a composite function. Most of the recent SCO algorithms have already reached the optimal expected convergence rate O(1/λT), but they often fail to deliver sparse solutions at the end either due to the limited sparsity regularization during stochastic optimization (SO) or due to the limitation in online-to-batch conversion. Even when the objective function is strongly convex, their high probability bounds can only attain O(√{log(1/δ)/T}) with δ is the failure probability, which is much worse than the expected convergence rate. To address these limitations, we propose a simple yet effective two-phase Stochastic Composite Optimization scheme by adding a novel powerful sparse online-to-batch conversion to the general Stochastic Optimization algorithms. We further develop three concrete algorithms, OptimalSL, LastSL and AverageSL, directly under our scheme to prove the effectiveness of the proposed scheme. Both the theoretical analysis and the experiment results show that our methods can really outperform the existing methods at the ability of sparse learning and at the meantime we can improve the high probability bound to approximately O(log(log(T)/δ)/λT).

Cluster membership probability: polarimetric approach

NASA Astrophysics Data System (ADS)

Medhi, Biman J.; Tamura, Motohide

2013-04-01

Interstellar polarimetric data of the six open clusters Hogg 15, NGC 6611, NGC 5606, NGC 6231, NGC 5749 and NGC 6250 have been used to estimate the membership probability for the stars within them. For proper-motion member stars, the membership probability estimated using the polarimetric data is in good agreement with the proper-motion cluster membership probability. However, for proper-motion non-member stars, the membership probability estimated by the polarimetric method is in total disagreement with the proper-motion cluster membership probability. The inconsistencies in the determined memberships may be because of the fundamental differences between the two methods of determination: one is based on stellar proper motion in space and the other is based on selective extinction of the stellar output by the asymmetric aligned dust grains present in the interstellar medium. The results and analysis suggest that the scatter of the Stokes vectors q (per cent) and u (per cent) for the proper-motion member stars depends on the interstellar and intracluster differential reddening in the open cluster. It is found that this method could be used to estimate the cluster membership probability if we have additional polarimetric and photometric information for a star to identify it as a probable member/non-member of a particular cluster, such as the maximum wavelength value (λmax), the unit weight error of the fit (σ1), the dispersion in the polarimetric position angles (overline{ɛ }), reddening (E(B - V)) or the differential intracluster reddening (ΔE(B - V)). This method could also be used to estimate the membership probability of known member stars having no membership probability as well as to resolve disagreements about membership among different proper-motion surveys.

Impaired Statistical Learning in Developmental Dyslexia

PubMed Central

Thiessen, Erik D.; Holt, Lori L.

2015-01-01

Purpose Developmental dyslexia (DD) is commonly thought to arise from phonological impairments. However, an emerging perspective is that a more general procedural learning deficit, not specific to phonological processing, may underlie DD. The current study examined if individuals with DD are capable of extracting statistical regularities across sequences of passively experienced speech and nonspeech sounds. Such statistical learning is believed to be domain-general, to draw upon procedural learning systems, and to relate to language outcomes. Method DD and control groups were familiarized with a continuous stream of syllables or sine-wave tones, the ordering of which was defined by high or low transitional probabilities across adjacent stimulus pairs. Participants subsequently judged two 3-stimulus test items with either high or low statistical coherence as being the most similar to the sounds heard during familiarization. Results As with control participants, the DD group was sensitive to the transitional probability structure of the familiarization materials as evidenced by above-chance performance. However, the performance of participants with DD was significantly poorer than controls across linguistic and nonlinguistic stimuli. In addition, reading-related measures were significantly correlated with statistical learning performance of both speech and nonspeech material. Conclusion Results are discussed in light of procedural learning impairments among participants with DD. PMID:25860795

Play to learn, teach by play.

PubMed

Palagi, Elisabetta; Stanyon, Roscoe; Demuru, Elisa

2015-01-01

The synthesis provided by Kline in the target article is noteworthy, but ignores the inseparable role of play in the evolution of learning and teaching in both humans and other animals. Play is distinguished and advantaged by its positive feedback reinforcement through pleasure. Play, especially between adults and infants, is probably the platform from which human learning and teaching evolved.

Reinforcement Learning for Constrained Energy Trading Games With Incomplete Information.

PubMed

Wang, Huiwei; Huang, Tingwen; Liao, Xiaofeng; Abu-Rub, Haitham; Chen, Guo

2017-10-01

This paper considers the problem of designing adaptive learning algorithms to seek the Nash equilibrium (NE) of the constrained energy trading game among individually strategic players with incomplete information. In this game, each player uses the learning automaton scheme to generate the action probability distribution based on his/her private information for maximizing his own averaged utility. It is shown that if one of admissible mixed-strategies converges to the NE with probability one, then the averaged utility and trading quantity almost surely converge to their expected ones, respectively. For the given discontinuous pricing function, the utility function has already been proved to be upper semicontinuous and payoff secure which guarantee the existence of the mixed-strategy NE. By the strict diagonal concavity of the regularized Lagrange function, the uniqueness of NE is also guaranteed. Finally, an adaptive learning algorithm is provided to generate the strategy probability distribution for seeking the mixed-strategy NE.

Learn-as-you-go acceleration of cosmological parameter estimates

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

Aslanyan, Grigor; Easther, Richard; Price, Layne C., E-mail: g.aslanyan@auckland.ac.nz, E-mail: r.easther@auckland.ac.nz, E-mail: lpri691@aucklanduni.ac.nz

2015-09-01

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitlymore » describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.« less

Teachers' Understandings of Probability

ERIC Educational Resources Information Center

Liu, Yan; Thompson, Patrick

2007-01-01

Probability is an important idea with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of probability among different populations across different settings. The purpose of this study is to develop a theoretical framework for…

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.

A probability space for quantum models

NASA Astrophysics Data System (ADS)

Lemmens, L. F.

2017-06-01

A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.

Discriminative Bayesian Dictionary Learning for Classification.

PubMed

Akhtar, Naveed; Shafait, Faisal; Mian, Ajmal

2016-12-01

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

Learning Problem-Solving Rules as Search Through a Hypothesis Space.

PubMed

Lee, Hee Seung; Betts, Shawn; Anderson, John R

2016-07-01

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem property such as computational difficulty of the rules biased the search process and so affected learning. Experiment 2 examined the impact of examples as instructional tools and found that their effectiveness was determined by whether they uniquely pointed to the correct rule. Experiment 3 compared verbal directions with examples and found that both could guide search. The final experiment tried to improve learning by using more explicit verbal directions or by adding scaffolding to the example. While both manipulations improved learning, learning still took the form of a search through a hypothesis space of possible rules. We describe a model that embodies two assumptions: (1) the instruction can bias the rules participants hypothesize rather than directly be encoded into a rule; (2) participants do not have memory for past wrong hypotheses and are likely to retry them. These assumptions are realized in a Markov model that fits all the data by estimating two sets of probabilities. First, the learning condition induced one set of Start probabilities of trying various rules. Second, should this first hypothesis prove wrong, the learning condition induced a second set of Choice probabilities of considering various rules. These findings broaden our understanding of effective instruction and provide implications for instructional design. Copyright © 2015 Cognitive Science Society, Inc.

A Method of Face Detection with Bayesian Probability

NASA Astrophysics Data System (ADS)

Sarker, Goutam

2010-10-01

The objective of face detection is to identify all images which contain a face, irrespective of its orientation, illumination conditions etc. This is a hard problem, because the faces are highly variable in size, shape lighting conditions etc. Many methods have been designed and developed to detect faces in a single image. The present paper is based on one `Appearance Based Method' which relies on learning the facial and non facial features from image examples. This in its turn is based on statistical analysis of examples and counter examples of facial images and employs Bayesian Conditional Classification Rule to detect the probability of belongingness of a face (or non-face) within an image frame. The detection rate of the present system is very high and thereby the number of false positive and false negative detection is substantially low.

Probability and Quantum Paradigms: the Interplay

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

Kracklauer, A. F.

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 fewmore » details, this variant is appealing in its reliance on well tested concepts and technology.« less

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.

Changing viewer perspectives reveals constraints to implicit visual statistical learning.

PubMed

Jiang, Yuhong V; Swallow, Khena M

2014-10-07

Statistical learning-learning environmental regularities to guide behavior-likely plays an important role in natural human behavior. One potential use is in search for valuable items. Because visual statistical learning can be acquired quickly and without intention or awareness, it could optimize search and thereby conserve energy. For this to be true, however, visual statistical learning needs to be viewpoint invariant, facilitating search even when people walk around. To test whether implicit visual statistical learning of spatial information is viewpoint independent, we asked participants to perform a visual search task from variable locations around a monitor placed flat on a stand. Unbeknownst to participants, the target was more often in some locations than others. In contrast to previous research on stationary observers, visual statistical learning failed to produce a search advantage for targets in high-probable regions that were stable within the environment but variable relative to the viewer. This failure was observed even when conditions for spatial updating were optimized. However, learning was successful when the rich locations were referenced relative to the viewer. We conclude that changing viewer perspective disrupts implicit learning of the target's location probability. This form of learning shows limited integration with spatial updating or spatiotopic representations. © 2014 ARVO.

Solving probability reasoning based on DNA strand displacement and probability modules.

PubMed

Zhang, Qiang; Wang, Xiaobiao; Wang, Xiaojun; Zhou, Changjun

2017-12-01

In computation biology, DNA strand displacement technology is used to simulate the computation process and has shown strong computing ability. Most researchers use it to solve logic problems, but it is only rarely used in probabilistic reasoning. To process probabilistic reasoning, a conditional probability derivation model and total probability model based on DNA strand displacement were established in this paper. The models were assessed through the game "read your mind." It has been shown to enable the application of probabilistic reasoning in genetic diagnosis. Copyright © 2017 Elsevier Ltd. All rights reserved.

Identifying Chinese Microblog Users With High Suicide Probability Using Internet-Based Profile and Linguistic Features: Classification Model

PubMed Central

Guan, Li; Hao, Bibo; Cheng, Qijin; Yip, Paul SF

2015-01-01

Background Traditional offline assessment of suicide probability is time consuming and difficult in convincing at-risk individuals to participate. Identifying individuals with high suicide probability through online social media has an advantage in its efficiency and potential to reach out to hidden individuals, yet little research has been focused on this specific field. Objective The objective of this study was to apply two classification models, Simple Logistic Regression (SLR) and Random Forest (RF), to examine the feasibility and effectiveness of identifying high suicide possibility microblog users in China through profile and linguistic features extracted from Internet-based data. Methods There were nine hundred and nine Chinese microblog users that completed an Internet survey, and those scoring one SD above the mean of the total Suicide Probability Scale (SPS) score, as well as one SD above the mean in each of the four subscale scores in the participant sample were labeled as high-risk individuals, respectively. Profile and linguistic features were fed into two machine learning algorithms (SLR and RF) to train the model that aims to identify high-risk individuals in general suicide probability and in its four dimensions. Models were trained and then tested by 5-fold cross validation; in which both training set and test set were generated under the stratified random sampling rule from the whole sample. There were three classic performance metrics (Precision, Recall, F1 measure) and a specifically defined metric “Screening Efficiency” that were adopted to evaluate model effectiveness. Results Classification performance was generally matched between SLR and RF. Given the best performance of the classification models, we were able to retrieve over 70% of the labeled high-risk individuals in overall suicide probability as well as in the four dimensions. Screening Efficiency of most models varied from 1/4 to 1/2. Precision of the models was generally below 30

A population-based tissue probability map-driven level set method for fully automated mammographic density estimations.

PubMed

Kim, Youngwoo; Hong, Byung Woo; Kim, Seung Ja; Kim, Jong Hyo

2014-07-01

A major challenge when distinguishing glandular tissues on mammograms, especially for area-based estimations, lies in determining a boundary on a hazy transition zone from adipose to glandular tissues. This stems from the nature of mammography, which is a projection of superimposed tissues consisting of different structures. In this paper, the authors present a novel segmentation scheme which incorporates the learned prior knowledge of experts into a level set framework for fully automated mammographic density estimations. The authors modeled the learned knowledge as a population-based tissue probability map (PTPM) that was designed to capture the classification of experts' visual systems. The PTPM was constructed using an image database of a selected population consisting of 297 cases. Three mammogram experts extracted regions for dense and fatty tissues on digital mammograms, which was an independent subset used to create a tissue probability map for each ROI based on its local statistics. This tissue class probability was taken as a prior in the Bayesian formulation and was incorporated into a level set framework as an additional term to control the evolution and followed the energy surface designed to reflect experts' knowledge as well as the regional statistics inside and outside of the evolving contour. A subset of 100 digital mammograms, which was not used in constructing the PTPM, was used to validate the performance. The energy was minimized when the initial contour reached the boundary of the dense and fatty tissues, as defined by experts. The correlation coefficient between mammographic density measurements made by experts and measurements by the proposed method was 0.93, while that with the conventional level set was 0.47. The proposed method showed a marked improvement over the conventional level set method in terms of accuracy and reliability. This result suggests that the proposed method successfully incorporated the learned knowledge of the experts

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. Copyright © 2015 Elsevier Ltd. All rights reserved.

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

PubMed

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

2013-07-01

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

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

NASA Astrophysics Data System (ADS)

Gao, Haixia; Li, Ting; Xiao, Changming

2016-05-01

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

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.

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

Learning probability distributions from smooth observables and the maximum entropy principle: some remarks

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Monasson, Rémi

2015-09-01

The maximum entropy principle (MEP) is a very useful working hypothesis in a wide variety of inference problems, ranging from biological to engineering tasks. To better understand the reasons of the success of MEP, we propose a statistical-mechanical formulation to treat the space of probability distributions constrained by the measures of (experimental) observables. In this paper we first review the results of a detailed analysis of the simplest case of randomly chosen observables. In addition, we investigate by numerical and analytical means the case of smooth observables, which is of practical relevance. Our preliminary results are presented and discussed with respect to the efficiency of the MEP.

Learning About Climate and Atmospheric Models Through Machine Learning

NASA Astrophysics Data System (ADS)

Lucas, D. D.

2017-12-01

From the analysis of ensemble variability to improving simulation performance, machine learning algorithms can play a powerful role in understanding the behavior of atmospheric and climate models. To learn about model behavior, we create training and testing data sets through ensemble techniques that sample different model configurations and values of input parameters, and then use supervised machine learning to map the relationships between the inputs and outputs. Following this procedure, we have used support vector machines, random forests, gradient boosting and other methods to investigate a variety of atmospheric and climate model phenomena. We have used machine learning to predict simulation crashes, estimate the probability density function of climate sensitivity, optimize simulations of the Madden Julian oscillation, assess the impacts of weather and emissions uncertainty on atmospheric dispersion, and quantify the effects of model resolution changes on precipitation. This presentation highlights recent examples of our applications of machine learning to improve the understanding of climate and atmospheric models. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Implicit Learning of Predictive Relationships in Three-element Visual Sequences by Young and Old Adults

PubMed Central

Howard, James H.; Howard, Darlene V.; Dennis, Nancy A.; Kelly, Andrew J.

2008-01-01

Knowledge of sequential relationships enables future events to be anticipated and processed efficiently. Research with the serial reaction time task (SRTT) has shown that sequence learning often occurs implicitly without effort or awareness. Here we report four experiments that use a triplet-learning task (TLT) to investigate sequence learning in young and older adults. In the TLT people respond only to the last target event in a series of discrete, three-event sequences or triplets. Target predictability is manipulated by varying the triplet frequency (joint probability) and/or the statistical relationships (conditional probabilities) among events within the triplets. Results revealed that both groups learned, though older adults showed less learning of both joint and conditional probabilities. Young people used the statistical information in both cues, but older adults relied primarily on information in the second cue alone. We conclude that the TLT complements and extends the SRTT and other tasks by offering flexibility in the kinds of sequential statistical regularities that may be studied as well as by controlling event timing and eliminating motor response sequencing. PMID:18763897

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…

Representing Learning With Graphical Models

NASA Technical Reports Server (NTRS)

Buntine, Wray L.; Lum, Henry, Jr. (Technical Monitor)

1994-01-01

Probabilistic graphical models are being used widely in artificial intelligence, for instance, in diagnosis and expert systems, as a unified qualitative and quantitative framework for representing and reasoning with probabilities and independencies. Their development and use spans several fields including artificial intelligence, decision theory and statistics, and provides an important bridge between these communities. This paper shows by way of example that these models can be extended to machine learning, neural networks and knowledge discovery by representing the notion of a sample on the graphical model. Not only does this allow a flexible variety of learning problems to be represented, it also provides the means for representing the goal of learning and opens the way for the automatic development of learning algorithms from specifications.

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…

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…

Social learning by following: an analysis1

PubMed Central

Bullock, Daniel; Neuringer, Allen

1977-01-01

Learning by “following”, probably a common means by which behaviors are socially transmitted from adults to young in many species, was analyzed. Pigeons first learned to eat from a human hand. When the hand then approached an operant key and pecked it, the pigeons followed and quickly learned to do the same, thereby demonstrating social learning. When the hand only led the birds to the area of the key, without demonstrating the key-peck response, the birds learned as rapidly as with a key-peck demonstration. Birds also learned, but less reliably and more slowly, when they could observe the hand's responses but were constrained and unable to follow. “Following” was also shown to engender very rapid learning of a more complex, two-member response chain. PMID:16811970

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

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. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

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. Copyright © 2013 Cognitive Science Society, Inc.

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…

Grammaticality, Acceptability, and Probability: A Probabilistic View of Linguistic Knowledge.

PubMed

Lau, Jey Han; Clark, Alexander; Lappin, Shalom

2017-07-01

The question of whether humans represent grammatical knowledge as a binary condition on membership in a set of well-formed sentences, or as a probabilistic property has been the subject of debate among linguists, psychologists, and cognitive scientists for many decades. Acceptability judgments present a serious problem for both classical binary and probabilistic theories of grammaticality. These judgements are gradient in nature, and so cannot be directly accommodated in a binary formal grammar. However, it is also not possible to simply reduce acceptability to probability. The acceptability of a sentence is not the same as the likelihood of its occurrence, which is, in part, determined by factors like sentence length and lexical frequency. In this paper, we present the results of a set of large-scale experiments using crowd-sourced acceptability judgments that demonstrate gradience to be a pervasive feature in acceptability judgments. We then show how one can predict acceptability judgments on the basis of probability by augmenting probabilistic language models with an acceptability measure. This is a function that normalizes probability values to eliminate the confounding factors of length and lexical frequency. We describe a sequence of modeling experiments with unsupervised language models drawn from state-of-the-art machine learning methods in natural language processing. Several of these models achieve very encouraging levels of accuracy in the acceptability prediction task, as measured by the correlation between the acceptability measure scores and mean human acceptability values. We consider the relevance of these results to the debate on the nature of grammatical competence, and we argue that they support the view that linguistic knowledge can be intrinsically probabilistic. Copyright © 2016 Cognitive Science Society, Inc.

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. Copyright © 2015 Stauffer et al.

ENKI - A tool for analysing the learning efficiency

NASA Astrophysics Data System (ADS)

Simona, Dudáková; Boris, Lacsný; Aba, Teleki

2017-01-01

Long-term memory plays a crucial role in learning mechanisms. We start to build up a probability model of learning (ENKI) ten years ago based on findings of micro genetics published in [1]. We accomplished a number of experiments in our department to testify the validity of the model with success. We described ENKI in detail here, giving the general mathematical formula of the learning curve. This paper pointed out that the model ENKI can detect its own strategy of learning in the brain as well as the simulation of the process of learning that will lead to the development of this method using its own strategy.

Interactive and collaborative learning in the classroom at the medical school Automated response systems and team-based learning.

PubMed

Nasr, Rihab; Antoun, Jumana; Sabra, Ramzi; Zgheib, Nathalie K

2016-01-01

There has been a pedagogic shift in higher education from the traditional teacher centered to the student centered approach in teaching, necessitating a change in the role of the teacher from a supplier of information to passive receptive students into a more facilitative role. Active learning activities are based on various learning theories such as self-directed learning, cooperative learning and adult learning. There exist many instructional activities that enhance active and collaborative learning. The aim of this manuscript is to describe two methods of interactive and collaborative learning in the classroom, automated response systems (ARS) and team-based learning (TBL), and to list some of their applications and advantages. The success of these innovative teaching and learning methods at a large scale depends on few elements, probably the most important of which is the support of the higher administration and leadership in addition to the availability of “champions” who are committed to lead the change.

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

PubMed Central

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

2015-01-01

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

Striatal activity is modulated by target probability.

PubMed

Hon, Nicholas

2017-06-14

Target probability has well-known neural effects. In the brain, target probability is known to affect frontal activity, with lower probability targets producing more prefrontal activation than those that occur with higher probability. Although the effect of target probability on cortical activity is well specified, its effect on subcortical structures such as the striatum is less well understood. Here, I examined this issue and found that the striatum was highly responsive to target probability. This is consistent with its hypothesized role in the gating of salient information into higher-order task representations. The current data are interpreted in light of that fact that different components of the striatum are sensitive to different types of task-relevant information.

Failure probability analysis of optical grid

NASA Astrophysics Data System (ADS)

Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng

2008-11-01

Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.

Probabilistic reversal learning is impaired in Parkinson's disease

PubMed Central

Peterson, David A.; Elliott, Christian; Song, David D.; Makeig, Scott; Sejnowski, Terrence J.; Poizner, Howard

2009-01-01

In many everyday settings, the relationship between our choices and their potentially rewarding outcomes is probabilistic and dynamic. In addition, the difficulty of the choices can vary widely. Although a large body of theoretical and empirical evidence suggests that dopamine mediates rewarded learning, the influence of dopamine in probabilistic and dynamic rewarded learning remains unclear. We adapted a probabilistic rewarded learning task originally used to study firing rates of dopamine cells in primate substantia nigra pars compacta (Morris et al. 2006) for use as a reversal learning task with humans. We sought to investigate how the dopamine depletion in Parkinson's disease (PD) affects probabilistic reward learning and adaptation to a reversal in reward contingencies. Over the course of 256 trials subjects learned to choose the more favorable from among pairs of images with small or large differences in reward probabilities. During a subsequent otherwise identical reversal phase, the reward probability contingencies for the stimuli were reversed. Seventeen Parkinson's disease (PD) patients of mild to moderate severity were studied off of their dopaminergic medications and compared to 15 age-matched controls. Compared to controls, PD patients had distinct pre- and post-reversal deficiencies depending upon the difficulty of the choices they had to learn. The patients also exhibited compromised adaptability to the reversal. A computational model of the subjects’ trial-by-trial choices demonstrated that the adaptability was sensitive to the gain with which patients weighted pre-reversal feedback. Collectively, the results implicate the nigral dopaminergic system in learning to make choices in environments with probabilistic and dynamic reward contingencies. PMID:19628022

Beyond Nonutilization: Irrelevant Cues Can Gate Learning in Probabilistic Categorization

ERIC Educational Resources Information Center

Little, Daniel R.; Lewandowsky, Stephan

2009-01-01

In probabilistic categorization, also known as multiple cue probability learning (MCPL), people learn to predict a discrete outcome on the basis of imperfectly valid cues. In MCPL, normatively irrelevant cues are usually ignored, which stands in apparent conflict with recent research in deterministic categorization that has shown that people…

Time-dependent earthquake probabilities

USGS Publications Warehouse

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

2005-01-01

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

Unsupervised Learning and Pattern Recognition of Biological Data Structures with Density Functional Theory and Machine Learning.

PubMed

Chen, Chien-Chang; Juan, Hung-Hui; Tsai, Meng-Yuan; Lu, Henry Horng-Shing

2018-01-11

By introducing the methods of machine learning into the density functional theory, we made a detour for the construction of the most probable density function, which can be estimated by learning relevant features from the system of interest. Using the properties of universal functional, the vital core of density functional theory, the most probable cluster numbers and the corresponding cluster boundaries in a studying system can be simultaneously and automatically determined and the plausibility is erected on the Hohenberg-Kohn theorems. For the method validation and pragmatic applications, interdisciplinary problems from physical to biological systems were enumerated. The amalgamation of uncharged atomic clusters validated the unsupervised searching process of the cluster numbers and the corresponding cluster boundaries were exhibited likewise. High accurate clustering results of the Fisher's iris dataset showed the feasibility and the flexibility of the proposed scheme. Brain tumor detections from low-dimensional magnetic resonance imaging datasets and segmentations of high-dimensional neural network imageries in the Brainbow system were also used to inspect the method practicality. The experimental results exhibit the successful connection between the physical theory and the machine learning methods and will benefit the clinical diagnoses.

Probability and Statistics: A Prelude.

ERIC Educational Resources Information Center

Goodman, A. F.; Blischke, W. R.

Probability and statistics have become indispensable to scientific, technical, and management progress. They serve as essential dialects of mathematics, the classical language of science, and as instruments necessary for intelligent generation and analysis of information. A prelude to probability and statistics is presented by examination of the…

Probability interpretations of intraclass reliabilities.

PubMed

Ellis, Jules L

2013-11-20

Research where many organizations are rated by different samples of individuals such as clients, patients, or employees frequently uses reliabilities computed from intraclass correlations. Consumers of statistical information, such as patients and policy makers, may not have sufficient background for deciding which levels of reliability are acceptable. It is shown that the reliability is related to various probabilities that may be easier to understand, for example, the proportion of organizations that will be classed significantly above (or below) the mean and the probability that an organization is classed correctly given that it is classed significantly above (or below) the mean. One can view these probabilities as the amount of information of the classification and the correctness of the classification. These probabilities have an inverse relationship: given a reliability, one can 'buy' correctness at the cost of informativeness and conversely. This article discusses how this can be used to make judgments about the required level of reliabilities. Copyright © 2013 John Wiley & Sons, Ltd.

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

Statistical learning and language acquisition

PubMed Central

Romberg, Alexa R.; Saffran, Jenny R.

2011-01-01

Human learners, including infants, are highly sensitive to structure in their environment. Statistical learning refers to the process of extracting this structure. A major question in language acquisition in the past few decades has been the extent to which infants use statistical learning mechanisms to acquire their native language. There have been many demonstrations showing infants’ ability to extract structures in linguistic input, such as the transitional probability between adjacent elements. This paper reviews current research on how statistical learning contributes to language acquisition. Current research is extending the initial findings of infants’ sensitivity to basic statistical information in many different directions, including investigating how infants represent regularities, learn about different levels of language, and integrate information across situations. These current directions emphasize studying statistical language learning in context: within language, within the infant learner, and within the environment as a whole. PMID:21666883

Defining Probability in Sex Offender Risk Assessment.

PubMed

Elwood, Richard W

2016-12-01

There is ongoing debate and confusion over using actuarial scales to predict individuals' risk of sexual recidivism. Much of the debate comes from not distinguishing Frequentist from Bayesian definitions of probability. Much of the confusion comes from applying Frequentist probability to individuals' risk. By definition, only Bayesian probability can be applied to the single case. The Bayesian concept of probability resolves most of the confusion and much of the debate in sex offender risk assessment. Although Bayesian probability is well accepted in risk assessment generally, it has not been widely used to assess the risk of sex offenders. I review the two concepts of probability and show how the Bayesian view alone provides a coherent scheme to conceptualize individuals' risk of sexual recidivism.

UT Biomedical Informatics Lab (BMIL) probability wheel

NASA Astrophysics Data System (ADS)

Huang, Sheng-Cheng; Lee, Sara; Wang, Allen; Cantor, Scott B.; Sun, Clement; Fan, Kaili; Reece, Gregory P.; Kim, Min Soon; Markey, Mia K.

A probability wheel app is intended to facilitate communication between two people, an "investigator" and a "participant", about uncertainties inherent in decision-making. Traditionally, a probability wheel is a mechanical prop with two colored slices. A user adjusts the sizes of the slices to indicate the relative value of the probabilities assigned to them. A probability wheel can improve the adjustment process and attenuate the effect of anchoring bias when it is used to estimate or communicate probabilities of outcomes. The goal of this work was to develop a mobile application of the probability wheel that is portable, easily available, and more versatile. We provide a motivating example from medical decision-making, but the tool is widely applicable for researchers in the decision sciences.

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.

[Biometric bases: basic concepts of probability calculation].

PubMed

Dinya, E

1998-04-26

The author gives or outline of the basic concepts of probability theory. The bases of the event algebra, definition of the probability, the classical probability model and the random variable are presented.

Learning to avoid spiders: fear predicts performance, not competence.

PubMed

Luo, Xijia; Becker, Eni S; Rinck, Mike

2018-01-05

We used an immersive virtual environment to examine avoidance learning in spider-fearful participants. In 3 experiments, participants were asked to repeatedly lift one of 3 virtual boxes, under which either a toy car or a spider appeared and then approached the participant. Participants were not told that the probability of encountering a spider differed across boxes. When the difference was large (Exps. 1 and 2), spider-fearfuls learned to avoid spiders by lifting the few-spiders-box more often and the many-spiders-box less often than non-fearful controls did. However, they hardly managed to do so when the probability differences were small (Exp. 3), and they did not escape from threat more quickly (Exp. 2). In contrast to the observed performance differences, spider-fearfuls and non-fearfuls showed equal competence, that is comparable post-experimental knowledge about the probability to encounter spiders under the 3 boxes. The limitations and implications of the present study are discussed.

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.…

Learning about Probability from Text and Tables: Do Color Coding and Labeling through an Interactive-User Interface Help?

ERIC Educational Resources Information Center

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

2016-01-01

Learning from visual representations is enhanced when learners appropriately integrate corresponding visual and verbal information. This study examined the effects of two methods of promoting integration, color coding and labeling, on learning about probabilistic reasoning from a table and text. Undergraduate students (N = 98) were randomly…

Training Teachers to Teach Probability

ERIC Educational Resources Information Center

Batanero, Carmen; Godino, Juan D.; Roa, Rafael

2004-01-01

In this paper we analyze the reasons why the teaching of probability is difficult for mathematics teachers, describe the contents needed in the didactical preparation of teachers to teach probability and analyze some examples of activities to carry out this training. These activities take into account the experience at the University of Granada,…

Guidance of Spatial Attention by Incidental Learning and Endogenous Cuing

ERIC Educational Resources Information Center

Jiang, Yuhong V.; Swallow, Khena M.; Rosenbaum, Gail M.

2013-01-01

Our visual system is highly sensitive to regularities in the environment. Locations that were important in one's previous experience are often prioritized during search, even though observers may not be aware of the learning. In this study we characterized the guidance of spatial attention by incidental learning of a target's spatial probability,…

Improving History Learning through Cultural Heritage, Local History and Technology

ERIC Educational Resources Information Center

Magro, Graça; de Carvalho, Joaquim Ramos; Marcelino, Maria José

2014-01-01

History learning is many times considered dull and demotivating by young students. Probably this is due because the learning process is disconnected from these students' reality and experience. One possible way to overcome this state of matters is to use technology like mobile devices with georeferencing software and local history and heritage…

Radar detection with the Neyman-Pearson criterion using supervised-learning-machines trained with the cross-entropy error

NASA Astrophysics Data System (ADS)

Jarabo-Amores, María-Pilar; la Mata-Moya, David de; Gil-Pita, Roberto; Rosa-Zurera, Manuel

2013-12-01

The application of supervised learning machines trained to minimize the Cross-Entropy error to radar detection is explored in this article. The detector is implemented with a learning machine that implements a discriminant function, which output is compared to a threshold selected to fix a desired probability of false alarm. The study is based on the calculation of the function the learning machine approximates to during training, and the application of a sufficient condition for a discriminant function to be used to approximate the optimum Neyman-Pearson (NP) detector. In this article, the function a supervised learning machine approximates to after being trained to minimize the Cross-Entropy error is obtained. This discriminant function can be used to implement the NP detector, which maximizes the probability of detection, maintaining the probability of false alarm below or equal to a predefined value. Some experiments about signal detection using neural networks are also presented to test the validity of the study.

Probability based models for estimation of wildfire risk

Treesearch

Haiganoush Preisler; D. R. Brillinger; R. E. Burgan; John Benoit

2004-01-01

We present a probability-based model for estimating fire risk. Risk is defined using three probabilities: the probability of fire occurrence; the conditional probability of a large fire given ignition; and the unconditional probability of a large fire. The model is based on grouped data at the 1 km²-day cell level. We fit a spatially and temporally explicit non-...

Impact of Learning Organization Culture on Performance in Higher Education Institutions

ERIC Educational Resources Information Center

Ponnuswamy, Indra; Manohar, Hansa Lysander

2016-01-01

In this paper, an adapted version of the Dimensions of Learning Organization Questionnaire (DLOQ) was employed to investigate the perception of academic staff on learning organization culture in Indian higher education institutions. The questionnaire was sent to 700 faculty members of different universities using a non-probability purposive…

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.

Learning Axes and Bridging Tools in a Technology-Based Design for Statistics

ERIC Educational Resources Information Center

Abrahamson, Dor; Wilensky, Uri

2007-01-01

We introduce a design-based research framework, "learning axes and bridging tools," and demonstrate its application in the preparation and study of an implementation of a middle-school experimental computer-based unit on probability and statistics, "ProbLab" (Probability Laboratory, Abrahamson and Wilensky 2002 [Abrahamson, D., & Wilensky, U.…

Risk-sensitive reinforcement learning.

PubMed

Shen, Yun; Tobia, Michael J; Sommer, Tobias; Obermayer, Klaus

2014-07-01

We derive a family of risk-sensitive reinforcement learning methods for agents, who face sequential decision-making tasks in uncertain environments. By applying a utility function to the temporal difference (TD) error, nonlinear transformations are effectively applied not only to the received rewards but also to the true transition probabilities of the underlying Markov decision process. When appropriate utility functions are chosen, the agents' behaviors express key features of human behavior as predicted by prospect theory (Kahneman & Tversky, 1979 ), for example, different risk preferences for gains and losses, as well as the shape of subjective probability curves. We derive a risk-sensitive Q-learning algorithm, which is necessary for modeling human behavior when transition probabilities are unknown, and prove its convergence. As a proof of principle for the applicability of the new framework, we apply it to quantify human behavior in a sequential investment task. We find that the risk-sensitive variant provides a significantly better fit to the behavioral data and that it leads to an interpretation of the subject's responses that is indeed consistent with prospect theory. The analysis of simultaneously measured fMRI signals shows a significant correlation of the risk-sensitive TD error with BOLD signal change in the ventral striatum. In addition we find a significant correlation of the risk-sensitive Q-values with neural activity in the striatum, cingulate cortex, and insula that is not present if standard Q-values are used.

An investigation of student understanding of classical ideas related to quantum mechanics: Potential energy diagrams and spatial probability density

NASA Astrophysics Data System (ADS)

Stephanik, Brian Michael

This dissertation describes the results of two related investigations into introductory student understanding of ideas from classical physics that are key elements of quantum mechanics. One investigation probes the extent to which students are able to interpret and apply potential energy diagrams (i.e., graphs of potential energy versus position). The other probes the extent to which students are able to reason classically about probability and spatial probability density. The results of these investigations revealed significant conceptual and reasoning difficulties that students encounter with these topics. The findings guided the design of instructional materials to address the major problems. Results from post-instructional assessments are presented that illustrate the impact of the curricula on student learning.

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.

Regional flood probabilities

USGS Publications Warehouse

Troutman, Brent M.; Karlinger, Michael 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.

Transition probability spaces in loop quantum gravity

NASA Astrophysics Data System (ADS)

Guo, Xiao-Kan

2018-03-01

We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.

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.

Active learning: learning a motor skill without a coach.

PubMed

Huang, Vincent S; Shadmehr, Reza; Diedrichsen, Jörn

2008-08-01

When we learn a new skill (e.g., golf) without a coach, we are "active learners": we have to choose the specific components of the task on which to train (e.g., iron, driver, putter, etc.). What guides our selection of the training sequence? How do choices that people make compare with choices made by machine learning algorithms that attempt to optimize performance? We asked subjects to learn the novel dynamics of a robotic tool while moving it in four directions. They were instructed to choose their practice directions to maximize their performance in subsequent tests. We found that their choices were strongly influenced by motor errors: subjects tended to immediately repeat an action if that action had produced a large error. This strategy was correlated with better performance on test trials. However, even when participants performed perfectly on a movement, they did not avoid repeating that movement. The probability of repeating an action did not drop below chance even when no errors were observed. This behavior led to suboptimal performance. It also violated a strong prediction of current machine learning algorithms, which solve the active learning problem by choosing a training sequence that will maximally reduce the learner's uncertainty about the task. While we show that these algorithms do not provide an adequate description of human behavior, our results suggest ways to improve human motor learning by helping people choose an optimal training sequence.

Error Discounting in Probabilistic Category Learning

PubMed Central

Craig, Stewart; Lewandowsky, Stephan; Little, Daniel R.

2011-01-01

Some current theories of probabilistic categorization assume that people gradually attenuate their learning in response to unavoidable error. However, existing evidence for this error discounting is sparse and open to alternative interpretations. We report two probabilistic-categorization experiments that investigated error discounting by shifting feedback probabilities to new values after different amounts of training. In both experiments, responding gradually became less responsive to errors, and learning was slowed for some time after the feedback shift. Both results are indicative of error discounting. Quantitative modeling of the data revealed that adding a mechanism for error discounting significantly improved the fits of an exemplar-based and a rule-based associative learning model, as well as of a recency-based model of categorization. We conclude that error discounting is an important component of probabilistic learning. PMID:21355666

Test-Potentiated Learning: Distinguishing Between Direct and Indirect Effects of Tests

PubMed Central

Arnold, Kathleen M.; McDermott, Kathleen B.

2013-01-01

The facilitative effect of retrieval practice, or testing, on the probability of later retrieval has been the focus of much recent empirical research. A lesser-known benefit of retrieval practice is that it may also enhance the ability of a learner to benefit from a subsequent restudy opportunity. This facilitative effect of retrieval practice on subsequent encoding is known as test-potentiated learning. Thus far, however, the literature has not isolated the indirect effect of retrieval practice on subsequent memory (via enhancing the effectiveness of restudy) from the direct effects of retrieval on subsequent memory. The experiment presented here uses conditional probability to disentangle test-potentiated learning from the direct effects of retrieval practice. The results indicate that unsuccessful retrieval attempts enhance the effectiveness of subsequent restudy, demonstrating that tests do potentiate subsequent learning. PMID:22774852

An Analysis of the Relationship between the Learning Process and Learning Motivation Profiles of Japanese Pharmacy Students Using Structural Equation Modeling.

PubMed

Yamamura, Shigeo; Takehira, Rieko

2018-04-23

Pharmacy students in Japan have to maintain strong motivation to learn for six years during their education. The authors explored the students’ learning structure. All pharmacy students in their 4th through to 6th year at Josai International University participated in the survey. The revised two factor study process questionnaire and science motivation questionnaire II were used to assess their learning process and learning motivation profiles, respectively. Structural equation modeling (SEM) was used to examine a causal relationship between the latent variables in the learning process and those in the learning motivation profile. The learning structure was modeled on the idea that the learning process affects the learning motivation profile of respondents. In the multi-group SEM, the estimated mean of the deep learning to learning motivation profile increased just after their clinical clerkship for 6th year students. This indicated that the clinical experience benefited students’ deep learning, which is probably because the experience of meeting with real patients encourages meaningful learning in pharmacy studies.

Computation of the Complex Probability Function

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

Trainer, Amelia Jo; Ledwith, Patrick John

The complex probability function is important in many areas of physics and many techniques have been developed in an attempt to compute it for some z quickly and e ciently. Most prominent are the methods that use Gauss-Hermite quadrature, which uses the roots of the n th degree Hermite polynomial and corresponding weights to approximate the complex probability function. This document serves as an overview and discussion of the use, shortcomings, and potential improvements on the Gauss-Hermite quadrature for the complex probability function.

The Probabilities of Unique Events

DTIC Science & Technology

2012-08-30

social justice and also participated in antinuclear demonstrations. The participants ranked the probability that Linda is a feminist bank teller as...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

New Zealand and Queensland Teachers' Conceptions of Learning: Transforming More than Reproducing

ERIC Educational Resources Information Center

Brown, Gavin T. L.; Lake, Robert; Matters, Gabrielle

2008-01-01

Background: Two major conceptions of learning exist: reproducing new material and transforming material to make meaning. Teachers' understandings of what learning is probably influence their teaching practices and student academic performance. Aims: To validate a short scale derived from Tait, Entwistle, & McCune's (1998) ASSIST inventory and…

What Do We Learn from Binding Features? Evidence for Multilevel Feature Integration

ERIC Educational Resources Information Center

Colzato, Lorenza S.; Raffone, Antonino; Hommel, Bernhard

2006-01-01

Four experiments were conducted to investigate the relationship between the binding of visual features (as measured by their after-effects on subsequent binding) and the learning of feature-conjunction probabilities. Both binding and learning effects were obtained, but they did not interact. Interestingly, (shape-color) binding effects…

High throughput nonparametric probability density estimation.

PubMed

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.

High throughput nonparametric probability density estimation

PubMed Central

Farmer, Jenny

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference. PMID:29750803

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.

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…

"I Don't Really Understand Probability at All": Final Year Pre-Service Teachers' Understanding of Probability

ERIC Educational Resources Information Center

Maher, Nicole; Muir, Tracey

2014-01-01

This paper reports on one aspect of a wider study that investigated a selection of final year pre-service primary teachers' responses to four probability tasks. The tasks focused on foundational ideas of probability including sample space, independence, variation and expectation. Responses suggested that strongly held intuitions appeared to…

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…

Quantum probability assignment limited by relativistic causality.

PubMed

Han, Yeong Deok; Choi, Taeseung

2016-03-14

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

Optimizing probability of detection point estimate demonstration

NASA Astrophysics Data System (ADS)

Koshti, Ajay M.

2017-04-01

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

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.

Learning with imperfectly labeled patterns

NASA Technical Reports Server (NTRS)

Chittineni, C. B.

1979-01-01

The problem of learning in pattern recognition using imperfectly labeled patterns is considered. The performance of the Bayes and nearest neighbor classifiers with imperfect labels is discussed using a probabilistic model for the mislabeling of the training patterns. Schemes for training the classifier using both parametric and non parametric techniques are presented. Methods for the correction of imperfect labels were developed. To gain an understanding of the learning process, expressions are derived for success probability as a function of training time for a one dimensional increment error correction classifier with imperfect labels. Feature selection with imperfectly labeled patterns is described.

Decentralized learning in Markov games.

PubMed

Vrancx, Peter; Verbeeck, Katja; Nowé, Ann

2008-08-01

Learning automata (LA) were recently shown to be valuable tools for designing multiagent reinforcement learning algorithms. One of the principal contributions of the LA theory is that a set of decentralized independent LA is able to control a finite Markov chain with unknown transition probabilities and rewards. In this paper, we propose to extend this algorithm to Markov games--a straightforward extension of single-agent Markov decision problems to distributed multiagent decision problems. We show that under the same ergodic assumptions of the original theorem, the extended algorithm will converge to a pure equilibrium point between agent policies.

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.

Time-course variation of statistics embedded in music: Corpus study on implicit learning and knowledge.

PubMed

Daikoku, Tatsuya

2018-01-01

Learning and knowledge of transitional probability in sequences like music, called statistical learning and knowledge, are considered implicit processes that occur without intention to learn and awareness of what one knows. This implicit statistical knowledge can be alternatively expressed via abstract medium such as musical melody, which suggests this knowledge is reflected in melodies written by a composer. This study investigates how statistics in music vary over a composer's lifetime. Transitional probabilities of highest-pitch sequences in Ludwig van Beethoven's Piano Sonata were calculated based on different hierarchical Markov models. Each interval pattern was ordered based on the sonata opus number. The transitional probabilities of sequential patterns that are musical universal in music gradually decreased, suggesting that time-course variations of statistics in music reflect time-course variations of a composer's statistical knowledge. This study sheds new light on novel methodologies that may be able to evaluate the time-course variation of composer's implicit knowledge using musical scores.

Automatic Sleep Stage Determination by Multi-Valued Decision Making Based on Conditional Probability with Optimal Parameters

NASA Astrophysics Data System (ADS)

Wang, Bei; Sugi, Takenao; Wang, Xingyu; Nakamura, Masatoshi

Data for human sleep study may be affected by internal and external influences. The recorded sleep data contains complex and stochastic factors, which increase the difficulties for the computerized sleep stage determination techniques to be applied for clinical practice. The aim of this study is to develop an automatic sleep stage determination system which is optimized for variable sleep data. The main methodology includes two modules: expert knowledge database construction and automatic sleep stage determination. Visual inspection by a qualified clinician is utilized to obtain the probability density function of parameters during the learning process of expert knowledge database construction. Parameter selection is introduced in order to make the algorithm flexible. Automatic sleep stage determination is manipulated based on conditional probability. The result showed close agreement comparing with the visual inspection by clinician. The developed system can meet the customized requirements in hospitals and institutions.

Trial type probability modulates the cost of antisaccades

PubMed Central

Chiau, Hui-Yan; Tseng, Philip; Su, Jia-Han; Tzeng, Ovid J. L.; Hung, Daisy L.; Muggleton, Neil G.

2011-01-01

The antisaccade task, where eye movements are made away from a target, has been used to investigate the flexibility of cognitive control of behavior. Antisaccades usually have longer saccade latencies than prosaccades, the so-called antisaccade cost. Recent studies have shown that this antisaccade cost can be modulated by event probability. This may mean that the antisaccade cost can be reduced, or even reversed, if the probability of surrounding events favors the execution of antisaccades. The probabilities of prosaccades and antisaccades were systematically manipulated by changing the proportion of a certain type of trial in an interleaved pro/antisaccades task. We aimed to disentangle the intertwined relationship between trial type probabilities and the antisaccade cost with the ultimate goal of elucidating how probabilities of trial types modulate human flexible behaviors, as well as the characteristics of such modulation effects. To this end, we examined whether implicit trial type probability can influence saccade latencies and also manipulated the difficulty of cue discriminability to see how effects of trial type probability would change when the demand on visual perceptual analysis was high or low. A mixed-effects model was applied to the analysis to dissect the factors contributing to the modulation effects of trial type probabilities. Our results suggest that the trial type probability is one robust determinant of antisaccade cost. These findings highlight the importance of implicit probability in the flexibility of cognitive control of behavior. PMID:21543748

Reading a Story: Different Degrees of Learning in Different Learning Environments.

PubMed

Giannini, Anna Maria; Cordellieri, Pierluigi; Piccardi, Laura

2017-01-01

The learning environment in which material is acquired may produce differences in delayed recall and in the elements that individuals focus on. These differences may appear even during development. In the present study, we compared three different learning environments in 450 normally developing 7-year-old children subdivided into three groups according to the type of learning environment. Specifically, children were asked to learn the same material shown in three different learning environments: reading illustrated books (TB); interacting with the same text displayed on a PC monitor and enriched with interactive activities (PC-IA); reading the same text on a PC monitor but not enriched with interactive narratives (PC-NoIA). Our results demonstrated that TB and PC-NoIA elicited better verbal memory recall. In contrast, PC-IA and PC-NoIA produced higher scores for visuo-spatial memory, enhancing memory for spatial relations, positions and colors with respect to TB. Interestingly, only TB seemed to produce a deeper comprehension of the story's moral. Our results indicated that PC-IA offered a different type of learning that favored visual details. In this sense, interactive activities demonstrate certain limitations, probably due to information overabundance, emotional mobilization, emphasis on images and effort exerted in interactive activities. Thus, interactive activities, although entertaining, act as disruptive elements which interfere with verbal memory and deep moral comprehension.

Reading a Story: Different Degrees of Learning in Different Learning Environments

PubMed Central

Giannini, Anna Maria; Cordellieri, Pierluigi; Piccardi, Laura

2017-01-01

The learning environment in which material is acquired may produce differences in delayed recall and in the elements that individuals focus on. These differences may appear even during development. In the present study, we compared three different learning environments in 450 normally developing 7-year-old children subdivided into three groups according to the type of learning environment. Specifically, children were asked to learn the same material shown in three different learning environments: reading illustrated books (TB); interacting with the same text displayed on a PC monitor and enriched with interactive activities (PC-IA); reading the same text on a PC monitor but not enriched with interactive narratives (PC-NoIA). Our results demonstrated that TB and PC-NoIA elicited better verbal memory recall. In contrast, PC-IA and PC-NoIA produced higher scores for visuo-spatial memory, enhancing memory for spatial relations, positions and colors with respect to TB. Interestingly, only TB seemed to produce a deeper comprehension of the story’s moral. Our results indicated that PC-IA offered a different type of learning that favored visual details. In this sense, interactive activities demonstrate certain limitations, probably due to information overabundance, emotional mobilization, emphasis on images and effort exerted in interactive activities. Thus, interactive activities, although entertaining, act as disruptive elements which interfere with verbal memory and deep moral comprehension. PMID:29085296

Competitive STDP Learning of Overlapping Spatial Patterns.

PubMed

Krunglevicius, Dalius

2015-08-01

Spike-timing-dependent plasticity (STDP) is a set of Hebbian learning rules firmly based on biological evidence. It has been demonstrated that one of the STDP learning rules is suited for learning spatiotemporal patterns. When multiple neurons are organized in a simple competitive spiking neural network, this network is capable of learning multiple distinct patterns. If patterns overlap significantly (i.e., patterns are mutually inclusive), however, competition would not preclude trained neuron's responding to a new pattern and adjusting synaptic weights accordingly. This letter presents a simple neural network that combines vertical inhibition and Euclidean distance-dependent synaptic strength factor. This approach helps to solve the problem of pattern size-dependent parameter optimality and significantly reduces the probability of a neuron's forgetting an already learned pattern. For demonstration purposes, the network was trained for the first ten letters of the Braille alphabet.

Vehicle Steering control: A model of learning

NASA Technical Reports Server (NTRS)

Smiley, A.; Reid, L.; Fraser, M.

1978-01-01

A hierarchy of strategies were postulated to describe the process of learning steering control. Vehicle motion and steering control data were recorded for twelve novices who drove an instrumented car twice a week during and after a driver training course. Car-driver describing functions were calculated, the probable control structure determined, and the driver-alone transfer function modelled. The data suggested that the largest changes in steering control with learning were in the way the driver used the lateral position cue.

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.

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 be...

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…

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.

Effects of NMDA receptor antagonists on probability discounting depend on the order of probability presentation.

PubMed

Yates, Justin R; Breitenstein, Kerry A; Gunkel, Benjamin T; Hughes, Mallory N; Johnson, Anthony B; Rogers, Katherine K; Shape, Sara M

Risky decision making can be measured using a probability-discounting procedure, in which animals choose between a small, certain reinforcer and a large, uncertain reinforcer. Recent evidence has identified glutamate as a mediator of risky decision making, as blocking the N-methyl-d-aspartate (NMDA) receptor with MK-801 increases preference for a large, uncertain reinforcer. Because the order in which probabilities associated with the large reinforcer can modulate the effects of drugs on choice, the current study determined if NMDA receptor ligands alter probability discounting using ascending and descending schedules. Sixteen rats were trained in a probability-discounting procedure in which the odds against obtaining the large reinforcer increased (n=8) or decreased (n=8) across blocks of trials. Following behavioral training, rats received treatments of the NMDA receptor ligands MK-801 (uncompetitive antagonist; 0, 0.003, 0.01, or 0.03mg/kg), ketamine (uncompetitive antagonist; 0, 1.0, 5.0, or 10.0mg/kg), and ifenprodil (NR2B-selective non-competitive antagonist; 0, 1.0, 3.0, or 10.0mg/kg). Results showed discounting was steeper (indicating increased risk aversion) for rats on an ascending schedule relative to rats on the descending schedule. Furthermore, the effects of MK-801, ketamine, and ifenprodil on discounting were dependent on the schedule used. Specifically, the highest dose of each drug decreased risk taking in rats in the descending schedule, but only MK-801 (0.03mg/kg) increased risk taking in rats on an ascending schedule. These results show that probability presentation order modulates the effects of NMDA receptor ligands on risky decision making. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

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…

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.

Impact of Homeland Security Communities of Learning: Developing a Strategy for Training and Collaboration

DTIC Science & Technology

2006-09-01

education. LCMS allow subject matter experts, with little technology skills to develop curriculum, deliver courses, and monitor e- learning. Distance...occurring in year seven and therefore it has zero probability of occurring in the first five years. The probability of Ev-2 occurring between years 7 and

Convergence of Transition Probability Matrix in CLVMarkov Models

NASA Astrophysics Data System (ADS)

Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.

2018-04-01

A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.

Probability Theory Plus Noise: Descriptive Estimation and Inferential Judgment.

PubMed

Costello, Fintan; Watts, Paul

2018-01-01

We describe a computational model of two central aspects of people's probabilistic reasoning: descriptive probability estimation and inferential probability judgment. This model assumes that people's reasoning follows standard frequentist probability theory, but it is subject to random noise. This random noise has a regressive effect in descriptive probability estimation, moving probability estimates away from normative probabilities and toward the center of the probability scale. This random noise has an anti-regressive effect in inferential judgement, however. These regressive and anti-regressive effects explain various reliable and systematic biases seen in people's descriptive probability estimation and inferential probability judgment. This model predicts that these contrary effects will tend to cancel out in tasks that involve both descriptive estimation and inferential judgement, leading to unbiased responses in those tasks. We test this model by applying it to one such task, described by Gallistel et al. ). Participants' median responses in this task were unbiased, agreeing with normative probability theory over the full range of responses. Our model captures the pattern of unbiased responses in this task, while simultaneously explaining systematic biases away from normatively correct probabilities seen in other tasks. Copyright © 2018 Cognitive Science Society, Inc.

Online Pairwise Learning Algorithms.

PubMed

Ying, Yiming; Zhou, Ding-Xuan

2016-04-01

Pairwise learning usually refers to a learning task that involves a loss function depending on pairs of examples, among which the most notable ones are bipartite ranking, metric learning, and AUC maximization. In this letter we study an online algorithm for pairwise learning with a least-square loss function in an unconstrained setting of a reproducing kernel Hilbert space (RKHS) that we refer to as the Online Pairwise lEaRning Algorithm (OPERA). In contrast to existing works (Kar, Sriperumbudur, Jain, & Karnick, 2013 ; Wang, Khardon, Pechyony, & Jones, 2012 ), which require that the iterates are restricted to a bounded domain or the loss function is strongly convex, OPERA is associated with a non-strongly convex objective function and learns the target function in an unconstrained RKHS. Specifically, we establish a general theorem that guarantees the almost sure convergence for the last iterate of OPERA without any assumptions on the underlying distribution. Explicit convergence rates are derived under the condition of polynomially decaying step sizes. We also establish an interesting property for a family of widely used kernels in the setting of pairwise learning and illustrate the convergence results using such kernels. Our methodology mainly depends on the characterization of RKHSs using its associated integral operators and probability inequalities for random variables with values in a Hilbert space.

Post-traumatic stress is associated with verbal learning, memory, and psychomotor speed in HIV-infected and HIV-uninfected women.

PubMed

Rubin, Leah H; Pyra, Maria; Cook, Judith A; Weber, Kathleen M; Cohen, Mardge H; Martin, Eileen; Valcour, Victor; Milam, Joel; Anastos, Kathryn; Young, Mary A; Alden, Christine; Gustafson, Deborah R; Maki, Pauline M

2016-04-01

The prevalence of post-traumatic stress disorder (PTSD) is higher among HIV-infected (HIV+) women compared with HIV-uninfected (HIV-) women, and deficits in episodic memory are a common feature of both PTSD and HIV infection. We investigated the association between a probable PTSD diagnosis using the PTSD Checklist-Civilian (PCL-C) version and verbal learning and memory using the Hopkins Verbal Learning Test in 1004 HIV+ and 496 at-risk HIV- women. HIV infection was not associated with a probable PTSD diagnosis (17% HIV+, 16% HIV-; p = 0.49) but was associated with lower verbal learning (p < 0.01) and memory scores (p < 0.01). Irrespective of HIV status, a probable PTSD diagnosis was associated with poorer performance in verbal learning (p < 0.01) and memory (p < 0.01) and psychomotor speed (p < 0.001). The particular pattern of cognitive correlates of probable PTSD varied depending on exposure to sexual abuse and/or violence, with exposure to either being associated with a greater number of cognitive domains and a worse cognitive profile. A statistical interaction between HIV serostatus and PTSD was observed on the fine motor skills domain (p = 0.03). Among women with probable PTSD, HIV- women performed worse than HIV+ women on fine motor skills (p = 0.01), but among women without probable PTSD, there was no significant difference in performance between the groups (p = 0.59). These findings underscore the importance of considering mental health factors as correlates to cognitive deficits in women with HIV.

Microstimulation of the Human Substantia Nigra Alters Reinforcement Learning

PubMed Central

Ramayya, Ashwin G.; Misra, Amrit

2014-01-01

Animal studies have shown that substantia nigra (SN) dopaminergic (DA) neurons strengthen action–reward associations during reinforcement learning, but their role in human learning is not known. Here, we applied microstimulation in the SN of 11 patients undergoing deep brain stimulation surgery for the treatment of Parkinson's disease as they performed a two-alternative probability learning task in which rewards were contingent on stimuli, rather than actions. Subjects demonstrated decreased learning from reward trials that were accompanied by phasic SN microstimulation compared with reward trials without stimulation. Subjects who showed large decreases in learning also showed an increased bias toward repeating actions after stimulation trials; therefore, stimulation may have decreased learning by strengthening action–reward associations rather than stimulus–reward associations. Our findings build on previous studies implicating SN DA neurons in preferentially strengthening action–reward associations during reinforcement learning. PMID:24828643

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.

Transitional probabilities count more than frequency, but might not be used for memorization.

PubMed

Endress, Ansgar D; Langus, Alan

2017-02-01

Learners often need to extract recurring items from continuous sequences, in both vision and audition. The best-known example is probably found in word-learning, where listeners have to determine where words start and end in fluent speech. This could be achieved through universal and experience-independent statistical mechanisms, for example by relying on Transitional Probabilities (TPs). Further, these mechanisms might allow learners to store items in memory. However, previous investigations have yielded conflicting evidence as to whether a sensitivity to TPs is diagnostic of the memorization of recurring items. Here, we address this issue in the visual modality. Participants were familiarized with a continuous sequence of visual items (i.e., arbitrary or everyday symbols), and then had to choose between (i) high-TP items that appeared in the sequence, (ii) high-TP items that did not appear in the sequence, and (iii) low-TP items that appeared in the sequence. Items matched in TPs but differing in (chunk) frequency were much harder to discriminate than items differing in TPs (with no significant sensitivity to chunk frequency), and learners preferred unattested high-TP items over attested low-TP items. Contrary to previous claims, these results cannot be explained on the basis of the similarity of the test items. Learners thus weigh within-item TPs higher than the frequency of the chunks, even when the TP differences are relatively subtle. We argue that these results are problematic for distributional clustering mechanisms that analyze continuous sequences, and provide supporting computational results. We suggest that the role of TPs might not be to memorize items per se, but rather to prepare learners to memorize recurring items once they are presented in subsequent learning situations with richer cues. Copyright © 2016 Elsevier Inc. All rights reserved.

LEAP: biomarker inference through learning and evaluating association patterns.

PubMed

Jiang, Xia; Neapolitan, Richard E

2015-03-01

Single nucleotide polymorphism (SNP) high-dimensional datasets are available from Genome Wide Association Studies (GWAS). Such data provide researchers opportunities to investigate the complex genetic basis of diseases. Much of genetic risk might be due to undiscovered epistatic interactions, which are interactions in which combination of several genes affect disease. Research aimed at discovering interacting SNPs from GWAS datasets proceeded in two directions. First, tools were developed to evaluate candidate interactions. Second, algorithms were developed to search over the space of candidate interactions. Another problem when learning interacting SNPs, which has not received much attention, is evaluating how likely it is that the learned SNPs are associated with the disease. A complete system should provide this information as well. We develop such a system. Our system, called LEAP, includes a new heuristic search algorithm for learning interacting SNPs, and a Bayesian network based algorithm for computing the probability of their association. We evaluated the performance of LEAP using 100 1,000-SNP simulated datasets, each of which contains 15 SNPs involved in interactions. When learning interacting SNPs from these datasets, LEAP outperformed seven others methods. Furthermore, only SNPs involved in interactions were found to be probable. We also used LEAP to analyze real Alzheimer's disease and breast cancer GWAS datasets. We obtained interesting and new results from the Alzheimer's dataset, but limited results from the breast cancer dataset. We conclude that our results support that LEAP is a useful tool for extracting candidate interacting SNPs from high-dimensional datasets and determining their probability. © 2015 The Authors. *Genetic Epidemiology published by Wiley Periodicals, Inc.

Optimizing Probability of Detection Point Estimate Demonstration

NASA Technical Reports Server (NTRS)

Koshti, Ajay M.

2017-01-01

Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.

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.

Learning and liking of melody and harmony: further studies in artificial grammar learning.

PubMed

Loui, Psyche

2012-10-01

Much of what we know and love about music is based on implicitly acquired mental representations of musical pitches and the relationships between them. While previous studies have shown that these mental representations of music can be acquired rapidly and can influence preference, it is still unclear which aspects of music influence learning and preference formation. This article reports two experiments that use an artificial musical system to examine two questions: (1) which aspects of music matter most for learning, and (2) which aspects of music matter most for preference formation. Two aspects of music are tested: melody and harmony. In Experiment 1 we tested the learning and liking of a new musical system that is manipulated melodically so that only some of the possible conditional probabilities between successive notes are presented. In Experiment 2 we administered the same tests for learning and liking, but we used a musical system that is manipulated harmonically to eliminate the property of harmonic whole-integer ratios between pitches. Results show that disrupting melody (Experiment 1) disabled the learning of music without disrupting preference formation, whereas disrupting harmony (Experiment 2) does not affect learning and memory but disrupts preference formation. Results point to a possible dissociation between learning and preference in musical knowledge. Copyright © 2012 Cognitive Science Society, Inc.

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…

Sex and boldness explain individual differences in spatial learning in a lizard.

PubMed

Carazo, Pau; Noble, Daniel W A; Chandrasoma, Dani; Whiting, Martin J

2014-05-07

Understanding individual differences in cognitive performance is a major challenge to animal behaviour and cognition studies. We used the Eastern water skink (Eulamprus quoyii) to examine associations between exploration, boldness and individual variability in spatial learning, a dimension of lizard cognition with important bearing on fitness. We show that males perform better than females in a biologically relevant spatial learning task. This is the first evidence for sex differences in learning in a reptile, and we argue that it is probably owing to sex-specific selective pressures that may be widespread in lizards. Across the sexes, we found a clear association between boldness after a simulated predatory attack and the probability of learning the spatial task. In contrast to previous studies, we found a nonlinear association between boldness and learning: both 'bold' and 'shy' behavioural types were more successful learners than intermediate males. Our results do not fit with recent predictions suggesting that individual differences in learning may be linked with behavioural types via high-low-risk/reward trade-offs. We suggest the possibility that differences in spatial cognitive performance may arise in lizards as a consequence of the distinct environmental variability and complexity experienced by individuals as a result of their sex and social tactics.

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…

Musical Experience Influences Statistical Learning of a Novel Language

PubMed Central

Shook, Anthony; Marian, Viorica; Bartolotti, James; Schroeder, Scott R.

2014-01-01

Musical experience may benefit learning a new language by enhancing the fidelity with which the auditory system encodes sound. In the current study, participants with varying degrees of musical experience were exposed to two statistically-defined languages consisting of auditory Morse-code sequences which varied in difficulty. We found an advantage for highly-skilled musicians, relative to less-skilled musicians, in learning novel Morse-code based words. Furthermore, in the more difficult learning condition, performance of lower-skilled musicians was mediated by their general cognitive abilities. We suggest that musical experience may lead to enhanced processing of statistical information and that musicians’ enhanced ability to learn statistical probabilities in a novel Morse-code language may extend to natural language learning. PMID:23505962

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.

Toward User Interfaces and Data Visualization Criteria for Learning Design of Digital Textbooks

ERIC Educational Resources Information Center

Railean, Elena

2014-01-01

User interface and data visualisation criteria are central issues in digital textbooks design. However, when applying mathematical modelling of learning process to the analysis of the possible solutions, it could be observed that results differ. Mathematical learning views cognition in on the base on statistics and probability theory, graph…

Statistical learning of an auditory sequence and reorganization of acquired knowledge: A time course of word segmentation and ordering.

PubMed

Daikoku, Tatsuya; Yatomi, Yutaka; Yumoto, Masato

2017-01-27

Previous neural studies have supported the hypothesis that statistical learning mechanisms are used broadly across different domains such as language and music. However, these studies have only investigated a single aspect of statistical learning at a time, such as recognizing word boundaries or learning word order patterns. In this study, we neutrally investigated how the two levels of statistical learning for recognizing word boundaries and word ordering could be reflected in neuromagnetic responses and how acquired statistical knowledge is reorganised when the syntactic rules are revised. Neuromagnetic responses to the Japanese-vowel sequence (a, e, i, o, and u), presented every .45s, were recorded from 14 right-handed Japanese participants. The vowel order was constrained by a Markov stochastic model such that five nonsense words (aue, eao, iea, oiu, and uoi) were chained with an either-or rule: the probability of the forthcoming word was statistically defined (80% for one word; 20% for the other word) by the most recent two words. All of the word transition probabilities (80% and 20%) were switched in the middle of the sequence. In the first and second quarters of the sequence, the neuromagnetic responses to the words that appeared with higher transitional probability were significantly reduced compared with those that appeared with a lower transitional probability. After switching the word transition probabilities, the response reduction was replicated in the last quarter of the sequence. The responses to the final vowels in the words were significantly reduced compared with those to the initial vowels in the last quarter of the sequence. The results suggest that both within-word and between-word statistical learning are reflected in neural responses. The present study supports the hypothesis that listeners learn larger structures such as phrases first, and they subsequently extract smaller structures, such as words, from the learned phrases. The present

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.

Lattice Theory, Measures and Probability

NASA Astrophysics Data System (ADS)

Knuth, Kevin H.

2007-11-01

In this tutorial, I will discuss the concepts behind generalizing ordering to measuring and apply these ideas to the derivation of probability theory. The fundamental concept is that anything that can be ordered can be measured. Since we are in the business of making statements about the world around us, we focus on ordering logical statements according to implication. This results in a Boolean lattice, which is related to the fact that the corresponding logical operations form a Boolean algebra. The concept of logical implication can be generalized to degrees of implication by generalizing the zeta function of the lattice. The rules of probability theory arise naturally as a set of constraint equations. Through this construction we are able to neatly connect the concepts of order, structure, algebra, and calculus. The meaning of probability is inherited from the meaning of the ordering relation, implication, rather than being imposed in an ad hoc manner at the start.

Correlation between the clinical pretest probability score and the lung ventilation and perfusion scan probability.

PubMed

Bhoobalan, Shanmugasundaram; Chakravartty, Riddhika; Dolbear, Gill; Al-Janabi, Mazin

2013-10-01

Aim of the study was to determine the accuracy of the clinical pretest probability (PTP) score and its association with lung ventilation and perfusion (VQ) scan. A retrospective analysis of 510 patients who had a lung VQ scan between 2008 and 2010 were included in the study. Out of 510 studies, the number of normal, low, and high probability VQ scans were 155 (30%), 289 (57%), and 55 (11%), respectively. A total of 103 patients underwent computed tomography pulmonary angiography (CTPA) scan in which 21 (20%) had a positive scan, 81 (79%) had a negative scan and one (1%) had an equivocal result. The rate of PE in the normal, low-probability, and high-probability scan categories were: 2 (9.5%), 10 (47.5%), and 9 (43%) respectively. A very low correlation (Pearson correlation coefficient r = 0.20) between the clinical PTP score and lung VQ scan. The area under the curve (AUC) of the clinical PTP score was 52% when compared with the CTPA results. However, the accuracy of lung VQ scan was better (AUC = 74%) when compared with CTPA scan. The clinical PTP score is unreliable on its own; however, it may still aid in the interpretation of lung VQ scan. The accuracy of the lung VQ scan was better in the assessment of underlying pulmonary embolism (PE).

Correlation between the clinical pretest probability score and the lung ventilation and perfusion scan probability

PubMed Central

Bhoobalan, Shanmugasundaram; Chakravartty, Riddhika; Dolbear, Gill; Al-Janabi, Mazin

2013-01-01

Purpose: Aim of the study was to determine the accuracy of the clinical pretest probability (PTP) score and its association with lung ventilation and perfusion (VQ) scan. Materials and Methods: A retrospective analysis of 510 patients who had a lung VQ scan between 2008 and 2010 were included in the study. Out of 510 studies, the number of normal, low, and high probability VQ scans were 155 (30%), 289 (57%), and 55 (11%), respectively. Results: A total of 103 patients underwent computed tomography pulmonary angiography (CTPA) scan in which 21 (20%) had a positive scan, 81 (79%) had a negative scan and one (1%) had an equivocal result. The rate of PE in the normal, low-probability, and high-probability scan categories were: 2 (9.5%), 10 (47.5%), and 9 (43%) respectively. A very low correlation (Pearson correlation coefficient r = 0.20) between the clinical PTP score and lung VQ scan. The area under the curve (AUC) of the clinical PTP score was 52% when compared with the CTPA results. However, the accuracy of lung VQ scan was better (AUC = 74%) when compared with CTPA scan. Conclusion: The clinical PTP score is unreliable on its own; however, it may still aid in the interpretation of lung VQ scan. The accuracy of the lung VQ scan was better in the assessment of underlying pulmonary embolism (PE). PMID:24379532

Analytic Neutrino Oscillation Probabilities in Matter: Revisited

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

Parke, Stephen J.; Denton, Peter B.; Minakata, Hisakazu

2018-01-02

We summarize our recent paper on neutrino oscillation probabilities in matter, explaining the importance, relevance and need for simple, highly accurate approximations to the neutrino oscillation probabilities in matter.

Crib Work--An Evaluation of a Problem-Based Learning Experiment: Preliminary Results

ERIC Educational Resources Information Center

Walsh, Vonda K.; Bush, H. Francis

2013-01-01

Problem-based learning has been proven to be successful in both medical colleges and physics classes, but not uniformly across all disciplines. A college course in probability and statistics was used as a setting to test the effectiveness of problem-based learning when applied to homework. This paper compares the performances of the students from…

Infants' statistical learning: 2- and 5-month-olds' segmentation of continuous visual sequences.

PubMed

Slone, Lauren Krogh; Johnson, Scott P

2015-05-01

Past research suggests that infants have powerful statistical learning abilities; however, studies of infants' visual statistical learning offer differing accounts of the developmental trajectory of and constraints on this learning. To elucidate this issue, the current study tested the hypothesis that young infants' segmentation of visual sequences depends on redundant statistical cues to segmentation. A sample of 20 2-month-olds and 20 5-month-olds observed a continuous sequence of looming shapes in which unit boundaries were defined by both transitional probability and co-occurrence frequency. Following habituation, only 5-month-olds showed evidence of statistically segmenting the sequence, looking longer to a statistically improbable shape pair than to a probable pair. These results reaffirm the power of statistical learning in infants as young as 5 months but also suggest considerable development of statistical segmentation ability between 2 and 5 months of age. Moreover, the results do not support the idea that infants' ability to segment visual sequences based on transitional probabilities and/or co-occurrence frequencies is functional at the onset of visual experience, as has been suggested previously. Rather, this type of statistical segmentation appears to be constrained by the developmental state of the learner. Factors contributing to the development of statistical segmentation ability during early infancy, including memory and attention, are discussed. Copyright © 2015 Elsevier Inc. All rights reserved.

Naive Probability: Model-Based Estimates of Unique Events.

PubMed

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

2015-08-01

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

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.

Probability, arrow of time and decoherence

NASA Astrophysics Data System (ADS)

Bacciagaluppi, Guido

This paper relates both to the metaphysics of probability and to the physics of time asymmetry. Using the formalism of decoherent histories, it investigates whether intuitions about intrinsic time directedness that are often associated with probability can be justified in the context of no-collapse approaches to quantum mechanics. The standard (two-vector) approach to time symmetry in the decoherent histories literature is criticised, and an alternative approach is proposed, based on two decoherence conditions ('forwards' and 'backwards') within the one-vector formalism. In turn, considerations of forwards and backwards decoherence and of decoherence and recoherence suggest that a time-directed interpretation of probabilities, if adopted, should be both contingent and perspectival.

Improving Grasp Skills Using Schema Structured Learning

NASA Technical Reports Server (NTRS)

Platt, Robert; Grupen, ROderic A.; Fagg, Andrew H.

2006-01-01

Abstract In the control-based approach to robotics, complex behavior is created by sequencing and combining control primitives. While it is desirable for the robot to autonomously learn the correct control sequence, searching through the large number of potential solutions can be time consuming. This paper constrains this search to variations of a generalized solution encoded in a framework known as an action schema. A new algorithm, SCHEMA STRUCTURED LEARNING, is proposed that repeatedly executes variations of the generalized solution in search of instantiations that satisfy action schema objectives. This approach is tested in a grasping task where Dexter, the UMass humanoid robot, learns which reaching and grasping controllers maximize the probability of grasp success.

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.

A short note on probability in clinical medicine.

PubMed

Upshur, Ross E G

2013-06-01

Probability claims are ubiquitous in clinical medicine, yet exactly how clinical events relate to interpretations of probability has been not been well explored. This brief essay examines the major interpretations of probability and how these interpretations may account for the probabilistic nature of clinical events. It is argued that there are significant problems with the unquestioned application of interpretation of probability to clinical events. The essay concludes by suggesting other avenues to understand uncertainty in clinical medicine. © 2013 John Wiley & Sons Ltd.

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.

Causal inference, probability theory, and graphical insights.

PubMed

Baker, Stuart G

2013-11-10

Causal inference from observational studies is a fundamental topic in biostatistics. The causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies. In contrast, the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons. First, probability theory is generally more flexible than causal graphs: Besides explaining such causal graph topics as M-bias (adjusting for a collider) and bias amplification and attenuation (when adjusting for instrumental variable), probability theory is also the foundation of the paired availability design for historical controls, which does not fit into a causal graph framework. Second, probability theory is the basis for insightful graphical displays including the BK-Plot for understanding Simpson's paradox with a binary confounder, the BK2-Plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder, and the PAD-Plot for understanding the principal stratification component of the paired availability design. Published 2013. This article is a US Government work and is in the public domain in the USA.

Fixation Probability in a Haploid-Diploid Population.

PubMed

Bessho, Kazuhiro; Otto, Sarah P

2017-01-01

Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with haploid-diploid life cycles. We develop a genetic model that considers the population dynamics using both the Moran model and Wright-Fisher model. Applying a branching process approximation, we obtain an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species. Copyright © 2017 by the Genetics Society of America.

Fixation Probability in a Haploid-Diploid Population

PubMed Central

Bessho, Kazuhiro; Otto, Sarah P.

2017-01-01

Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with haploid-diploid life cycles. We develop a genetic model that considers the population dynamics using both the Moran model and Wright–Fisher model. Applying a branching process approximation, we obtain an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species. PMID:27866168

Chance, determinism and the classical theory of probability.

PubMed

Vasudevan, Anubav

2018-02-01

This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning. Copyright © 2017 Elsevier Ltd. All rights reserved.

Faster computation of exact RNA shape probabilities.

PubMed

Janssen, Stefan; Giegerich, Robert

2010-03-01

Abstract shape analysis allows efficient computation of a representative sample of low-energy foldings of an RNA molecule. More comprehensive information is obtained by computing shape probabilities, accumulating the Boltzmann probabilities of all structures within each abstract shape. Such information is superior to free energies because it is independent of sequence length and base composition. However, up to this point, computation of shape probabilities evaluates all shapes simultaneously and comes with a computation cost which is exponential in the length of the sequence. We device an approach called RapidShapes that computes the shapes above a specified probability threshold T by generating a list of promising shapes and constructing specialized folding programs for each shape to compute its share of Boltzmann probability. This aims at a heuristic improvement of runtime, while still computing exact probability values. Evaluating this approach and several substrategies, we find that only a small proportion of shapes have to be actually computed. For an RNA sequence of length 400, this leads, depending on the threshold, to a 10-138 fold speed-up compared with the previous complete method. Thus, probabilistic shape analysis has become feasible in medium-scale applications, such as the screening of RNA transcripts in a bacterial genome. RapidShapes is available via http://bibiserv.cebitec.uni-bielefeld.de/rnashapes

Series approximation to probability densities

NASA Astrophysics Data System (ADS)

Cohen, L.

2018-04-01

One of the historical and fundamental uses of the Edgeworth and Gram-Charlier series is to "correct" a Gaussian density when it is determined that the probability density under consideration has moments that do not correspond to the Gaussian [5, 6]. There is a fundamental difficulty with these methods in that if the series are truncated, then the resulting approximate density is not manifestly positive. The aim of this paper is to attempt to expand a probability density so that if it is truncated it will still be manifestly positive.

Match probabilities in a finite, subdivided population

PubMed Central

Malaspinas, Anna-Sapfo; Slatkin, Montgomery; Song, Yun S.

2011-01-01

We generalize a recently introduced graphical framework to compute the probability that haplotypes or genotypes of two individuals drawn from a finite, subdivided population match. As in the previous work, we assume an infinite-alleles model. We focus on the case of a population divided into two subpopulations, but the underlying framework can be applied to a general model of population subdivision. We examine the effect of population subdivision on the match probabilities and the accuracy of the product rule which approximates multi-locus match probabilities as a product of one-locus match probabilities. We quantify the deviation from predictions of the product rule by R, the ratio of the multi-locus match probability to the product of the one-locus match probabilities.We carry out the computation for two loci and find that ignoring subdivision can lead to underestimation of the match probabilities if the population under consideration actually has subdivision structure and the individuals originate from the same subpopulation. On the other hand, under a given model of population subdivision, we find that the ratio R for two loci is only slightly greater than 1 for a large range of symmetric and asymmetric migration rates. Keeping in mind that the infinite-alleles model is not the appropriate mutation model for STR loci, we conclude that, for two loci and biologically reasonable parameter values, population subdivision may lead to results that disfavor innocent suspects because of an increase in identity-by-descent in finite populations. On the other hand, for the same range of parameters, population subdivision does not lead to a substantial increase in linkage disequilibrium between loci. Those results are consistent with established practice. PMID:21266180

Students' Understanding of Conditional Probability on Entering University

ERIC Educational Resources Information Center

Reaburn, Robyn

2013-01-01

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

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…

Land use and land cover classification for rural residential areas in China using soft-probability cascading of multifeatures

NASA Astrophysics Data System (ADS)

Zhang, Bin; Liu, Yueyan; Zhang, Zuyu; Shen, Yonglin

2017-10-01

A multifeature soft-probability cascading scheme to solve the problem of land use and land cover (LULC) classification using high-spatial-resolution images to map rural residential areas in China is proposed. The proposed method is used to build midlevel LULC features. Local features are frequently considered as low-level feature descriptors in a midlevel feature learning method. However, spectral and textural features, which are very effective low-level features, are neglected. The acquisition of the dictionary of sparse coding is unsupervised, and this phenomenon reduces the discriminative power of the midlevel feature. Thus, we propose to learn supervised features based on sparse coding, a support vector machine (SVM) classifier, and a conditional random field (CRF) model to utilize the different effective low-level features and improve the discriminability of midlevel feature descriptors. First, three kinds of typical low-level features, namely, dense scale-invariant feature transform, gray-level co-occurrence matrix, and spectral features, are extracted separately. Second, combined with sparse coding and the SVM classifier, the probabilities of the different LULC classes are inferred to build supervised feature descriptors. Finally, the CRF model, which consists of two parts: unary potential and pairwise potential, is employed to construct an LULC classification map. Experimental results show that the proposed classification scheme can achieve impressive performance when the total accuracy reached about 87%.

Naive Probability: A Mental Model Theory of Extensional Reasoning.

ERIC Educational Resources Information Center

Johnson-Laird, P. N.; Legrenzi, Paolo; Girotto, Vittorio; Legrenzi, Maria Sonino; Caverni, Jean-Paul

1999-01-01

Outlines a theory of naive probability in which individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an "extensional" way. The theory accommodates reasoning based on numerical premises, and explains how naive reasoners can infer posterior probabilities without relying on Bayes's theorem.…

Memory disorders in probable Alzheimer's disease: the role of hippocampal atrophy as shown with MRI.

PubMed Central

Deweer, B; Lehéricy, S; Pillon, B; Baulac, M; Chiras, J; Marsault, C; Agid, Y; Dubois, B

1995-01-01

Magnetic resonance based volumetric measures of hippocampal formation, amygdala (A), caudate nucleus (CN), normalised for total intracranial volume (TIV), were analysed in relation to measures of cognitive deterioration and specific features of memory functions in 18 patients with probable Alzheimer's disease. Neuropsychological examination included the mini mental state examination (MMSE), the Mattis dementia rating scale (DRS), tests of executive functions, assessment of language abilities and praxis, the Wechsler memory scale (WMS), the California verbal learning test (CVLT) and the Grober and Buschke test. The volume of the hippocampal formation (HF/TIV) was correlated with specific memory variables: memory quotient and paired associates of the WMS; intrusions and discriminability at recognition for the Grober and Buschke test. By contrast, except for intrusions, no correlations were found between memory variables and the volume of amygdala (A/TIV). No correlations were found between the volume of caudate nuclei (CN/TIV) and any neuropsychological score. The volume of the hippocampal formation was therefore selectively related to quantitative and qualitative aspects of memory performance in patients with probable Alzheimer's disease. Images PMID:7745409

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

Fixation probability on clique-based graphs

NASA Astrophysics Data System (ADS)

Choi, Jeong-Ok; Yu, Unjong

2018-02-01

The fixation probability of a mutant in the evolutionary dynamics of Moran process is calculated by the Monte-Carlo method on a few families of clique-based graphs. It is shown that the complete suppression of fixation can be realized with the generalized clique-wheel graph in the limit of small wheel-clique ratio and infinite size. The family of clique-star is an amplifier, and clique-arms graph changes from amplifier to suppressor as the fitness of the mutant increases. We demonstrate that the overall structure of a graph can be more important to determine the fixation probability than the degree or the heat heterogeneity. The dependence of the fixation probability on the position of the first mutant is discussed.

Estimating inverse probability weights using super learner when weight-model specification is unknown in a marginal structural Cox model context.

PubMed

Karim, Mohammad Ehsanul; Platt, Robert W

2017-06-15

Correct specification of the inverse probability weighting (IPW) model is necessary for consistent inference from a marginal structural Cox model (MSCM). In practical applications, researchers are typically unaware of the true specification of the weight model. Nonetheless, IPWs are commonly estimated using parametric models, such as the main-effects logistic regression model. In practice, assumptions underlying such models may not hold and data-adaptive statistical learning methods may provide an alternative. Many candidate statistical learning approaches are available in the literature. However, the optimal approach for a given dataset is impossible to predict. Super learner (SL) has been proposed as a tool for selecting an optimal learner from a set of candidates using cross-validation. In this study, we evaluate the usefulness of a SL in estimating IPW in four different MSCM simulation scenarios, in which we varied the specification of the true weight model specification (linear and/or additive). Our simulations show that, in the presence of weight model misspecification, with a rich and diverse set of candidate algorithms, SL can generally offer a better alternative to the commonly used statistical learning approaches in terms of MSE as well as the coverage probabilities of the estimated effect in an MSCM. The findings from the simulation studies guided the application of the MSCM in a multiple sclerosis cohort from British Columbia, Canada (1995-2008), to estimate the impact of beta-interferon treatment in delaying disability progression. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Dynamics of EEG functional connectivity during statistical learning.

PubMed

Tóth, Brigitta; Janacsek, Karolina; Takács, Ádám; Kóbor, Andrea; Zavecz, Zsófia; Nemeth, Dezso

2017-10-01

Statistical learning is a fundamental mechanism of the brain, which extracts and represents regularities of our environment. Statistical learning is crucial in predictive processing, and in the acquisition of perceptual, motor, cognitive, and social skills. Although previous studies have revealed competitive neurocognitive processes underlying statistical learning, the neural communication of the related brain regions (functional connectivity, FC) has not yet been investigated. The present study aimed to fill this gap by investigating FC networks that promote statistical learning in humans. Young adults (N=28) performed a statistical learning task while 128-channels EEG was acquired. The task involved probabilistic sequences, which enabled to measure incidental/implicit learning of conditional probabilities. Phase synchronization in seven frequency bands was used to quantify FC between cortical regions during the first, second, and third periods of the learning task, respectively. Here we show that statistical learning is negatively correlated with FC of the anterior brain regions in slow (theta) and fast (beta) oscillations. These negative correlations increased as the learning progressed. Our findings provide evidence that dynamic antagonist brain networks serve a hallmark of statistical learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Knotting probability of a shaken ball-chain.

PubMed

Hickford, J; Jones, R; du Pont, S Courrech; Eggers, J

2006-11-01

We study the formation of knots on a macroscopic ball chain, which is shaken on a horizontal plate at 12 times the acceleration of gravity. We find that above a certain critical length, the knotting probability is independent of chain length, while the time to shake out a knot increases rapidly with chain length. The probability of finding a knot after a certain time is the result of the balance of these two processes. In particular, the knotting probability tends to a constant for long chains.

Crash probability estimation via quantifying driver hazard perception.

PubMed

Li, Yang; Zheng, Yang; Wang, Jianqiang; Kodaka, Kenji; Li, Keqiang

2018-07-01

Crash probability estimation is an important method to predict the potential reduction of crash probability contributed by forward collision avoidance technologies (FCATs). In this study, we propose a practical approach to estimate crash probability, which combines a field operational test and numerical simulations of a typical rear-end crash model. To consider driver hazard perception characteristics, we define a novel hazard perception measure, called as driver risk response time, by considering both time-to-collision (TTC) and driver braking response to impending collision risk in a near-crash scenario. Also, we establish a driving database under mixed Chinese traffic conditions based on a CMBS (Collision Mitigation Braking Systems)-equipped vehicle. Applying the crash probability estimation in this database, we estimate the potential decrease in crash probability owing to use of CMBS. A comparison of the results with CMBS on and off shows a 13.7% reduction of crash probability in a typical rear-end near-crash scenario with a one-second delay of driver's braking response. These results indicate that CMBS is positive in collision prevention, especially in the case of inattentive drivers or ole drivers. The proposed crash probability estimation offers a practical way for evaluating the safety benefits in the design and testing of FCATs. Copyright © 2017 Elsevier Ltd. All rights reserved.

Minimal entropy probability paths between genome families.

PubMed

Ahlbrandt, Calvin; Benson, Gary; Casey, William

2004-05-01

We develop a metric for probability distributions with applications to biological sequence analysis. Our distance metric is obtained by minimizing a functional defined on the class of paths over probability measures on N categories. The underlying mathematical theory is connected to a constrained problem in the calculus of variations. The solution presented is a numerical solution, which approximates the true solution in a set of cases called rich paths where none of the components of the path is zero. The functional to be minimized is motivated by entropy considerations, reflecting the idea that nature might efficiently carry out mutations of genome sequences in such a way that the increase in entropy involved in transformation is as small as possible. We characterize sequences by frequency profiles or probability vectors, in the case of DNA where N is 4 and the components of the probability vector are the frequency of occurrence of each of the bases A, C, G and T. Given two probability vectors a and b, we define a distance function based as the infimum of path integrals of the entropy function H( p) over all admissible paths p(t), 0 < or = t< or =1, with p(t) a probability vector such that p(0)=a and p(1)=b. If the probability paths p(t) are parameterized as y(s) in terms of arc length s and the optimal path is smooth with arc length L, then smooth and "rich" optimal probability paths may be numerically estimated by a hybrid method of iterating Newton's method on solutions of a two point boundary value problem, with unknown distance L between the abscissas, for the Euler-Lagrange equations resulting from a multiplier rule for the constrained optimization problem together with linear regression to improve the arc length estimate L. Matlab code for these numerical methods is provided which works only for "rich" optimal probability vectors. These methods motivate a definition of an elementary distance function which is easier and faster to calculate, works on non

The role of probabilities in physics.

PubMed

Le Bellac, Michel

2012-09-01

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

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." (c) 2015 APA, all rights reserved).

Microstimulation of the human substantia nigra alters reinforcement learning.

PubMed

Ramayya, Ashwin G; Misra, Amrit; Baltuch, Gordon H; Kahana, Michael J

2014-05-14

Animal studies have shown that substantia nigra (SN) dopaminergic (DA) neurons strengthen action-reward associations during reinforcement learning, but their role in human learning is not known. Here, we applied microstimulation in the SN of 11 patients undergoing deep brain stimulation surgery for the treatment of Parkinson's disease as they performed a two-alternative probability learning task in which rewards were contingent on stimuli, rather than actions. Subjects demonstrated decreased learning from reward trials that were accompanied by phasic SN microstimulation compared with reward trials without stimulation. Subjects who showed large decreases in learning also showed an increased bias toward repeating actions after stimulation trials; therefore, stimulation may have decreased learning by strengthening action-reward associations rather than stimulus-reward associations. Our findings build on previous studies implicating SN DA neurons in preferentially strengthening action-reward associations during reinforcement learning. Copyright © 2014 the authors 0270-6474/14/346887-09$15.00/0.

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.)

Simulation of noisy dynamical system by Deep Learning

NASA Astrophysics Data System (ADS)

Yeo, Kyongmin

2017-11-01

Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

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.

A discussion on the origin of quantum probabilities

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

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

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

How well do elderly people cope with uncertainty in a learning task?

PubMed

Chasseigne, G; Grau, S; Mullet, E; Cama, V

1999-11-01

The relation between age, task complexity and learning performance in a Multiple Cue Probability Learning task was studied by systematically varying the level of uncertainty present in the task, keeping constant the direction of relationships. Four age groups were constituted: young adults (mean age = 21), middle-aged adults (45), elderly people (69) and very elderly people (81). Five uncertainty levels were considered: predictability = 0.96, 0.80, 0.64, 0.48, and 0.32. All relationships involved were direct ones. A strong effect of uncertainty on 'control', a measure of the subject's consistency with respect to a linear model, was found. This effect was essentially a linear one. To each decrement in predictability of the task corresponded an equal decrement in participants' level of control. This level of decrement was the same, regardless of the age of the participant. It can be concluded that elderly people cope with uncertainty in probability learning tasks as well as young adults.

The impossibility of probabilities

NASA Astrophysics Data System (ADS)

Zimmerman, Peter D.

2017-11-01

This paper discusses the problem of assigning probabilities to the likelihood of nuclear terrorism events, in particular examining the limitations of using Bayesian priors for this purpose. It suggests an alternate approach to analyzing the threat of nuclear terrorism.

Learning to play Go using recursive neural networks.

PubMed

Wu, Lin; Baldi, Pierre

2008-11-01

Go is an ancient board game that poses unique opportunities and challenges for artificial intelligence. Currently, there are no computer Go programs that can play at the level of a good human player. However, the emergence of large repositories of games is opening the door for new machine learning approaches to address this challenge. Here we develop a machine learning approach to Go, and related board games, focusing primarily on the problem of learning a good evaluation function in a scalable way. Scalability is essential at multiple levels, from the library of local tactical patterns, to the integration of patterns across the board, to the size of the board itself. The system we propose is capable of automatically learning the propensity of local patterns from a library of games. Propensity and other local tactical information are fed into recursive neural networks, derived from a probabilistic Bayesian network architecture. The recursive neural networks in turn integrate local information across the board in all four cardinal directions and produce local outputs that represent local territory ownership probabilities. The aggregation of these probabilities provides an effective strategic evaluation function that is an estimate of the expected area at the end, or at various other stages, of the game. Local area targets for training can be derived from datasets of games played by human players. In this approach, while requiring a learning time proportional to N(4), skills learned on a board of size N(2) can easily be transferred to boards of other sizes. A system trained using only 9 x 9 amateur game data performs surprisingly well on a test set derived from 19 x 19 professional game data. Possible directions for further improvements are briefly discussed.

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. (c) 2014 APA, all rights reserved.

Eruption probabilities for the Lassen Volcanic Center and regional volcanism, northern California, and probabilities for large explosive eruptions in the Cascade Range

USGS Publications Warehouse

Nathenson, Manuel; Clynne, Michael A.; Muffler, L.J. Patrick

2012-01-01

Chronologies for eruptive activity of the Lassen Volcanic Center and for eruptions from the regional mafic vents in the surrounding area of the Lassen segment of the Cascade Range are here used to estimate probabilities of future eruptions. For the regional mafic volcanism, the ages of many vents are known only within broad ranges, and two models are developed that should bracket the actual eruptive ages. These chronologies are used with exponential, Weibull, and mixed-exponential probability distributions to match the data for time intervals between eruptions. For the Lassen Volcanic Center, the probability of an eruption in the next year is 1.4x10-4 for the exponential distribution and 2.3x10-4 for the mixed exponential distribution. For the regional mafic vents, the exponential distribution gives a probability of an eruption in the next year of 6.5x10-4, but the mixed exponential distribution indicates that the current probability, 12,000 years after the last event, could be significantly lower. For the exponential distribution, the highest probability is for an eruption from a regional mafic vent. Data on areas and volumes of lava flows and domes of the Lassen Volcanic Center and of eruptions from the regional mafic vents provide constraints on the probable sizes of future eruptions. Probabilities of lava-flow coverage are similar for the Lassen Volcanic Center and for regional mafic vents, whereas the probable eruptive volumes for the mafic vents are generally smaller. Data have been compiled for large explosive eruptions (>≈ 5 km3 in deposit volume) in the Cascade Range during the past 1.2 m.y. in order to estimate probabilities of eruption. For erupted volumes >≈5 km3, the rate of occurrence since 13.6 ka is much higher than for the entire period, and we use these data to calculate the annual probability of a large eruption at 4.6x10-4. For erupted volumes ≥10 km3, the rate of occurrence has been reasonably constant from 630 ka to the present, giving

Characteristic length of the knotting probability revisited

NASA Astrophysics Data System (ADS)

Uehara, Erica; Deguchi, Tetsuo

2015-09-01

We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(-N/NK), where the estimates of parameter NK are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius rex, i.e. the screening length of double-stranded DNA.

Establishment probability in newly founded populations.

PubMed

Gusset, Markus; Müller, Michael S; Grimm, Volker

2012-06-20

Establishment success in newly founded populations relies on reaching the established phase, which is defined by characteristic fluctuations of the population's state variables. Stochastic population models can be used to quantify the establishment probability of newly founded populations; however, so far no simple but robust method for doing so existed. To determine a critical initial number of individuals that need to be released to reach the established phase, we used a novel application of the "Wissel plot", where -ln(1 - P0(t)) is plotted against time t. This plot is based on the equation P(0)t=1-c(1)e(-ω(1t)), which relates the probability of extinction by time t, P(0)(t), to two constants: c(1) describes the probability of a newly founded population to reach the established phase, whereas ω(1) describes the population's probability of extinction per short time interval once established. For illustration, we applied the method to a previously developed stochastic population model of the endangered African wild dog (Lycaon pictus). A newly founded population reaches the established phase if the intercept of the (extrapolated) linear parts of the "Wissel plot" with the y-axis, which is -ln(c(1)), is negative. For wild dogs in our model, this is the case if a critical initial number of four packs, consisting of eight individuals each, are released. The method we present to quantify the establishment probability of newly founded populations is generic and inferences thus are transferable to other systems across the field of conservation biology. In contrast to other methods, our approach disaggregates the components of a population's viability by distinguishing establishment from persistence.

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 1316.10 Food and Drugs DRUG ENFORCEMENT ADMINISTRATION, DEPARTMENT OF JUSTICE ADMINISTRATIVE FUNCTIONS, PRACTICES, AND PROCEDURES Administrative Inspections § 1316.10 Administrative probable cause. If the judge...

Neural correlates of decision making with explicit information about probabilities and incentives in elderly healthy subjects.

PubMed

Labudda, Kirsten; Woermann, Friedrich G; Mertens, Markus; Pohlmann-Eden, Bernd; Markowitsch, Hans J; Brand, Matthias

2008-06-01

Recent functional neuroimaging and lesion studies demonstrate the involvement of the orbitofrontal/ventromedial prefrontal cortex as a key structure in decision making processes. This region seems to be particularly crucial when contingencies between options and consequences are unknown but have to be learned by the use of feedback following previous decisions (decision making under ambiguity). However, little is known about the neural correlates of decision making under risk conditions in which information about probabilities and potential outcomes is given. In the present study, we used functional magnetic resonance imaging to measure blood-oxygenation-level-dependent (BOLD) responses in 12 subjects during a decision making task. This task provided explicit information about probabilities and associated potential incentives. The responses were compared to BOLD signals in a control condition without information about incentives. In contrast to previous decision making studies, we completely removed the outcome phase following a decision to exclude the potential influence of feedback previously received on current decisions. The results indicate that the integration of information about probabilities and incentives leads to activations within the dorsolateral prefrontal cortex, the posterior parietal lobe, the anterior cingulate and the right lingual gyrus. We assume that this pattern of activation is due to the involvement of executive functions, conflict detection mechanisms and arithmetic operations during the deliberation phase of decisional processes that are based on explicit information.

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.

Probability calculations for three-part mineral resource assessments

USGS Publications Warehouse

Ellefsen, Karl J.

2017-06-27

Three-part mineral resource assessment is a methodology for predicting, in a specified geographic region, both the number of undiscovered mineral deposits and the amount of mineral resources in those deposits. These predictions are based on probability calculations that are performed with computer software that is newly implemented. Compared to the previous implementation, the new implementation includes new features for the probability calculations themselves and for checks of those calculations. The development of the new implementation lead to a new understanding of the probability calculations, namely the assumptions inherent in the probability calculations. Several assumptions strongly affect the mineral resource predictions, so it is crucial that they are checked during an assessment. The evaluation of the new implementation leads to new findings about the probability calculations,namely findings regarding the precision of the computations,the computation time, and the sensitivity of the calculation results to the input.

Phonotactic Probability Effects in Children Who Stutter

PubMed Central

Anderson, Julie D.; Byrd, Courtney T.

2008-01-01

Purpose The purpose of this study was to examine the influence of phonotactic probability, the frequency of different sound segments and segment sequences, on the overall fluency with which words are produced by preschool children who stutter (CWS), as well as to determine whether it has an effect on the type of stuttered disfluency produced. Method A 500+ word language sample was obtained from 19 CWS. Each stuttered word was randomly paired with a fluently produced word that closely matched it in grammatical class, word length, familiarity, word and neighborhood frequency, and neighborhood density. Phonotactic probability values were obtained for the stuttered and fluent words from an online database. Results Phonotactic probability did not have a significant influence on the overall susceptibility of words to stuttering, but it did impact the type of stuttered disfluency produced. In specific, single-syllable word repetitions were significantly lower in phonotactic probability than fluently produced words, as well as part-word repetitions and sound prolongations. Conclusions In general, the differential impact of phonotactic probability on the type of stuttering-like disfluency produced by young CWS provides some support for the notion that different disfluency types may originate in the disruption of different levels of processing. PMID:18658056

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.

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.

Uncertainty and probability for branching selves

NASA Astrophysics Data System (ADS)

Lewis, Peter J.

Everettian accounts of quantum mechanics entail that people branch; every possible result of a measurement actually occurs, and I have one successor for each result. Is there room for probability in such an account? The prima facie answer is no; there are no ontic chances here, and no ignorance about what will happen. But since any adequate quantum mechanical theory must make probabilistic predictions, much recent philosophical labor has gone into trying to construct an account of probability for branching selves. One popular strategy involves arguing that branching selves introduce a new kind of subjective uncertainty. I argue here that the variants of this strategy in the literature all fail, either because the uncertainty is spurious, or because it is in the wrong place to yield probabilistic predictions. I conclude that uncertainty cannot be the ground for probability in Everettian quantum mechanics.

Interaction in Asynchronous Web-Based Learning Environments

ERIC Educational Resources Information Center

Woo, Younghee; Reeves, Thomas C.

2008-01-01

Because of the perceived advantages and the promotion of Web-based learning environments (WBLEs) by commercial interests as well as educational technologists, knowing how to develop and implement WBLEs will probably not be a choice, but a necessity for most educators and trainers in the future. However, many instructors still don't understand the…

Autonomous learning derived from experimental modeling of physical laws.

PubMed

Grabec, Igor

2013-05-01

This article deals with experimental description of physical laws by probability density function of measured data. The Gaussian mixture model specified by representative data and related probabilities is utilized for this purpose. The information cost function of the model is described in terms of information entropy by the sum of the estimation error and redundancy. A new method is proposed for searching the minimum of the cost function. The number of the resulting prototype data depends on the accuracy of measurement. Their adaptation resembles a self-organized, highly non-linear cooperation between neurons in an artificial NN. A prototype datum corresponds to the memorized content, while the related probability corresponds to the excitability of the neuron. The method does not include any free parameters except objectively determined accuracy of the measurement system and is therefore convenient for autonomous execution. Since representative data are generally less numerous than the measured ones, the method is applicable for a rather general and objective compression of overwhelming experimental data in automatic data-acquisition systems. Such compression is demonstrated on analytically determined random noise and measured traffic flow data. The flow over a day is described by a vector of 24 components. The set of 365 vectors measured over one year is compressed by autonomous learning to just 4 representative vectors and related probabilities. These vectors represent the flow in normal working days and weekends or holidays, while the related probabilities correspond to relative frequencies of these days. This example reveals that autonomous learning yields a new basis for interpretation of representative data and the optimal model structure. Copyright © 2012 Elsevier Ltd. All rights reserved.

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...

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.

Help-Seeking Decisions of Battered Women: A Test of Learned Helplessness and Two Stress Theories.

ERIC Educational Resources Information Center

Wauchope, Barbara A.

This study tested the learned helplessness theory, stress theory, and a modified stress theory to determine the best model for predicting the probability that a woman would seek help when she experienced severe violence from a male partner. The probability was hypothesized to increase as the stress of the violence experienced increased. Data were…

Imprecise Probability Methods for Weapons UQ

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

Picard, Richard Roy; Vander Wiel, Scott Alan

Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Quantum temporal probabilities in tunneling systems

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

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

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

Probability-based hazard avoidance guidance for planetary landing

NASA Astrophysics Data System (ADS)

Yuan, Xu; Yu, Zhengshi; Cui, Pingyuan; Xu, Rui; Zhu, Shengying; Cao, Menglong; Luan, Enjie

2018-03-01

Future landing and sample return missions on planets and small bodies will seek landing sites with high scientific value, which may be located in hazardous terrains. Autonomous landing in such hazardous terrains and highly uncertain planetary environments is particularly challenging. Onboard hazard avoidance ability is indispensable, and the algorithms must be robust to uncertainties. In this paper, a novel probability-based hazard avoidance guidance method is developed for landing in hazardous terrains on planets or small bodies. By regarding the lander state as probabilistic, the proposed guidance algorithm exploits information on the uncertainty of lander position and calculates the probability of collision with each hazard. The collision probability serves as an accurate safety index, which quantifies the impact of uncertainties on the lander safety. Based on the collision probability evaluation, the state uncertainty of the lander is explicitly taken into account in the derivation of the hazard avoidance guidance law, which contributes to enhancing the robustness to the uncertain dynamics of planetary landing. The proposed probability-based method derives fully analytic expressions and does not require off-line trajectory generation. Therefore, it is appropriate for real-time implementation. The performance of the probability-based guidance law is investigated via a set of simulations, and the effectiveness and robustness under uncertainties are demonstrated.

Introducing Disjoint and Independent Events in Probability.

ERIC Educational Resources Information Center

Kelly, I. W.; Zwiers, F. W.

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…

Preserved learning of novel information in amnesia: evidence for multiple memory systems.

PubMed

Gordon, B

1988-06-01

Four of five patients with marked global amnesia, and others with new learning impairments, showed normal processing facilitation for novel stimuli (nonwords) and/or for familiar stimuli (words) on a word/nonword (lexical) decision task. The data are interpreted as a reflection of the learning capabilities of in-line neural processing stages with multiple, distinct, informational codes. These in-line learning processes are separate from the recognition/recall memory impaired by amygdalohippocampal/dosomedial thalamic damage, but probably supplement such memory in some tasks in normal individuals. Preserved learning of novel information seems incompatible with explanations of spared learning in amnesia that are based on the episodic/semantic or memory/habit distinctions, but is consistent with the procedural/declarative hypothesis.

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. Copyright © 2015 Elsevier B.V. All rights reserved.

Skill of Ensemble Seasonal Probability Forecasts

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

On probability-possibility transformations

NASA Technical Reports Server (NTRS)

Klir, George J.; Parviz, Behzad

1992-01-01

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

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…

Attitudes and Perceptions of Medical Undergraduates Towards Mobile Learning (M-learning).

PubMed

Patil, Rakesh Narayan; Almale, Balaji D; Patil, Mrunal; Gujrathi, Amit; Dhakne-Palwe, Supriya; Patil, Anuradha R; Gosavi, Shriram

2016-10-01

found that 47 (52.2%) students had deep learning approach, 10 (11.1%) students had surface learning approach. An 80% of students had positive attitude towards M-learning and 76.7% students had perceived the importance of M-learning. A 52.2% of students were actively involved in M-learning group for learning purpose. But 57.8% students did not download (at least twice weekly) the shared reference material, 38.9% students never read and/or replied to the questions asked and 60.0% students never asked any doubts/questions related to the discussion. Students had positive attitude and perceived the importance of M-learning. But when they were provided with the opportunity, they did not show appreciable M-learning utilization. This could be because, M-learning was not implemented by all departments; also it was not the part of student's regular assessment and probably a lesser study duration.

Introducing computational thinking through hands-on projects using R with applications to calculus, probability and data analysis

NASA Astrophysics Data System (ADS)

Benakli, Nadia; Kostadinov, Boyan; Satyanarayana, Ashwin; Singh, Satyanand

2017-04-01

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data analysis. We present nine computer experiments and suggest a few more, with applications to calculus, probability and data analysis, which engage computational thinking through simulations, visualizations and data analysis. We are using the free (open-source) statistical programming language R. Our goal is to give a taste of what R offers rather than to present a comprehensive tutorial on the R language. In our experience, these kinds of interactive computer activities can be easily integrated into a smart classroom. Furthermore, these activities do tend to keep students motivated and actively engaged in the process of learning, problem solving and developing a better intuition for understanding complex mathematical concepts.

An Evaluation of the High-Probability Instruction Sequence with and without Programmed Reinforcement for Compliance with High-Probability Instructions

ERIC Educational Resources Information Center

Zuluaga, Carlos A.; Normand, Matthew P.

2008-01-01

We assessed the effects of reinforcement and no reinforcement for compliance to high-probability (high-p) instructions on compliance to low-probability (low-p) instructions using a reversal design. For both participants, compliance with the low-p instruction increased only when compliance with high-p instructions was followed by reinforcement.…

Zero field reversal probability in thermally assisted magnetization reversal

NASA Astrophysics Data System (ADS)

Prasetya, E. B.; Utari; Purnama, B.

2017-11-01

This paper discussed about zero field reversal probability in thermally assisted magnetization reversal (TAMR). Appearance of reversal probability in zero field investigated through micromagnetic simulation by solving stochastic Landau-Lifshitz-Gibert (LLG). The perpendicularly anisotropy magnetic dot of 50×50×20 nm3 is considered as single cell magnetic storage of magnetic random acces memory (MRAM). Thermally assisted magnetization reversal was performed by cooling writing process from near/almost Curie point to room temperature on 20 times runs for different randomly magnetized state. The results show that the probability reversal under zero magnetic field decreased with the increase of the energy barrier. The zero-field probability switching of 55% attained for energy barrier of 60 k B T and the reversal probability become zero noted at energy barrier of 2348 k B T. The higest zero-field switching probability of 55% attained for energy barrier of 60 k B T which corespond to magnetif field of 150 Oe for switching.

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.

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.

From Movements to Actions: Two Mechanisms for Learning Action Sequences

ERIC Educational Resources Information Center

Endress, Ansgar D.; Wood, Justin N.

2011-01-01

When other individuals move, we interpret their movements as discrete, hierarchically-organized, goal-directed actions. However, the mechanisms that integrate visible movement features into actions are poorly understood. Here, we consider two sequence learning mechanisms--transitional probability-based (TP) and position-based encoding…

Viral peptides-MHC interaction: Binding probability and distance from human peptides.

PubMed

Santoni, Daniele

2018-05-23

Identification of peptides binding to MHC class I complex can play a crucial role in retrieving potential targets able to trigger an immune response. Affinity binding of viral peptides can be estimated through effective computational methods that in the most of cases are based on machine learning approach. Achieving a better insight into peptide features that impact on the affinity binding rate is a challenging issue. In the present work we focused on 9-mer peptides of Human immunodeficiency virus type 1 and Human herpes simplex virus 1, studying their binding to MHC class I. Viral 9-mers were partitioned into different classes, where each class is characterized by how far (in terms of mutation steps) the peptides belonging to that class are from human 9-mers. Viral 9-mers were partitioned in different classes, based on the number of mutation steps they are far from human 9-mers. We showed that the overall binding probability significantly differs among classes, and it typically increases as the distance, computed in terms of number of mutation steps from the human set of 9-mers, increases. The binding probability is particularly high when considering viral 9-mers that are far from all human 9-mers more than three mutation steps. A further evidence, providing significance to those special viral peptides and suggesting a potential role they can play, comes from the analysis of their distribution along viral genomes, as it revealed they are not randomly located, but they preferentially occur in specific genes. Copyright © 2018 Elsevier B.V. All rights reserved.

Nonparametric Estimation of the Probability of Ruin.

DTIC Science & Technology

1985-02-01

MATHEMATICS RESEARCH CENTER I E N FREES FEB 85 MRC/TSR...in NONPARAMETRIC ESTIMATION OF THE PROBABILITY OF RUIN Lf Edward W. Frees * Mathematics Research Center University of Wisconsin-Madison 610 Walnut...34 - .. --- - • ’. - -:- - - ..- . . .- -- .-.-. . -. . .- •. . - . . - . . .’ . ’- - .. -’vi . .-" "-- -" ,’- UNIVERSITY OF WISCONSIN-MADISON MATHEMATICS RESEARCH CENTER NONPARAMETRIC ESTIMATION OF THE PROBABILITY

The left hemisphere learns what is right: Hemispatial reward learning depends on reinforcement learning processes in the contralateral hemisphere.

PubMed

Aberg, Kristoffer Carl; Doell, Kimberly Crystal; Schwartz, Sophie

2016-08-01

Orienting biases refer to consistent, trait-like direction of attention or locomotion toward one side of space. Recent studies suggest that such hemispatial biases may determine how well people memorize information presented in the left or right hemifield. Moreover, lesion studies indicate that learning rewarded stimuli in one hemispace depends on the integrity of the contralateral striatum. However, the exact neural and computational mechanisms underlying the influence of individual orienting biases on reward learning remain unclear. Because reward-based behavioural adaptation depends on the dopaminergic system and prediction error (PE) encoding in the ventral striatum, we hypothesized that hemispheric asymmetries in dopamine (DA) function may determine individual spatial biases in reward learning. To test this prediction, we acquired fMRI in 33 healthy human participants while they performed a lateralized reward task. Learning differences between hemispaces were assessed by presenting stimuli, assigned to different reward probabilities, to the left or right of central fixation, i.e. presented in the left or right visual hemifield. Hemispheric differences in DA function were estimated through differential fMRI responses to positive vs. negative feedback in the left vs. right ventral striatum, and a computational approach was used to identify the neural correlates of PEs. Our results show that spatial biases favoring reward learning in the right (vs. left) hemifield were associated with increased reward responses in the left hemisphere and relatively better neural encoding of PEs for stimuli presented in the right (vs. left) hemifield. These findings demonstrate that trait-like spatial biases implicate hemisphere-specific learning mechanisms, with individual differences between hemispheres contributing to reinforcing spatial biases. Copyright © 2016 Elsevier Ltd. All rights reserved.

Public attitudes toward stuttering in Turkey: probability versus convenience sampling.

PubMed

Ozdemir, R Sertan; St Louis, Kenneth O; Topbaş, Seyhun

2011-12-01

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. A convenience sample of adults in Eskişehir, Turkey was compared with two replicates of a school-based, probability cluster sampling scheme. The two replicates of the probability sampling scheme yielded similar demographic samples, both of which were different from the convenience sample. Components of subscores on the POSHA-S were significantly different in more than half of the comparisons between convenience and probability samples, indicating important differences in public attitudes. If POSHA-S users intend to generalize to specific geographic areas, results of this study indicate that probability sampling is a better research strategy than convenience sampling. The reader will be able to: (1) discuss the difference between convenience sampling and probability sampling; (2) describe a school-based probability sampling scheme; and (3) describe differences in POSHA-S results from convenience sampling versus probability sampling. Copyright © 2011 Elsevier Inc. All rights reserved.

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.

The nature of the language input affects brain activation during learning from a natural language

PubMed Central

Plante, Elena; Patterson, Dianne; Gómez, Rebecca; Almryde, Kyle R.; White, Milo G.; Asbjørnsen, Arve E.

2015-01-01

Artificial language studies have demonstrated that learners are able to segment individual word-like units from running speech using the transitional probability information. However, this skill has rarely been examined in the context of natural languages, where stimulus parameters can be quite different. In this study, two groups of English-speaking learners were exposed to Norwegian sentences over the course of three fMRI scans. One group was provided with input in which transitional probabilities predicted the presence of target words in the sentences. This group quickly learned to identify the target words and fMRI data revealed an extensive and highly dynamic learning network. These results were markedly different from activation seen for a second group of participants. This group was provided with highly similar input that was modified so that word learning based on syllable co-occurrences was not possible. These participants showed a much more restricted network. The results demonstrate that the nature of the input strongly influenced the nature of the network that learners employ to learn the properties of words in a natural language. PMID:26257471

Machine Learning Principles Can Improve Hip Fracture Prediction.

PubMed

Kruse, Christian; Eiken, Pia; Vestergaard, Peter

2017-04-01

Apply machine learning principles to predict hip fractures and estimate predictor importance in Dual-energy X-ray absorptiometry (DXA)-scanned men and women. Dual-energy X-ray absorptiometry data from two Danish regions between 1996 and 2006 were combined with national Danish patient data to comprise 4722 women and 717 men with 5 years of follow-up time (original cohort n = 6606 men and women). Twenty-four statistical models were built on 75% of data points through k-5, 5-repeat cross-validation, and then validated on the remaining 25% of data points to calculate area under the curve (AUC) and calibrate probability estimates. The best models were retrained with restricted predictor subsets to estimate the best subsets. For women, bootstrap aggregated flexible discriminant analysis ("bagFDA") performed best with a test AUC of 0.92 [0.89; 0.94] and well-calibrated probabilities following Naïve Bayes adjustments. A "bagFDA" model limited to 11 predictors (among them bone mineral densities (BMD), biochemical glucose measurements, general practitioner and dentist use) achieved a test AUC of 0.91 [0.88; 0.93]. For men, eXtreme Gradient Boosting ("xgbTree") performed best with a test AUC of 0.89 [0.82; 0.95], but with poor calibration in higher probabilities. A ten predictor subset (BMD, biochemical cholesterol and liver function tests, penicillin use and osteoarthritis diagnoses) achieved a test AUC of 0.86 [0.78; 0.94] using an "xgbTree" model. Machine learning can improve hip fracture prediction beyond logistic regression using ensemble models. Compiling data from international cohorts of longer follow-up and performing similar machine learning procedures has the potential to further improve discrimination and calibration.

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

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

Korhonen, Marko; Lee, Eunghyun

2014-01-15

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

Switching probability of all-perpendicular spin valve nanopillars

NASA Astrophysics Data System (ADS)

Tzoufras, M.

2018-05-01

In all-perpendicular spin valve nanopillars the probability density of the free-layer magnetization is independent of the azimuthal angle and its evolution equation simplifies considerably compared to the general, nonaxisymmetric geometry. Expansion of the time-dependent probability density to Legendre polynomials enables analytical integration of the evolution equation and yields a compact expression for the practically relevant switching probability. This approach is valid when the free layer behaves as a single-domain magnetic particle and it can be readily applied to fitting experimental data.

Linking sounds to meanings: infant statistical learning in a natural language.

PubMed

Hay, Jessica F; Pelucchi, Bruna; Graf Estes, Katharine; Saffran, Jenny R

2011-09-01

The processes of infant word segmentation and infant word learning have largely been studied separately. However, the ease with which potential word forms are segmented from fluent speech seems likely to influence subsequent mappings between words and their referents. To explore this process, we tested the link between the statistical coherence of sequences presented in fluent speech and infants' subsequent use of those sequences as labels for novel objects. Notably, the materials were drawn from a natural language unfamiliar to the infants (Italian). The results of three experiments suggest that there is a close relationship between the statistics of the speech stream and subsequent mapping of labels to referents. Mapping was facilitated when the labels contained high transitional probabilities in the forward and/or backward direction (Experiment 1). When no transitional probability information was available (Experiment 2), or when the internal transitional probabilities of the labels were low in both directions (Experiment 3), infants failed to link the labels to their referents. Word learning appears to be strongly influenced by infants' prior experience with the distribution of sounds that make up words in natural languages. Copyright © 2011 Elsevier Inc. All rights reserved.

Probability versus representativeness in infancy: can infants use naïve physics to adjust population base rates in probabilistic inference?

PubMed

Denison, Stephanie; Trikutam, Pallavi; Xu, Fei

2014-08-01

A rich tradition in developmental psychology explores physical reasoning in infancy. However, no research to date has investigated whether infants can reason about physical objects that behave probabilistically, rather than deterministically. Physical events are often quite variable, in that similar-looking objects can be placed in similar contexts with different outcomes. Can infants rapidly acquire probabilistic physical knowledge, such as some leaves fall and some glasses break by simply observing the statistical regularity with which objects behave and apply that knowledge in subsequent reasoning? We taught 11-month-old infants physical constraints on objects and asked them to reason about the probability of different outcomes when objects were drawn from a large distribution. Infants could have reasoned either by using the perceptual similarity between the samples and larger distributions or by applying physical rules to adjust base rates and estimate the probabilities. Infants learned the physical constraints quickly and used them to estimate probabilities, rather than relying on similarity, a version of the representativeness heuristic. These results indicate that infants can rapidly and flexibly acquire physical knowledge about objects following very brief exposure and apply it in subsequent reasoning. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Transition probabilities of Br II

NASA Technical Reports Server (NTRS)

Bengtson, R. D.; Miller, M. H.

1976-01-01

Absolute transition probabilities of the three most prominent visible Br II lines are measured in emission. Results compare well with Coulomb approximations and with line strengths extrapolated from trends in homologous atoms.

Estimation of post-test probabilities by residents: Bayesian reasoning versus heuristics?

PubMed

Hall, Stacey; Phang, Sen Han; Schaefer, Jeffrey P; Ghali, William; Wright, Bruce; McLaughlin, Kevin

2014-08-01

Although the process of diagnosing invariably begins with a heuristic, we encourage our learners to support their diagnoses by analytical cognitive processes, such as Bayesian reasoning, in an attempt to mitigate the effects of heuristics on diagnosing. There are, however, limited data on the use ± impact of Bayesian reasoning on the accuracy of disease probability estimates. In this study our objective was to explore whether Internal Medicine residents use a Bayesian process to estimate disease probabilities by comparing their disease probability estimates to literature-derived Bayesian post-test probabilities. We gave 35 Internal Medicine residents four clinical vignettes in the form of a referral letter and asked them to estimate the post-test probability of the target condition in each case. We then compared these to literature-derived probabilities. For each vignette the estimated probability was significantly different from the literature-derived probability. For the two cases with low literature-derived probability our participants significantly overestimated the probability of these target conditions being the correct diagnosis, whereas for the two cases with high literature-derived probability the estimated probability was significantly lower than the calculated value. Our results suggest that residents generate inaccurate post-test probability estimates. Possible explanations for this include ineffective application of Bayesian reasoning, attribute substitution whereby a complex cognitive task is replaced by an easier one (e.g., a heuristic), or systematic rater bias, such as central tendency bias. Further studies are needed to identify the reasons for inaccuracy of disease probability estimates and to explore ways of improving accuracy.

Survival probabilities at spherical frontiers.

PubMed

Lavrentovich, Maxim O; Nelson, David R

2015-06-01

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: R(t) = R0(1 + t/t(∗))Θ, where Θ is a growth exponent, R0 is the initial radius, and t(∗) is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters t(∗) and Θ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary Θ. We compare our results to simulations of linearly inflating expansions (Θ = 1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations (Θ = 0, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" (Θ = 1/2) expansions. Copyright © 2015 Elsevier Inc. All rights reserved.

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…

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.

Dynamic Influence of Emotional States on Novel Word Learning

PubMed Central

Guo, Jingjing; Zou, Tiantian; Peng, Danling

2018-01-01

Many researchers realize that it's unrealistic to isolate language learning and processing from emotions. However, few studies on language learning have taken emotions into consideration so far, so that the probable influences of emotions on language learning are unclear. The current study thereby aimed to examine the effects of emotional states on novel word learning and their dynamic changes with learning continuing and task varying. Positive, negative or neutral pictures were employed to induce a given emotional state, and then participants learned the novel words through association with line-drawing pictures in four successive learning phases. At the end of each learning phase, participants were instructed to fulfill a semantic category judgment task (in Experiment 1) or a word-picture semantic consistency judgment task (in Experiment 2) to explore the effects of emotional states on different depths of word learning. Converging results demonstrated that negative emotional state led to worse performance compared with neutral condition; however, how positive emotional state affected learning varied with learning task. Specifically, a facilitative role of positive emotional state in semantic category learning was observed but disappeared in word specific meaning learning. Moreover, the emotional modulation on novel word learning was quite dynamic and changeable with learning continuing, and the final attainment of the learned words tended to be similar under different emotional states. The findings suggest that the impact of emotion can be offset when novel words became more and more familiar and a part of existent lexicon. PMID:29695994

Dynamic Influence of Emotional States on Novel Word Learning.

PubMed

Guo, Jingjing; Zou, Tiantian; Peng, Danling

2018-01-01

Many researchers realize that it's unrealistic to isolate language learning and processing from emotions. However, few studies on language learning have taken emotions into consideration so far, so that the probable influences of emotions on language learning are unclear. The current study thereby aimed to examine the effects of emotional states on novel word learning and their dynamic changes with learning continuing and task varying. Positive, negative or neutral pictures were employed to induce a given emotional state, and then participants learned the novel words through association with line-drawing pictures in four successive learning phases. At the end of each learning phase, participants were instructed to fulfill a semantic category judgment task (in Experiment 1) or a word-picture semantic consistency judgment task (in Experiment 2) to explore the effects of emotional states on different depths of word learning. Converging results demonstrated that negative emotional state led to worse performance compared with neutral condition; however, how positive emotional state affected learning varied with learning task. Specifically, a facilitative role of positive emotional state in semantic category learning was observed but disappeared in word specific meaning learning. Moreover, the emotional modulation on novel word learning was quite dynamic and changeable with learning continuing, and the final attainment of the learned words tended to be similar under different emotional states. The findings suggest that the impact of emotion can be offset when novel words became more and more familiar and a part of existent lexicon.

Strengthening the Student Toolbox: Study Strategies to Boost Learning

ERIC Educational Resources Information Center

Dunlosky, John

2013-01-01

Before the "big test" did you use the following study strategies: highlighting, rereading, and cramming? As students many of us probably did, yet research shows that while these three strategies are commonly used, they have been ineffective in retaining information. Learning strategies have been discussed in almost every textbook on…

Theoretical Analysis of Rain Attenuation Probability

NASA Astrophysics Data System (ADS)

Roy, Surendra Kr.; Jha, Santosh Kr.; Jha, Lallan

2007-07-01

Satellite communication technologies are now highly developed and high quality, distance-independent services have expanded over a very wide area. As for the system design of the Hokkaido integrated telecommunications(HIT) network, it must first overcome outages of satellite links due to rain attenuation in ka frequency bands. In this paper theoretical analysis of rain attenuation probability on a slant path has been made. The formula proposed is based Weibull distribution and incorporates recent ITU-R recommendations concerning the necessary rain rates and rain heights inputs. The error behaviour of the model was tested with the loading rain attenuation prediction model recommended by ITU-R for large number of experiments at different probability levels. The novel slant path rain attenuastion prediction model compared to the ITU-R one exhibits a similar behaviour at low time percentages and a better root-mean-square error performance for probability levels above 0.02%. The set of presented models exhibits the advantage of implementation with little complexity and is considered useful for educational and back of the envelope computations.

Probability Quantization for Multiplication-Free Binary Arithmetic Coding

NASA Technical Reports Server (NTRS)

Cheung, K. -M.

1995-01-01

A method has been developed to improve on Witten's binary arithmetic coding procedure of tracking a high value and a low value. The new method approximates the probability of the less probable symbol, which improves the worst-case coding efficiency.

Feature Discovery by Competitive Learning.

DTIC Science & Technology

1984-06-01

Probably the first such attempt occurred in 1951 when Dean Edmonds and Marvin Minsky built their learning machine. The flavor of this machine and...Bernstein, J. (1961). Profiles: Al, Marvin Minsky . The New Yorker. 57, 50-126. Bienenstock, E. L., Cooper, L. N., & Munro, P. W. (1982). Theory for the...This machine actually worked and was so fascinating to watch that Minsky remembers: We sort of quit science for awhile to watch the machine. We were

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)

Attitudes and Perceptions of Medical Undergraduates Towards Mobile Learning (M-learning)

PubMed Central

Almale, Balaji D; Patil, Mrunal; Gujrathi, Amit; Dhakne-Palwe, Supriya; Patil, Anuradha R; Gosavi, Shriram

2016-01-01

of M-learning was also studied. Results It was found that 47 (52.2%) students had deep learning approach, 10 (11.1%) students had surface learning approach. An 80% of students had positive attitude towards M-learning and 76.7% students had perceived the importance of M-learning. A 52.2% of students were actively involved in M-learning group for learning purpose. But 57.8% students did not download (at least twice weekly) the shared reference material, 38.9% students never read and/or replied to the questions asked and 60.0% students never asked any doubts/questions related to the discussion. Conclusion Students had positive attitude and perceived the importance of M-learning. But when they were provided with the opportunity, they did not show appreciable M-learning utilization. This could be because, M-learning was not implemented by all departments; also it was not the part of student’s regular assessment and probably a lesser study duration. PMID:27891356

Explosion probability of unexploded ordnance: expert beliefs.

PubMed

MacDonald, Jacqueline Anne; Small, Mitchell J; Morgan, M G

2008-08-01

This article reports on a study to quantify expert beliefs about the explosion probability of unexploded ordnance (UXO). Some 1,976 sites at closed military bases in the United States are contaminated with UXO and are slated for cleanup, at an estimated cost of $15-140 billion. Because no available technology can guarantee 100% removal of UXO, information about explosion probability is needed to assess the residual risks of civilian reuse of closed military bases and to make decisions about how much to invest in cleanup. This study elicited probability distributions for the chance of UXO explosion from 25 experts in explosive ordnance disposal, all of whom have had field experience in UXO identification and deactivation. The study considered six different scenarios: three different types of UXO handled in two different ways (one involving children and the other involving construction workers). We also asked the experts to rank by sensitivity to explosion 20 different kinds of UXO found at a case study site at Fort Ord, California. We found that the experts do not agree about the probability of UXO explosion, with significant differences among experts in their mean estimates of explosion probabilities and in the amount of uncertainty that they express in their estimates. In three of the six scenarios, the divergence was so great that the average of all the expert probability distributions was statistically indistinguishable from a uniform (0, 1) distribution-suggesting that the sum of expert opinion provides no information at all about the explosion risk. The experts' opinions on the relative sensitivity to explosion of the 20 UXO items also diverged. The average correlation between rankings of any pair of experts was 0.41, which, statistically, is barely significant (p= 0.049) at the 95% confidence level. Thus, one expert's rankings provide little predictive information about another's rankings. The lack of consensus among experts suggests that empirical studies

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…

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

SureTrak Probability of Impact Display

NASA Technical Reports Server (NTRS)

Elliott, John

2012-01-01

The SureTrak Probability of Impact Display software was developed for use during rocket launch operations. The software displays probability of impact information for each ship near the hazardous area during the time immediately preceding the launch of an unguided vehicle. Wallops range safety officers need to be sure that the risk to humans is below a certain threshold during each use of the Wallops Flight Facility Launch Range. Under the variable conditions that can exist at launch time, the decision to launch must be made in a timely manner to ensure a successful mission while not exceeding those risk criteria. Range safety officers need a tool that can give them the needed probability of impact information quickly, and in a format that is clearly understandable. This application is meant to fill that need. The software is a reuse of part of software developed for an earlier project: Ship Surveillance Software System (S4). The S4 project was written in C++ using Microsoft Visual Studio 6. The data structures and dialog templates from it were copied into a new application that calls the implementation of the algorithms from S4 and displays the results as needed. In the S4 software, the list of ships in the area was received from one local radar interface and from operators who entered the ship information manually. The SureTrak Probability of Impact Display application receives ship data from two local radars as well as the SureTrak system, eliminating the need for manual data entry.

Diverse strategy-learning styles promote cooperation in evolutionary spatial prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Liu, Run-Ran; Jia, Chun-Xiao; Rong, Zhihai

2015-11-01

Observational learning and practice learning are two important learning styles and play important roles in our information acquisition. In this paper, we study a spacial evolutionary prisoner's dilemma game, where players can choose the observational learning rule or the practice learning rule when updating their strategies. In the proposed model, we use a parameter p controlling the preference of players choosing the observational learning rule, and found that there exists an optimal value of p leading to the highest cooperation level, which indicates that the cooperation can be promoted by these two learning rules collaboratively and one single learning rule is not favor the promotion of cooperation. By analysing the dynamical behavior of the system, we find that the observational learning rule can make the players residing on cooperative clusters more easily realize the bad sequence of mutual defection. However, a too high observational learning probability suppresses the players to form compact cooperative clusters. Our results highlight the importance of a strategy-updating rule, more importantly, the observational learning rule in the evolutionary cooperation.

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. © 2015 The Author(s).

Fast adaptation of the internal model of gravity for manual interceptions: evidence for event-dependent learning.

PubMed

Zago, Myrka; Bosco, Gianfranco; Maffei, Vincenzo; Iosa, Marco; Ivanenko, Yuri P; Lacquaniti, Francesco

2005-02-01

We studied how subjects learn to deal with two conflicting sensory environments as a function of the probability of each environment and the temporal distance between repeated events. Subjects were asked to intercept a visual target moving downward on a screen with randomized laws of motion. We compared five protocols that differed in the probability of constant speed (0g) targets and accelerated (1g) targets. Probability ranged from 9 to 100%, and the time interval between consecutive repetitions of the same target ranged from about 1 to 20 min. We found that subjects systematically timed their responses consistent with the assumption of gravity effects, for both 1 and 0g trials. With training, subjects rapidly adapted to 0g targets by shifting the time of motor activation. Surprisingly, the adaptation rate was independent of both the probability of 0g targets and their temporal distance. Very few 0g trials sporadically interspersed as catch trials during immersive practice with 1g trials were sufficient for learning and consolidation in long-term memory, as verified by retesting after 24 h. We argue that the memory store for adapted states of the internal gravity model is triggered by individual events and can be sustained for prolonged periods of time separating sporadic repetitions. This form of event-related learning could depend on multiple-stage memory, with exponential rise and decay in the initial stages followed by a sample-and-hold module.

Development, direction, and damage limitation: social learning in domestic fowl.

PubMed

Nicol, Christine J

2004-02-01

This review highlights two areas of particular interest in the study of social learning in fowl. First, the role of social learning in the development of feeding and foraging behavior in young chicks and older birds is described. The role of the hen as a demonstrator and possible teacher is considered, and the subsequent social influence of brood mates and other companions on food avoidance and food preference learning is discussed. Second, the way in which work on domestic fowl has contributed to an understanding of the importance of directed social learning is examined. The well-characterized hierarchical social organization of small chicken flocks has been used to design studies which demonstrate that the probability of social transmission is strongly influenced by social relationships between birds. The practical implications of understanding the role of social learning in the spread of injurious behaviors in this economically important species are briefly considered.

Hydrogeologic unit flow characterization using transition probability geostatistics.

PubMed

Jones, Norman L; Walker, Justin R; Carle, Steven F

2005-01-01

This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has some advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upward sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids and/or grids with nonuniform cell thicknesses.

Assessing the effectiveness of a hybrid-flipped model of learning on fluid mechanics instruction: overall course performance, homework, and far- and near-transfer of learning

NASA Astrophysics Data System (ADS)

Harrison, David J.; Saito, Laurel; Markee, Nancy; Herzog, Serge

2017-11-01

To examine the impact of a hybrid-flipped model utilising active learning techniques, the researchers inverted one section of an undergraduate fluid mechanics course, reduced seat time, and engaged in active learning sessions in the classroom. We compared this model to the traditional section on four performance measures. We employed a propensity score method entailing a two-stage regression analysis that considered eight covariates to address the potential bias of treatment selection. First, we estimated the probability score based on the eight covariates, and second, we used the inverse of the probability score as a regression weight on the performance of learners who did not select into the hybrid course. Results suggest that enrolment in the hybrid-flipped section had a marginally significant negative impact on the total course score and a significant negative impact on homework performance, possibly because of poor video usage by the hybrid-flipped learners. Suggested considerations are also discussed.

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…

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 with...

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 with...

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 with...

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 with...

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 with...

Oil spill contamination probability in the southeastern Levantine basin.

PubMed

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

2015-02-15

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

Collision probability at low altitudes resulting from elliptical orbits

NASA Technical Reports Server (NTRS)

Kessler, Donald J.

1990-01-01

The probability of collision between a spacecraft and another object is calculated for various altitude and orbit conditions, and factors affecting the probability are discussed. It is shown that a collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object and that the probability per unit time is largest when the orbit of the object is nearly circular. However, at low altitudes, the atmospheric drag causes changes with time of the perigee and the apogee, such that circular orbits have a much shorter lifetime than many of the elliptical orbits. Thus, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have much higher total collision probability than circular orbits. Rocket bodies used to boost payloads from low earth orbit to geosynchronous orbit are an example of objects in these elliptical orbits.

Macaque monkeys can learn token values from human models through vicarious reward.

PubMed

Bevacqua, Sara; Cerasti, Erika; Falcone, Rossella; Cervelloni, Milena; Brunamonti, Emiliano; Ferraina, Stefano; Genovesio, Aldo

2013-01-01

Monkeys can learn the symbolic meaning of tokens, and exchange them to get a reward. Monkeys can also learn the symbolic value of a token by observing conspecifics but it is not clear if they can learn passively by observing other actors, e.g., humans. To answer this question, we tested two monkeys in a token exchange paradigm in three experiments. Monkeys learned token values through observation of human models exchanging them. We used, after a phase of object familiarization, different sets of tokens. One token of each set was rewarded with a bit of apple. Other tokens had zero value (neutral tokens). Each token was presented only in one set. During the observation phase, monkeys watched the human model exchange tokens and watched them consume rewards (vicarious rewards). In the test phase, the monkeys were asked to exchange one of the tokens for food reward. Sets of three tokens were used in the first experiment and sets of two tokens were used in the second and third experiments. The valuable token was presented with different probabilities in the observation phase during the first and second experiments in which the monkeys exchanged the valuable token more frequently than any of the neutral tokens. The third experiments examined the effect of unequal probabilities. Our results support the view that monkeys can learn from non-conspecific actors through vicarious reward, even a symbolic task like the token-exchange task.

On the asymptotic improvement of supervised learning by utilizing additional unlabeled samples - Normal mixture density case

NASA Technical Reports Server (NTRS)

Shahshahani, Behzad M.; Landgrebe, David A.

1992-01-01

The effect of additional unlabeled samples in improving the supervised learning process is studied in this paper. Three learning processes. supervised, unsupervised, and combined supervised-unsupervised, are compared by studying the asymptotic behavior of the estimates obtained under each process. Upper and lower bounds on the asymptotic covariance matrices are derived. It is shown that under a normal mixture density assumption for the probability density function of the feature space, the combined supervised-unsupervised learning is always superior to the supervised learning in achieving better estimates. Experimental results are provided to verify the theoretical concepts.

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.

Does my high blood pressure improve your survival? Overall and subgroup learning curves in health.

PubMed

Van Gestel, Raf; Müller, Tobias; Bosmans, Johan

2017-09-01

Learning curves in health are of interest for a wide range of medical disciplines, healthcare providers, and policy makers. In this paper, we distinguish between three types of learning when identifying overall learning curves: economies of scale, learning from cumulative experience, and human capital depreciation. In addition, we approach the question of how treating more patients with specific characteristics predicts provider performance. To soften collinearity problems, we explore the use of least absolute shrinkage and selection operator regression as a variable selection method and Theil-Goldberger mixed estimation to augment the available information. We use data from the Belgian Transcatheter Aorta Valve Implantation (TAVI) registry, containing information on the first 860 TAVI procedures in Belgium. We find that treating an additional TAVI patient is associated with an increase in the probability of 2-year survival by about 0.16%-points. For adverse events like renal failure and stroke, we find that an extra day between procedures is associated with an increase in the probability for these events by 0.12%-points and 0.07%-points, respectively. Furthermore, we find evidence for positive learning effects from physicians' experience with defibrillation, treating patients with hypertension, and the use of certain types of replacement valves during the TAVI procedure. Copyright © 2017 John Wiley & Sons, Ltd.

Fast and Epsilon-Optimal Discretized Pursuit Learning Automata.

PubMed

Zhang, JunQi; Wang, Cheng; Zhou, MengChu

2015-10-01

Learning automata (LA) are powerful tools for reinforcement learning. A discretized pursuit LA is the most popular one among them. During an iteration its operation consists of three basic phases: 1) selecting the next action; 2) finding the optimal estimated action; and 3) updating the state probability. However, when the number of actions is large, the learning becomes extremely slow because there are too many updates to be made at each iteration. The increased updates are mostly from phases 1 and 3. A new fast discretized pursuit LA with assured ε -optimality is proposed to perform both phases 1 and 3 with the computational complexity independent of the number of actions. Apart from its low computational complexity, it achieves faster convergence speed than the classical one when operating in stationary environments. This paper can promote the applications of LA toward the large-scale-action oriented area that requires efficient reinforcement learning tools with assured ε -optimality, fast convergence speed, and low computational complexity for each iteration.

A collision probability analysis of the double-heterogeneity problem

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

Hebert, A.

1993-10-01

A practical collision probability model is presented for the description of geometries with many levels of heterogeneity. Regular regions of the macrogeometry are assumed to contain a stochastic mixture of spherical grains or cylindrical tubes. Simple expressions for the collision probabilities in the global geometry are obtained as a function of the collision probabilities in the macro- and microgeometries. This model was successfully implemented in the collision probability kernel of the APOLLO-1, APOLLO-2, and DRAGON lattice codes for the description of a broad range of reactor physics problems. Resonance self-shielding and depletion calculations in the microgeometries are possible because eachmore » microregion is explicitly represented.« less

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…

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…

Reinforcement Probability Modulates Temporal Memory Selection and Integration Processes

PubMed Central

Matell, Matthew S.; Kurti, Allison N.

2013-01-01

We have previously shown that rats trained in a mixed-interval peak procedure (tone = 4s, light = 12s) respond in a scalar manner at a time in between the trained peak times when presented with the stimulus compound (Swanton & Matell, 2011). In our previous work, the two component cues were reinforced with different probabilities (short = 20%, long = 80%) to equate response rates, and we found that the compound peak time was biased toward the cue with the higher reinforcement probability. Here, we examined the influence that different reinforcement probabilities have on the temporal location and shape of the compound response function. We found that the time of peak responding shifted as a function of the relative reinforcement probability of the component cues, becoming earlier as the relative likelihood of reinforcement associated with the short cue increased. However, as the relative probabilities of the component cues grew dissimilar, the compound peak became non-scalar, suggesting that the temporal control of behavior shifted from a process of integration to one of selection. As our previous work has utilized durations and reinforcement probabilities more discrepant than those used here, these data suggest that the processes underlying the integration/selection decision for time are based on cue value. PMID:23896560

Probability Elicitation Under Severe Time Pressure: A Rank-Based Method.

PubMed

Jaspersen, Johannes G; Montibeller, Gilberto

2015-07-01

Probability elicitation protocols are used to assess and incorporate subjective probabilities in risk and decision analysis. While most of these protocols use methods that have focused on the precision of the elicited probabilities, the speed of the elicitation process has often been neglected. However, speed is also important, particularly when experts need to examine a large number of events on a recurrent basis. Furthermore, most existing elicitation methods are numerical in nature, but there are various reasons why an expert would refuse to give such precise ratio-scale estimates, even if highly numerate. This may occur, for instance, when there is lack of sufficient hard evidence, when assessing very uncertain events (such as emergent threats), or when dealing with politicized topics (such as terrorism or disease outbreaks). In this article, we adopt an ordinal ranking approach from multicriteria decision analysis to provide a fast and nonnumerical probability elicitation process. Probabilities are subsequently approximated from the ranking by an algorithm based on the principle of maximum entropy, a rule compatible with the ordinal information provided by the expert. The method can elicit probabilities for a wide range of different event types, including new ways of eliciting probabilities for stochastically independent events and low-probability events. We use a Monte Carlo simulation to test the accuracy of the approximated probabilities and try the method in practice, applying it to a real-world risk analysis recently conducted for DEFRA (the U.K. Department for the Environment, Farming and Rural Affairs): the prioritization of animal health threats. © 2015 Society for Risk Analysis.

Cytologic diagnosis: expression of probability by clinical pathologists.

PubMed

Christopher, Mary M; Hotz, Christine S

2004-01-01

Clinical pathologists use descriptive terms or modifiers to express the probability or likelihood of a cytologic diagnosis. Words are imprecise in meaning, however, and may be used and interpreted differently by pathologists and clinicians. The goals of this study were to 1) assess the frequency of use of 18 modifiers, 2) determine the probability of a positive diagnosis implied by the modifiers, 3) identify preferred modifiers for different levels of probability, 4) ascertain the importance of factors that affect expression of diagnostic certainty, and 5) evaluate differences based on gender, employment, and experience. We surveyed 202 clinical pathologists who were board-certified by the American College of Veterinary Pathologists (Clinical Pathology). Surveys were distributed in October 2001 and returned by e-mail, fax, or surface mail over a 2-month period. Results were analyzed by parametric and nonparametric tests. Survey response rate was 47.5% (n = 96) and primarily included clinical pathologists at veterinary schools (n = 58) and diagnostic laboratories (n = 31). Eleven of 18 terms were used "often" or "sometimes" by >/= 50% of respondents. Broad variability was found in the probability assigned to each term, especially those with median values of 75 to 90%. Preferred modifiers for 7 numerical probabilities ranging from 0 to 100% included 68 unique terms; however, a set of 10 terms was used by >/= 50% of respondents. Cellularity and quality of the sample, experience of the pathologist, and implications of the diagnosis were the most important factors affecting the expression of probability. Because of wide discrepancy in the implied likelihood of a diagnosis using words, defined terminology and controlled vocabulary may be useful in improving communication and the quality of data in cytology reporting.

High probability neurotransmitter release sites represent an energy efficient design

PubMed Central

Lu, Zhongmin; Chouhan, Amit K.; Borycz, Jolanta A.; Lu, Zhiyuan; Rossano, Adam J; Brain, Keith L.; Zhou, You; Meinertzhagen, Ian A.; Macleod, Gregory T.

2016-01-01

Nerve terminals contain multiple sites specialized for the release of neurotransmitters. Release usually occurs with low probability, a design thought to confer many advantages. High probability release sites are not uncommon but their advantages are not well understood. Here we test the hypothesis that high probability release sites represent an energy efficient design. We examined release site probabilities and energy efficiency at the terminals of two glutamatergic motor neurons synapsing on the same muscle fiber in Drosophila larvae. Through electrophysiological and ultrastructural measurements we calculated release site probabilities to differ considerably between terminals (0.33 vs. 0.11). We estimated the energy required to release and recycle glutamate from the same measurements. The energy required to remove calcium and sodium ions subsequent to nerve excitation was estimated through microfluorimetric and morphological measurements. We calculated energy efficiency as the number of glutamate molecules released per ATP molecule hydrolyzed, and high probability release site terminals were found to be more efficient (0.13 vs. 0.06). Our analytical model indicates that energy efficiency is optimal (~0.15) at high release site probabilities (~0.76). As limitations in energy supply constrain neural function, high probability release sites might ameliorate such constraints by demanding less energy. Energy efficiency can be viewed as one aspect of nerve terminal function, in balance with others, because high efficiency terminals depress significantly during episodic bursts of activity. PMID:27593375

BELM: Bayesian extreme learning machine.

PubMed

Soria-Olivas, Emilio; Gómez-Sanchis, Juan; Martín, José D; Vila-Francés, Joan; Martínez, Marcelino; Magdalena, José R; Serrano, Antonio J

2011-03-01

The theory of extreme learning machine (ELM) has become very popular on the last few years. ELM is a new approach for learning the parameters of the hidden layers of a multilayer neural network (as the multilayer perceptron or the radial basis function neural network). Its main advantage is the lower computational cost, which is especially relevant when dealing with many patterns defined in a high-dimensional space. This brief proposes a bayesian approach to ELM, which presents some advantages over other approaches: it allows the introduction of a priori knowledge; obtains the confidence intervals (CIs) without the need of applying methods that are computationally intensive, e.g., bootstrap; and presents high generalization capabilities. Bayesian ELM is benchmarked against classical ELM in several artificial and real datasets that are widely used for the evaluation of machine learning algorithms. Achieved results show that the proposed approach produces a competitive accuracy with some additional advantages, namely, automatic production of CIs, reduction of probability of model overfitting, and use of a priori knowledge.

Probable Gastrointestinal Toxicity of Kombucha Tea

PubMed Central

Srinivasan, Radhika; Smolinske, Susan; Greenbaum, David

1997-01-01

Kombucha tea is a health beverage made by incubating the Kombucha “mushroom” in tea and sugar. Although therapeutic benefits have been attributed to the drink, neither its beneficial effects nor adverse side effects have been reported widely in the scientific literature. Side effects probably related to consumption of Kombucha tea are reported in four patients. Two presented with symptoms of allergic reaction, the third with jaundice, and the fourth with nausea, vomiting, and head and neck pain. In all four, use of Kombucha tea in proximity to onset of symptoms and symptom resolution on cessation of tea drinking suggest a probable etiologic association. PMID:9346462

Neurophysiological Markers of Statistical Learning in Music and Language: Hierarchy, Entropy, and Uncertainty.

PubMed

Daikoku, Tatsuya

2018-06-19

Statistical learning (SL) is a method of learning based on the transitional probabilities embedded in sequential phenomena such as music and language. It has been considered an implicit and domain-general mechanism that is innate in the human brain and that functions independently of intention to learn and awareness of what has been learned. SL is an interdisciplinary notion that incorporates information technology, artificial intelligence, musicology, and linguistics, as well as psychology and neuroscience. A body of recent study has suggested that SL can be reflected in neurophysiological responses based on the framework of information theory. This paper reviews a range of work on SL in adults and children that suggests overlapping and independent neural correlations in music and language, and that indicates disability of SL. Furthermore, this article discusses the relationships between the order of transitional probabilities (TPs) (i.e., hierarchy of local statistics) and entropy (i.e., global statistics) regarding SL strategies in human's brains; claims importance of information-theoretical approaches to understand domain-general, higher-order, and global SL covering both real-world music and language; and proposes promising approaches for the application of therapy and pedagogy from various perspectives of psychology, neuroscience, computational studies, musicology, and linguistics.

Probabilistic Cloning of Three Real States with Optimal Success Probabilities

NASA Astrophysics Data System (ADS)

Rui, Pin-shu

2017-06-01

We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→ N PQC case.