Statistical analyses of the relative risk.

PubMed Central

Gart, J J

1979-01-01

Let P1 be the probability of a disease in one population and P2 be the probability of a disease in a second population. The ratio of these quantities, R = P1/P2, is termed the relative risk. We consider first the analyses of the relative risk from retrospective studies. The relation between the relative risk and the odds ratio (or cross-product ratio) is developed. The odds ratio can be considered a parameter of an exponential model possessing sufficient statistics. This permits the development of exact significance tests and confidence intervals in the conditional space. Unconditional tests and intervals are also considered briefly. The consequences of misclassification errors and ignoring matching or stratifying are also considered. The various methods are extended to combination of results over the strata. Examples of case-control studies testing the association between HL-A frequencies and cancer illustrate the techniques. The parallel analyses of prospective studies are given. If P1 and P2 are small with large samples sizes the appropriate model is a Poisson distribution. This yields a exponential model with sufficient statistics. Exact conditional tests and confidence intervals can then be developed. Here we consider the case where two populations are compared adjusting for sex differences as well as for the strata (or covariate) differences such as age. The methods are applied to two examples: (1) testing in the two sexes the ratio of relative risks of skin cancer in people living in different latitudes, and (2) testing over time the ratio of the relative risks of cancer in two cities, one of which fluoridated its drinking water and one which did not. PMID:540589

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers

PubMed Central

Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-01-01

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio (C/N0) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C/N0 can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis. PMID:29207546

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers.

PubMed

Jin, Tian; Yuan, Heliang; Zhao, Na; Qin, Honglei; Sun, Kewen; Ji, Yuanfa

2017-12-04

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio ( C / N ₀) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C / N ₀ can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis.

Climate change and the detection of trends in annual runoff

USGS Publications Warehouse

McCabe, G.J.; Wolock, D.M.

1997-01-01

This study examines the statistical likelihood of detecting a trend in annual runoff given an assumed change in mean annual runoff, the underlying year-to-year variability in runoff, and serial correlation of annual runoff. Means, standard deviations, and lag-1 serial correlations of annual runoff were computed for 585 stream gages in the conterminous United States, and these statistics were used to compute the probability of detecting a prescribed trend in annual runoff. Assuming a linear 20% change in mean annual runoff over a 100 yr period and a significance level of 95%, the average probability of detecting a significant trend was 28% among the 585 stream gages. The largest probability of detecting a trend was in the northwestern U.S., the Great Lakes region, the northeastern U.S., the Appalachian Mountains, and parts of the northern Rocky Mountains. The smallest probability of trend detection was in the central and southwestern U.S., and in Florida. Low probabilities of trend detection were associated with low ratios of mean annual runoff to the standard deviation of annual runoff and with high lag-1 serial correlation in the data.

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.

Change-in-ratio estimators for populations with more than two subclasses

USGS Publications Warehouse

Udevitz, Mark S.; Pollock, Kenneth H.

1991-01-01

Change-in-ratio methods have been developed to estimate the size of populations with two or three population subclasses. Most of these methods require the often unreasonable assumption of equal sampling probabilities for individuals in all subclasses. This paper presents new models based on the weaker assumption that ratios of sampling probabilities are constant over time for populations with three or more subclasses. Estimation under these models requires that a value be assumed for one of these ratios when there are two samples. Explicit expressions are given for the maximum likelihood estimators under models for two samples with three or more subclasses and for three samples with two subclasses. A numerical method using readily available statistical software is described for obtaining the estimators and their standard errors under all of the models. Likelihood ratio tests that can be used in model selection are discussed. Emphasis is on the two-sample, three-subclass models for which Monte-Carlo simulation results and an illustrative example are presented.

Log-Normality and Multifractal Analysis of Flame Surface Statistics

NASA Astrophysics Data System (ADS)

Saha, Abhishek; Chaudhuri, Swetaprovo; Law, Chung K.

2013-11-01

The turbulent flame surface is typically highly wrinkled and folded at a multitude of scales controlled by various flame properties. It is useful if the information contained in this complex geometry can be projected onto a simpler regular geometry for the use of spectral, wavelet or multifractal analyses. Here we investigate local flame surface statistics of turbulent flame expanding under constant pressure. First the statistics of local length ratio is experimentally obtained from high-speed Mie scattering images. For spherically expanding flame, length ratio on the measurement plane, at predefined equiangular sectors is defined as the ratio of the actual flame length to the length of a circular-arc of radius equal to the average radius of the flame. Assuming isotropic distribution of such flame segments we convolute suitable forms of the length-ratio probability distribution functions (pdfs) to arrive at corresponding area-ratio pdfs. Both the pdfs are found to be near log-normally distributed and shows self-similar behavior with increasing radius. Near log-normality and rather intermittent behavior of the flame-length ratio suggests similarity with dissipation rate quantities which stimulates multifractal analysis. Currently at Indian Institute of Science, India.

Statistical Characterization of the Mechanical Parameters of Intact Rock Under Triaxial Compression: An Experimental Proof of the Jinping Marble

NASA Astrophysics Data System (ADS)

Jiang, Quan; Zhong, Shan; Cui, Jie; Feng, Xia-Ting; Song, Leibo

2016-12-01

We investigated the statistical characteristics and probability distribution of the mechanical parameters of natural rock using triaxial compression tests. Twenty cores of Jinping marble were tested under each different levels of confining stress (i.e., 5, 10, 20, 30, and 40 MPa). From these full stress-strain data, we summarized the numerical characteristics and determined the probability distribution form of several important mechanical parameters, including deformational parameters, characteristic strength, characteristic strains, and failure angle. The statistical proofs relating to the mechanical parameters of rock presented new information about the marble's probabilistic distribution characteristics. The normal and log-normal distributions were appropriate for describing random strengths of rock; the coefficients of variation of the peak strengths had no relationship to the confining stress; the only acceptable random distribution for both Young's elastic modulus and Poisson's ratio was the log-normal function; and the cohesive strength had a different probability distribution pattern than the frictional angle. The triaxial tests and statistical analysis also provided experimental evidence for deciding the minimum reliable number of experimental sample and for picking appropriate parameter distributions to use in reliability calculations for rock engineering.

The Two-Dimensional Gabor Function Adapted to Natural Image Statistics: A Model of Simple-Cell Receptive Fields and Sparse Structure in Images.

PubMed

Loxley, P N

2017-10-01

The two-dimensional Gabor function is adapted to natural image statistics, leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles, or generate basis functions for sparse coding applications. Learning is found to be most pronounced in three Gabor function parameters representing the size and spatial frequency of the two-dimensional Gabor function and characterized by a nonuniform probability distribution with heavy tails. All three parameters are found to be strongly correlated, resulting in a basis of multiscale Gabor functions with similar aspect ratios and size-dependent spatial frequencies. A key finding is that the distribution of receptive-field sizes is scale invariant over a wide range of values, so there is no characteristic receptive field size selected by natural image statistics. The Gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics. This allows for three distinct solutions: a basis of Gabor functions with sharp orientation resolution at the expense of spatial-frequency resolution, a basis of Gabor functions with sharp spatial-frequency resolution at the expense of orientation resolution, or a basis with unit aspect ratio. Arbitrary mixtures of all three cases are also possible. Two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions. The best-performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with Pareto marginal probability density functions.

Application of random match probability calculations to mixed STR profiles.

PubMed

Bille, Todd; Bright, Jo-Anne; Buckleton, John

2013-03-01

Mixed DNA profiles are being encountered more frequently as laboratories analyze increasing amounts of touch evidence. If it is determined that an individual could be a possible contributor to the mixture, it is necessary to perform a statistical analysis to allow an assignment of weight to the evidence. Currently, the combined probability of inclusion (CPI) and the likelihood ratio (LR) are the most commonly used methods to perform the statistical analysis. A third method, random match probability (RMP), is available. This article compares the advantages and disadvantages of the CPI and LR methods to the RMP method. We demonstrate that although the LR method is still considered the most powerful of the binary methods, the RMP and LR methods make similar use of the observed data such as peak height, assumed number of contributors, and known contributors where the CPI calculation tends to waste information and be less informative. © 2013 American Academy of Forensic Sciences.

Unified picture of strong-coupling stochastic thermodynamics and time reversals

NASA Astrophysics Data System (ADS)

Aurell, Erik

2018-04-01

Strong-coupling statistical thermodynamics is formulated as the Hamiltonian dynamics of an observed system interacting with another unobserved system (a bath). It is shown that the entropy production functional of stochastic thermodynamics, defined as the log ratio of forward and backward system path probabilities, is in a one-to-one relation with the log ratios of the joint initial conditions of the system and the bath. A version of strong-coupling statistical thermodynamics where the system-bath interaction vanishes at the beginning and at the end of a process is, as is also weak-coupling stochastic thermodynamics, related to the bath initially in equilibrium by itself. The heat is then the change of bath energy over the process, and it is discussed when this heat is a functional of the system history alone. The version of strong-coupling statistical thermodynamics introduced by Seifert and Jarzynski is related to the bath initially in conditional equilibrium with respect to the system. This leads to heat as another functional of the system history which needs to be determined by thermodynamic integration. The log ratio of forward and backward system path probabilities in a stochastic process is finally related to log ratios of the initial conditions of a combined system and bath. It is shown that the entropy production formulas of stochastic processes under a general class of time reversals are given by the differences of bath energies in a larger underlying Hamiltonian system. The paper highlights the centrality of time reversal in stochastic thermodynamics, also in the case of strong coupling.

Exact one-sided confidence limits for the difference between two correlated proportions.

PubMed

Lloyd, Chris J; Moldovan, Max V

2007-08-15

We construct exact and optimal one-sided upper and lower confidence bounds for the difference between two probabilities based on matched binary pairs using well-established optimality theory of Buehler. Starting with five different approximate lower and upper limits, we adjust them to have coverage probability exactly equal to the desired nominal level and then compare the resulting exact limits by their mean size. Exact limits based on the signed root likelihood ratio statistic are preferred and recommended for practical use.

A statistical method to estimate low-energy hadronic cross sections

NASA Astrophysics Data System (ADS)

Balassa, Gábor; Kovács, Péter; Wolf, György

2018-02-01

In this article we propose a model based on the Statistical Bootstrap approach to estimate the cross sections of different hadronic reactions up to a few GeV in c.m.s. energy. The method is based on the idea, when two particles collide a so-called fireball is formed, which after a short time period decays statistically into a specific final state. To calculate the probabilities we use a phase space description extended with quark combinatorial factors and the possibility of more than one fireball formation. In a few simple cases the probability of a specific final state can be calculated analytically, where we show that the model is able to reproduce the ratios of the considered cross sections. We also show that the model is able to describe proton-antiproton annihilation at rest. In the latter case we used a numerical method to calculate the more complicated final state probabilities. Additionally, we examined the formation of strange and charmed mesons as well, where we used existing data to fit the relevant model parameters.

Comparison of spectra using a Bayesian approach. An argument using oil spills as an example.

PubMed

Li, Jianfeng; Hibbert, D Brynn; Fuller, Steven; Cattle, Julie; Pang Way, Christopher

2005-01-15

The problem of assigning a probability of matching a number of spectra is addressed. The context is in environmental spills when an EPA needs to show that the material from a polluting spill (e.g., oil) is likely to have originated at a particular site (factory, refinery) or from a vehicle (road tanker or ship). Samples are taken from the spill, and candidate sources and are analyzed by spectroscopy (IR, fluorescence) or chromatography (GC or GC/MS). A matching algorithm is applied to pairs of spectra giving a single statistic (R). This can be a point-to-point match giving a correlation coefficient or a Euclidean distance or a derivative of these parameters. The distributions of R for same and different samples are established from existing data. For matching statistics with values in the range {0,1} corresponding to no match (0) to a perfect match (1) a beta distribution can be fitted to most data. The values of R from the match of the spectrum of a spilled oil and of each of a number of suspects are calculated and Bayes' theorem is applied to give a probability of matches between spill sample and each candidate and the probability of no match at all. The method is most effective when simple inspection of the matching parameters does not lead to an obvious conclusion; i.e., there is overlap of the distributions giving rise to dubiety of an assignment. The probability of finding a matching statistic if there were a match to the probability of finding it if there were no match, expressed as a ratio (called the likelihood ratio), is a sensitive and useful parameter to guide the analyst. It is proposed that this approach may be acceptable to a court of law and avoid challenges of apparently subjective opinion of an analyst. Examples of matching the fluorescence and infrared spectra of diesel oils are given.

Computerized Classification Testing with the Rasch Model

ERIC Educational Resources Information Center

Eggen, Theo J. H. M.

2011-01-01

If classification in a limited number of categories is the purpose of testing, computerized adaptive tests (CATs) with algorithms based on sequential statistical testing perform better than estimation-based CATs (e.g., Eggen & Straetmans, 2000). In these computerized classification tests (CCTs), the Sequential Probability Ratio Test (SPRT) (Wald,…

Significance of noisy signals in periodograms

NASA Astrophysics Data System (ADS)

Süveges, Maria

2015-08-01

The detection of tiny periodic signals in noisy and irregularly sampled time series is a challenging task. Once a small peak is found in the periodogram, the next step is to see how probable it is that pure noise produced a peak so extreme - that is to say, compute its False Alarm Probability (FAP). This useful measure quantifies the statistical plausibility of the found signal among the noise. However, its derivation from statistical principles is very hard due to the specificities of astronomical periodograms, such as oversampling and the ensuing strong correlation among its values at different frequencies. I will present a method to compute the FAP based on extreme-value statistics (Süveges 2014), and compare it to two other methods proposed by Baluev (2008) and Paltani (2004) and Schwarzenberg-Czerny (2012) on signals with various signal shapes and at different signal-to-noise ratios.

Reduced N-acetylaspartate content in the frontal part of the brain in patients with probable Alzheimer's disease.

PubMed

Christiansen, P; Schlosser, A; Henriksen, O

1995-01-01

The fully relaxed water signal was used as an internal standard in a STEAM experiment to calculate the concentrations of the metabolites: N-acetylaspartate (NAA), creatine + phosphocreatine [Cr + PCr], and choline-containing metabolites (Cho) in the frontal part of the brain in 12 patients with probable Alzheimer's disease. Eight age-matched healthy volunteers served as controls. Furthermore, T1 and T2 relaxation times of the metabolites and signal ratios: NAA/Cho, NAA/[Cr + PCr], and [Cr + PCr]/Cho at four different echo times (TE) and two different repetition times (TR) were calculated. The experiments were carried out using a Siemens Helicon SP 63/84 wholebody MR-scanner at 1.5 T. The concentration of NAA was significantly lower in the patients with probable Alzheimer's disease than in the healthy volunteers. No significant difference was found for any other metabolite concentration. For the signal ratios the only statistically significant difference was that the NAA/Cho ratio at TE = 92 ms and TR = 1.6 s was lower in the patients with probable Alzheimer's disease compared with the control group. A trend towards a longer T2 relaxation time for NAA in the patients with probable Alzheimer's disease than among the healthy volunteers was found, but no significant difference was found concerning the T1 and T2 relaxation times.

Automated segmentation of ultrasonic breast lesions using statistical texture classification and active contour based on probability distance.

PubMed

Liu, Bo; Cheng, H D; Huang, Jianhua; Tian, Jiawei; Liu, Jiafeng; Tang, Xianglong

2009-08-01

Because of its complicated structure, low signal/noise ratio, low contrast and blurry boundaries, fully automated segmentation of a breast ultrasound (BUS) image is a difficult task. In this paper, a novel segmentation method for BUS images without human intervention is proposed. Unlike most published approaches, the proposed method handles the segmentation problem by using a two-step strategy: ROI generation and ROI segmentation. First, a well-trained texture classifier categorizes the tissues into different classes, and the background knowledge rules are used for selecting the regions of interest (ROIs) from them. Second, a novel probability distance-based active contour model is applied for segmenting the ROIs and finding the accurate positions of the breast tumors. The active contour model combines both global statistical information and local edge information, using a level set approach. The proposed segmentation method was performed on 103 BUS images (48 benign and 55 malignant). To validate the performance, the results were compared with the corresponding tumor regions marked by an experienced radiologist. Three error metrics, true-positive ratio (TP), false-negative ratio (FN) and false-positive ratio (FP) were used for measuring the performance of the proposed method. The final results (TP = 91.31%, FN = 8.69% and FP = 7.26%) demonstrate that the proposed method can segment BUS images efficiently, quickly and automatically.

Statistics 101 for Radiologists.

PubMed

Anvari, Arash; Halpern, Elkan F; Samir, Anthony E

2015-10-01

Diagnostic tests have wide clinical applications, including screening, diagnosis, measuring treatment effect, and determining prognosis. Interpreting diagnostic test results requires an understanding of key statistical concepts used to evaluate test efficacy. This review explains descriptive statistics and discusses probability, including mutually exclusive and independent events and conditional probability. In the inferential statistics section, a statistical perspective on study design is provided, together with an explanation of how to select appropriate statistical tests. Key concepts in recruiting study samples are discussed, including representativeness and random sampling. Variable types are defined, including predictor, outcome, and covariate variables, and the relationship of these variables to one another. In the hypothesis testing section, we explain how to determine if observed differences between groups are likely to be due to chance. We explain type I and II errors, statistical significance, and study power, followed by an explanation of effect sizes and how confidence intervals can be used to generalize observed effect sizes to the larger population. Statistical tests are explained in four categories: t tests and analysis of variance, proportion analysis tests, nonparametric tests, and regression techniques. We discuss sensitivity, specificity, accuracy, receiver operating characteristic analysis, and likelihood ratios. Measures of reliability and agreement, including κ statistics, intraclass correlation coefficients, and Bland-Altman graphs and analysis, are introduced. © RSNA, 2015.

Bayesian statistical inference enhances the interpretation of contemporary randomized controlled trials.

PubMed

Wijeysundera, Duminda N; Austin, Peter C; Hux, Janet E; Beattie, W Scott; Laupacis, Andreas

2009-01-01

Randomized trials generally use "frequentist" statistics based on P-values and 95% confidence intervals. Frequentist methods have limitations that might be overcome, in part, by Bayesian inference. To illustrate these advantages, we re-analyzed randomized trials published in four general medical journals during 2004. We used Medline to identify randomized superiority trials with two parallel arms, individual-level randomization and dichotomous or time-to-event primary outcomes. Studies with P<0.05 in favor of the intervention were deemed "positive"; otherwise, they were "negative." We used several prior distributions and exact conjugate analyses to calculate Bayesian posterior probabilities for clinically relevant effects. Of 88 included studies, 39 were positive using a frequentist analysis. Although the Bayesian posterior probabilities of any benefit (relative risk or hazard ratio<1) were high in positive studies, these probabilities were lower and variable for larger benefits. The positive studies had only moderate probabilities for exceeding the effects that were assumed for calculating the sample size. By comparison, there were moderate probabilities of any benefit in negative studies. Bayesian and frequentist analyses complement each other when interpreting the results of randomized trials. Future reports of randomized trials should include both.

Social consequences of multiple sclerosis. Part 2. Divorce and separation: a historical prospective cohort study.

PubMed

Pfleger, C C H; Flachs, E M; Koch-Henriksen, Nils

2010-07-01

There is a need for follow-up studies of the familial situation of multiple sclerosis (MS) patients. To evaluate the probability of MS patients to remain in marriage or relationship with the same partner after onset of MS in comparison with the population. All 2538 Danes with onset of MS 1980-1989, retrieved from the Danish MS-Registry, and 50,760 matched and randomly drawn control persons were included. Information on family status was retrieved from Statistics Denmark. Cox analyses were used with onset as starting point. Five years after onset, the cumulative probability of remaining in the same relationship was 86% in patients vs. 89% in controls. The probabilities continued to deviate, and at 24 years, the probability was 33% in patients vs. 53% in the control persons (p < 0.001). Among patients with young onset (< 36 years of age), those with no children had a higher risk of divorce than those having children less than 7 years (Hazard Ratio 1.51; p < 0.0001), and men had a higher risk of divorce than women (Hazard Ratio 1.33; p < 0.01). MS significantly affects the probability of remaining in the same relationship compared with the background population.

A statistical-based material and process guidelines for design of carbon nanotube field-effect transistors in gigascale integrated circuits.

PubMed

Ghavami, Behnam; Raji, Mohsen; Pedram, Hossein

2011-08-26

Carbon nanotube field-effect transistors (CNFETs) show great promise as building blocks of future integrated circuits. However, synthesizing single-walled carbon nanotubes (CNTs) with accurate chirality and exact positioning control has been widely acknowledged as an exceedingly complex task. Indeed, density and chirality variations in CNT growth can compromise the reliability of CNFET-based circuits. In this paper, we present a novel statistical compact model to estimate the failure probability of CNFETs to provide some material and process guidelines for the design of CNFETs in gigascale integrated circuits. We use measured CNT spacing distributions within the framework of detailed failure analysis to demonstrate that both the CNT density and the ratio of metallic to semiconducting CNTs play dominant roles in defining the failure probability of CNFETs. Besides, it is argued that the large-scale integration of these devices within an integrated circuit will be feasible only if a specific range of CNT density with an acceptable ratio of semiconducting to metallic CNTs can be adjusted in a typical synthesis process.

Diversity Order Analysis of Dual-Hop Relaying with Partial Relay Selection

NASA Astrophysics Data System (ADS)

Bao, Vo Nguyen Quoc; Kong, Hyung Yun

In this paper, we study the performance of dual hop relaying in which the best relay selected by partial relay selection will help the source-destination link to overcome the channel impairment. Specifically, closed-form expressions for outage probability, symbol error probability and achievable diversity gain are derived using the statistical characteristic of the signal-to-noise ratio. Numerical investigation shows that the system achieves diversity of two regardless of relay number and also confirms the correctness of the analytical results. Furthermore, the performance loss due to partial relay selection is investigated.

Statistical Characteristics of the Gaussian-Noise Spikes Exceeding the Specified Threshold as Applied to Discharges in a Thundercloud

NASA Astrophysics Data System (ADS)

Klimenko, V. V.

2017-12-01

We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.

Some Interesting Applications of Probabilistic Techiques in Structural Dynamic Analysis of Rocket Engines

NASA Technical Reports Server (NTRS)

Brown, Andrew M.

2014-01-01

Numerical and Analytical methods developed to determine damage accumulation in specific engine components when speed variation included. Dither Life Ratio shown to be well over factor of 2 for specific example. Steady-State assumption shown to be accurate for most turbopump cases, allowing rapid calculation of DLR. If hot-fire speed data unknown, Monte Carlo method developed that uses speed statistics for similar engines. Application of techniques allow analyst to reduce both uncertainty and excess conservatism. High values of DLR could allow previously unacceptable part to pass HCF criteria without redesign. Given benefit and ease of implementation, recommend that any finite life turbomachine component analysis adopt these techniques. Probability Values calculated, compared, and evaluated for several industry-proposed methods for combining random and harmonic loads. Two new excel macros written to calculate combined load for any specific probability level. Closed form Curve fits generated for widely used 3(sigma) and 2(sigma) probability levels. For design of lightweight aerospace components, obtaining accurate, reproducible, statistically meaningful answer critical.

Tunnel ionization of highly excited atoms in a noncoherent laser radiation field

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

Krainov, V.P.; Todirashku, S.S.

1982-10-01

A theory is developed of the ionization of highly excited atomic states by a low-frequency field of noncoherent laser radiation with a large number of modes. Analytic formulas are obtained for the probability of the tunnel ionization in such a field. An analysis is made of the case of the hydrogen atom when the parabolic quantum numbers are sufficiently good in the low-frequency limit, as well as of the case of highly excited states of complex atoms when these states are characterized by a definite orbital momentum and parity. It is concluded that the statistical factor representing the ratio ofmore » the probability in a stochastic field to the probability in a monochromatic field decreases, compared with the case of a short-range potential, if the ''Coulomb tail'' is included. It is shown that at a given field intensity the statistical factor decreases on increase in the principal quantum number of the state being ionized.« less

Uncommon knowledge of a common phenomenon: intuitions and statistical thinking about gender birth ratio

NASA Astrophysics Data System (ADS)

Peled, Ofra N.; Peled, Irit; Peled, Jonathan U.

2013-01-01

The phenomenon of birth of a baby is a common and familiar one, and yet college students participating in a general biology class did not possess the expected common knowledge of the equal probability of gender births. We found that these students held strikingly skewed conceptions regarding gender birth ratio, estimating the number of female births to be more than twice the number of male births. Possible sources of these beliefs were analysed, showing flaws in statistical thinking such as viewing small unplanned samples as representing the whole population and making inferences from an inappropriate population. Some educational implications are discussed and a short teaching example (using data assembly) demonstrates an instructional direction that might facilitate conceptual change.

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Laser induced breakdown in gas mixtures. Experimental and statistical investigation on n-decane ignition: Pressure, mixture composition and equivalence ratio effects.

PubMed

Mokrani, Nabil; Gillard, Philippe

2018-03-26

This paper presents a physical and statistical approach to laser-induced breakdown in n-decane/N 2  + O 2 mixtures as a function of incident or absorbed energy. A parametric study, with pressure, fuel purity and equivalence ratio, was conducted to determine the incident and absorbed energies involved in producing breakdown, followed or not by ignition. The experiments were performed using a Q-switched Nd-YAG laser (1064 nm) inside a cylindrical 1-l combustion chamber in the range of 1-100 mJ of incident energy. A stochastic study of breakdown and ignition probabilities showed that the mixture composition had a significant effect on ignition with large variation of incident or absorbed energy required to obtain 50% of breakdown. It was observed that the combustion products absorb more energy coming from the laser. The effect of pressure on the ignition probabilities of lean and near stoichiometric mixtures was also investigated. It was found that a high ignition energy E50% is required for lean mixtures at high pressures (3 bar). The present study provides new data obtained on an original experimental setup and the results, close to laboratory-produced laser ignition phenomena, will enhance the understanding of initial conditions on the breakdown or ignition probabilities for different mixtures. Copyright © 2018 Elsevier B.V. All rights reserved.

The thresholds for statistical and clinical significance – a five-step procedure for evaluation of intervention effects in randomised clinical trials

PubMed Central

2014-01-01

Background Thresholds for statistical significance are insufficiently demonstrated by 95% confidence intervals or P-values when assessing results from randomised clinical trials. First, a P-value only shows the probability of getting a result assuming that the null hypothesis is true and does not reflect the probability of getting a result assuming an alternative hypothesis to the null hypothesis is true. Second, a confidence interval or a P-value showing significance may be caused by multiplicity. Third, statistical significance does not necessarily result in clinical significance. Therefore, assessment of intervention effects in randomised clinical trials deserves more rigour in order to become more valid. Methods Several methodologies for assessing the statistical and clinical significance of intervention effects in randomised clinical trials were considered. Balancing simplicity and comprehensiveness, a simple five-step procedure was developed. Results For a more valid assessment of results from a randomised clinical trial we propose the following five-steps: (1) report the confidence intervals and the exact P-values; (2) report Bayes factor for the primary outcome, being the ratio of the probability that a given trial result is compatible with a ‘null’ effect (corresponding to the P-value) divided by the probability that the trial result is compatible with the intervention effect hypothesised in the sample size calculation; (3) adjust the confidence intervals and the statistical significance threshold if the trial is stopped early or if interim analyses have been conducted; (4) adjust the confidence intervals and the P-values for multiplicity due to number of outcome comparisons; and (5) assess clinical significance of the trial results. Conclusions If the proposed five-step procedure is followed, this may increase the validity of assessments of intervention effects in randomised clinical trials. PMID:24588900

Math: Data Relationships. Graphs, Ratios and Proportions, Statistics and Probability. Grades K-9. Revised Edition.

ERIC Educational Resources Information Center

Instructional Objectives Exchange, Los Angeles, CA.

To help classroom teachers in grades K-9 construct mathematics tests, fifteen general objectives, corresponding sub-objectives, sample test items, and answers are presented. In general, sub-objectives are arranged in increasing order of difficulty. The objectives were written to comprehensively cover three categories. The first, graphs, covers the…

Fishnet statistics for probabilistic strength and scaling of nacreous imbricated lamellar materials

NASA Astrophysics Data System (ADS)

Luo, Wen; Bažant, Zdeněk P.

2017-12-01

Similar to nacre (or brick masonry), imbricated (or staggered) lamellar structures are widely found in nature and man-made materials, and are of interest for biomimetics. They can achieve high defect insensitivity and fracture toughness, as demonstrated in previous studies. But the probability distribution with a realistic far-left tail is apparently unknown. Here, strictly for statistical purposes, the microstructure of nacre is approximated by a diagonally pulled fishnet with quasibrittle links representing the shear bonds between parallel lamellae (or platelets). The probability distribution of fishnet strength is calculated as a sum of a rapidly convergent series of the failure probabilities after the rupture of one, two, three, etc., links. Each of them represents a combination of joint probabilities and of additive probabilities of disjoint events, modified near the zone of failed links by the stress redistributions caused by previously failed links. Based on previous nano- and multi-scale studies at Northwestern, the strength distribution of each link, characterizing the interlamellar shear bond, is assumed to be a Gauss-Weibull graft, but with a deeper Weibull tail than in Type 1 failure of non-imbricated quasibrittle materials. The autocorrelation length is considered equal to the link length. The size of the zone of failed links at maximum load increases with the coefficient of variation (CoV) of link strength, and also with fishnet size. With an increasing width-to-length aspect ratio, a rectangular fishnet gradually transits from the weakest-link chain to the fiber bundle, as the limit cases. The fishnet strength at failure probability 10-6 grows with the width-to-length ratio. For a square fishnet boundary, the strength at 10-6 failure probability is about 11% higher, while at fixed load the failure probability is about 25-times higher than it is for the non-imbricated case. This is a major safety advantage of the fishnet architecture over particulate or fiber reinforced materials. There is also a strong size effect, partly similar to that of Type 1 while the curves of log-strength versus log-size for different sizes could cross each other. The predicted behavior is verified by about a million Monte Carlo simulations for each of many fishnet geometries, sizes and CoVs of link strength. In addition to the weakest-link or fiber bundle, the fishnet becomes the third analytically tractable statistical model of structural strength, and has the former two as limit cases.

Detection methods for non-Gaussian gravitational wave stochastic backgrounds

NASA Astrophysics Data System (ADS)

Drasco, Steve; Flanagan, Éanna É.

2003-04-01

A gravitational wave stochastic background can be produced by a collection of independent gravitational wave events. There are two classes of such backgrounds, one for which the ratio of the average time between events to the average duration of an event is small (i.e., many events are on at once), and one for which the ratio is large. In the first case the signal is continuous, sounds something like a constant hiss, and has a Gaussian probability distribution. In the second case, the discontinuous or intermittent signal sounds something like popcorn popping, and is described by a non-Gaussian probability distribution. In this paper we address the issue of finding an optimal detection method for such a non-Gaussian background. As a first step, we examine the idealized situation in which the event durations are short compared to the detector sampling time, so that the time structure of the events cannot be resolved, and we assume white, Gaussian noise in two collocated, aligned detectors. For this situation we derive an appropriate version of the maximum likelihood detection statistic. We compare the performance of this statistic to that of the standard cross-correlation statistic both analytically and with Monte Carlo simulations. In general the maximum likelihood statistic performs better than the cross-correlation statistic when the stochastic background is sufficiently non-Gaussian, resulting in a gain factor in the minimum gravitational-wave energy density necessary for detection. This gain factor ranges roughly between 1 and 3, depending on the duty cycle of the background, for realistic observing times and signal strengths for both ground and space based detectors. The computational cost of the statistic, although significantly greater than that of the cross-correlation statistic, is not unreasonable. Before the statistic can be used in practice with real detector data, further work is required to generalize our analysis to accommodate separated, misaligned detectors with realistic, colored, non-Gaussian noise.

Selection of a cardiac surgery provider in the managed care era.

PubMed

Shahian, D M; Yip, W; Westcott, G; Jacobson, J

2000-11-01

Many health planners promote the use of competition to contain cost and improve quality of care. Using a standard econometric model, we examined the evidence for "value-based" cardiac surgery provider selection in eastern Massachusetts, where there is significant competition and managed care penetration. McFadden's conditional logit model was used to study cardiac surgery provider selection among 6952 patients and eight metropolitan Boston hospitals in 1997. Hospital predictor variables included beds, cardiac surgery case volume, objective clinical and financial performance, reputation (percent out-of-state referrals, cardiac residency program), distance from patient's home to hospital, and historical referral patterns. Subgroup analyses were performed for each major payer category. Distance from patient's home to hospital (odds ratio 0.90; P =.000) and the historical referral pattern from each patient's hometown (z = 45.305; P =.000) were important predictors in all models. A cardiac surgery residency enhanced the probability of selection (odds ratio 5.25; P =.000), as did percent out-of-state referrals (odds ratio 1.10; P =.001). Higher mortality rates were associated with decreased probability of selection (odds ratio 0.51; P =.027), but higher length of stay was paradoxically associated with greater probability (odds ratio 1.72; P =.000). Total hospital costs were irrelevant (odds ratio 1.00; P =.179). When analyzed by payer subgroup, Medicare patients appeared to select hospitals with both low mortality (odds ratio 0.43; P =.176) and short length of stay (odds ratio 0.76; P =.213), although the results did not achieve statistical significance. The commercial managed care subgroup exhibited the least "value-based" behavior. The odds ratio for length of stay was the highest of any group (odds ratio = 2.589; P =.000) and there was a subset of hospitals for which higher mortality was actually associated with greater likelihood of selection. The observable determinants of cardiac surgery provider selection are related to hospital reputation, historical referral patterns, and patient proximity, not objective clinical or cost performance. The paradoxic behavior of commercial managed care probably results from unobserved choice factors that are not primarily based on objective provider performance.

Dynamically biased statistical model for the ortho/para conversion in the H2 + H3+ → H3+ + H2 reaction.

PubMed

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-07

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007)]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H(5)(+) complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H(5)(+) complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011)] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Dynamically biased statistical model for the ortho/para conversion in the H2+H3+ --> H3++ H2 reaction

NASA Astrophysics Data System (ADS)

Gómez-Carrasco, Susana; González-Sánchez, Lola; Aguado, Alfredo; Sanz-Sanz, Cristina; Zanchet, Alexandre; Roncero, Octavio

2012-09-01

In this work we present a dynamically biased statistical model to describe the evolution of the title reaction from statistical to a more direct mechanism, using quasi-classical trajectories (QCT). The method is based on the one previously proposed by Park and Light [J. Chem. Phys. 126, 044305 (2007), 10.1063/1.2430711]. A recent global potential energy surface is used here to calculate the capture probabilities, instead of the long-range ion-induced dipole interactions. The dynamical constraints are introduced by considering a scrambling matrix which depends on energy and determine the probability of the identity/hop/exchange mechanisms. These probabilities are calculated using QCT. It is found that the high zero-point energy of the fragments is transferred to the rest of the degrees of freedom, what shortens the lifetime of H_5^+ complexes and, as a consequence, the exchange mechanism is produced with lower proportion. The zero-point energy (ZPE) is not properly described in quasi-classical trajectory calculations and an approximation is done in which the initial ZPE of the reactants is reduced in QCT calculations to obtain a new ZPE-biased scrambling matrix. This reduction of the ZPE is explained by the need of correcting the pure classical level number of the H_5^+ complex, as done in classical simulations of unimolecular processes and to get equivalent quantum and classical rate constants using Rice-Ramsperger-Kassel-Marcus theory. This matrix allows to obtain a ratio of hop/exchange mechanisms, α(T), in rather good agreement with recent experimental results by Crabtree et al. [J. Chem. Phys. 134, 194311 (2011), 10.1063/1.3587246] at room temperature. At lower temperatures, however, the present simulations predict too high ratios because the biased scrambling matrix is not statistical enough. This demonstrates the importance of applying quantum methods to simulate this reaction at the low temperatures of astrophysical interest.

Statistical power in parallel group point exposure studies with time-to-event outcomes: an empirical comparison of the performance of randomized controlled trials and the inverse probability of treatment weighting (IPTW) approach.

PubMed

Austin, Peter C; Schuster, Tibor; Platt, Robert W

2015-10-15

Estimating statistical power is an important component of the design of both randomized controlled trials (RCTs) and observational studies. Methods for estimating statistical power in RCTs have been well described and can be implemented simply. In observational studies, statistical methods must be used to remove the effects of confounding that can occur due to non-random treatment assignment. Inverse probability of treatment weighting (IPTW) using the propensity score is an attractive method for estimating the effects of treatment using observational data. However, sample size and power calculations have not been adequately described for these methods. We used an extensive series of Monte Carlo simulations to compare the statistical power of an IPTW analysis of an observational study with time-to-event outcomes with that of an analysis of a similarly-structured RCT. We examined the impact of four factors on the statistical power function: number of observed events, prevalence of treatment, the marginal hazard ratio, and the strength of the treatment-selection process. We found that, on average, an IPTW analysis had lower statistical power compared to an analysis of a similarly-structured RCT. The difference in statistical power increased as the magnitude of the treatment-selection model increased. The statistical power of an IPTW analysis tended to be lower than the statistical power of a similarly-structured RCT.

Streamflow statistics for development of water rights claims for the Jarbidge Wild and Scenic River, Owyhee Canyonlands Wilderness, Idaho, 2013-14: a supplement to Scientific Investigations Report 2013-5212

USGS Publications Warehouse

Wood, Molly S.

2014-01-01

The U.S. Geological Survey (USGS), in cooperation with the Bureau of Land Management (BLM), estimated streamflow statistics for stream segments designated “Wild,” “Scenic,” or “Recreational” under the National Wild and Scenic Rivers System in the Owyhee Canyonlands Wilderness in southwestern Idaho. The streamflow statistics were used by the BLM to develop and file a draft, federal reserved water right claim to protect federally designated “outstanding remarkable values” in the Jarbidge River. The BLM determined that the daily mean streamflow equaled or exceeded 20, 50, and 80 percent of the time during bimonthly periods (two periods per month) and the bankfull (66.7-percent annual exceedance probability) streamflow are important thresholds for maintaining outstanding remarkable values. Although streamflow statistics for the Jarbidge River below Jarbidge, Nevada (USGS 13162225) were published previously in 2013 and used for the draft water right claim, the BLM and USGS have since recognized the need to refine streamflow statistics given the approximate 40 river mile distance and intervening tributaries between the original point of estimation (USGS 13162225) and at the mouth of the Jarbidge River, which is the downstream end of the Wild and Scenic River segment. A drainage-area-ratio method was used in 2013 to estimate bimonthly exceedance probability streamflow statistics at the mouth of the Jarbidge River based on available streamgage data on the Jarbidge and East Fork Jarbidge Rivers. The resulting bimonthly streamflow statistics were further adjusted using a scaling factor calculated from a water balance on streamflow statistics calculated for the Bruneau and East Fork Bruneau Rivers and Sheep Creek. The final, adjusted bimonthly exceedance probability and bankfull streamflow statistics compared well with available verification datasets (including discrete streamflow measurements made at the mouth of the Jarbidge River) and are considered the best available estimates for streamflow statistics in the Jarbidge Wild and Scenic River segment.

Significance of stress transfer in time-dependent earthquake probability calculations

USGS Publications Warehouse

Parsons, T.

2005-01-01

A sudden change in stress is seen to modify earthquake rates, but should it also revise earthquake probability? Data used to derive input parameters permits an array of forecasts; so how large a static stress change is require to cause a statistically significant earthquake probability change? To answer that question, effects of parameter and philosophical choices are examined through all phases of sample calculations, Drawing at random from distributions of recurrence-aperiodicity pairs identifies many that recreate long paleoseismic and historic earthquake catalogs. Probability density funtions built from the recurrence-aperiodicity pairs give the range of possible earthquake forecasts under a point process renewal model. Consequences of choices made in stress transfer calculations, such as different slip models, fault rake, dip, and friction are, tracked. For interactions among large faults, calculated peak stress changes may be localized, with most of the receiving fault area changed less than the mean. Thus, to avoid overstating probability change on segments, stress change values should be drawn from a distribution reflecting the spatial pattern rather than using the segment mean. Disparity resulting from interaction probability methodology is also examined. For a fault with a well-understood earthquake history, a minimum stress change to stressing rate ratio of 10:1 to 20:1 is required to significantly skew probabilities with >80-85% confidence. That ratio must be closer to 50:1 to exceed 90-95% confidence levels. Thus revision to earthquake probability is achievable when a perturbing event is very close to the fault in question or the tectonic stressing rate is low.

Statistical Performance Evaluation Of Soft Seat Pressure Relief Valves

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

Harris, Stephen P.; Gross, Robert E.

2013-03-26

Risk-based inspection methods enable estimation of the probability of failure on demand for spring-operated pressure relief valves at the United States Department of Energy's Savannah River Site in Aiken, South Carolina. This paper presents a statistical performance evaluation of soft seat spring operated pressure relief valves. These pressure relief valves are typically smaller and of lower cost than hard seat (metal to metal) pressure relief valves and can provide substantial cost savings in fluid service applications (air, gas, liquid, and steam) providing that probability of failure on demand (the probability that the pressure relief valve fails to perform its intendedmore » safety function during a potentially dangerous over pressurization) is at least as good as that for hard seat valves. The research in this paper shows that the proportion of soft seat spring operated pressure relief valves failing is the same or less than that of hard seat valves, and that for failed valves, soft seat valves typically have failure ratios of proof test pressure to set pressure less than that of hard seat valves.« less

Statistics of multi-look AIRSAR imagery: A comparison of theory with measurements

NASA Technical Reports Server (NTRS)

Lee, J. S.; Hoppel, K. W.; Mango, S. A.

1993-01-01

The intensity and amplitude statistics of SAR images, such as L-Band HH for SEASAT and SIR-B, and C-Band VV for ERS-1 have been extensively investigated for various terrain, ground cover and ocean surfaces. Less well-known are the statistics between multiple channels of polarimetric of interferometric SAR's, especially for the multi-look processed data. In this paper, we investigate the probability density functions (PDF's) of phase differences, the magnitude of complex products and the amplitude ratios, between polarization channels (i.e. HH, HV, and VV) using 1-look and 4-look AIRSAR polarimetric data. Measured histograms are compared with theoretical PDF's which were recently derived based on a complex Gaussian model.

From reading numbers to seeing ratios: a benefit of icons for risk comprehension.

PubMed

Tubau, Elisabet; Rodríguez-Ferreiro, Javier; Barberia, Itxaso; Colomé, Àngels

2018-06-21

Promoting a better understanding of statistical data is becoming increasingly important for improving risk comprehension and decision-making. In this regard, previous studies on Bayesian problem solving have shown that iconic representations help infer frequencies in sets and subsets. Nevertheless, the mechanisms by which icons enhance performance remain unclear. Here, we tested the hypothesis that the benefit offered by icon arrays lies in a better alignment between presented and requested relationships, which should facilitate the comprehension of the requested ratio beyond the represented quantities. To this end, we analyzed individual risk estimates based on data presented either in standard verbal presentations (percentages and natural frequency formats) or as icon arrays. Compared to the other formats, icons led to estimates that were more accurate, and importantly, promoted the use of equivalent expressions for the requested probability. Furthermore, whereas the accuracy of the estimates based on verbal formats depended on their alignment with the text, all the estimates based on icons were equally accurate. Therefore, these results support the proposal that icons enhance the comprehension of the ratio and its mapping onto the requested probability and point to relational misalignment as potential interference for text-based Bayesian reasoning. The present findings also argue against an intrinsic difficulty with understanding single-event probabilities.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference.

PubMed

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications.

Outage Probability of MRC for κ-μ Shadowed Fading Channels under Co-Channel Interference

PubMed Central

Chen, Changfang; Shu, Minglei; Wang, Yinglong; Yang, Ming; Zhang, Chongqing

2016-01-01

In this paper, exact closed-form expressions are derived for the outage probability (OP) of the maximal ratio combining (MRC) scheme in the κ-μ shadowed fading channels, in which both the independent and correlated shadowing components are considered. The scenario assumes the received desired signals are corrupted by the independent Rayleigh-faded co-channel interference (CCI) and background white Gaussian noise. To this end, first, the probability density function (PDF) of the κ-μ shadowed fading distribution is obtained in the form of a power series. Then the incomplete generalized moment-generating function (IG-MGF) of the received signal-to-interference-plus-noise ratio (SINR) is derived in the closed form. By using the IG-MGF results, closed-form expressions for the OP of MRC scheme are obtained over the κ-μ shadowed fading channels. Simulation results are included to validate the correctness of the analytical derivations. These new statistical results can be applied to the modeling and analysis of several wireless communication systems, such as body centric communications. PMID:27851817

P values are only an index to evidence: 20th- vs. 21st-century statistical science.

PubMed

Burnham, K P; Anderson, D R

2014-03-01

Early statistical methods focused on pre-data probability statements (i.e., data as random variables) such as P values; these are not really inferences nor are P values evidential. Statistical science clung to these principles throughout much of the 20th century as a wide variety of methods were developed for special cases. Looking back, it is clear that the underlying paradigm (i.e., testing and P values) was weak. As Kuhn (1970) suggests, new paradigms have taken the place of earlier ones: this is a goal of good science. New methods have been developed and older methods extended and these allow proper measures of strength of evidence and multimodel inference. It is time to move forward with sound theory and practice for the difficult practical problems that lie ahead. Given data the useful foundation shifts to post-data probability statements such as model probabilities (Akaike weights) or related quantities such as odds ratios and likelihood intervals. These new methods allow formal inference from multiple models in the a prior set. These quantities are properly evidential. The past century was aimed at finding the "best" model and making inferences from it. The goal in the 21st century is to base inference on all the models weighted by their model probabilities (model averaging). Estimates of precision can include model selection uncertainty leading to variances conditional on the model set. The 21st century will be about the quantification of information, proper measures of evidence, and multi-model inference. Nelder (1999:261) concludes, "The most important task before us in developing statistical science is to demolish the P-value culture, which has taken root to a frightening extent in many areas of both pure and applied science and technology".

Six new mechanics corresponding to further shape theories

NASA Astrophysics Data System (ADS)

Anderson, Edward

2016-02-01

In this paper, suite of relational notions of shape are presented at the level of configuration space geometry, with corresponding new theories of shape mechanics and shape statistics. These further generalize two quite well known examples: (i) Kendall’s (metric) shape space with his shape statistics and Barbour’s mechanics thereupon. (ii) Leibnizian relational space alias metric scale-and-shape space to which corresponds Barbour-Bertotti mechanics. This paper’s new theories include, using the invariant and group namings, (iii) Angle alias conformal shape mechanics. (iv) Area ratio alias e shape mechanics. (v) Area alias e scale-and-shape mechanics. (iii)-(v) rest respectively on angle space, area-ratio space, and area space configuration spaces. Probability and statistics applications are also pointed to in outline. (vi) Various supersymmetric counterparts of (i)-(v) are considered. Since supergravity differs considerably from GR-based conceptions of background independence, some of the new supersymmetric shape mechanics are compared with both. These reveal compatibility between supersymmetry and GR-based conceptions of background independence, at least within these simpler model arenas.

Order-restricted inference for means with missing values.

PubMed

Wang, Heng; Zhong, Ping-Shou

2017-09-01

Missing values appear very often in many applications, but the problem of missing values has not received much attention in testing order-restricted alternatives. Under the missing at random (MAR) assumption, we impute the missing values nonparametrically using kernel regression. For data with imputation, the classical likelihood ratio test designed for testing the order-restricted means is no longer applicable since the likelihood does not exist. This article proposes a novel method for constructing test statistics for assessing means with an increasing order or a decreasing order based on jackknife empirical likelihood (JEL) ratio. It is shown that the JEL ratio statistic evaluated under the null hypothesis converges to a chi-bar-square distribution, whose weights depend on missing probabilities and nonparametric imputation. Simulation study shows that the proposed test performs well under various missing scenarios and is robust for normally and nonnormally distributed data. The proposed method is applied to an Alzheimer's disease neuroimaging initiative data set for finding a biomarker for the diagnosis of the Alzheimer's disease. © 2017, The International Biometric Society.

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.

In-beam Fission Study at JAEA

NASA Astrophysics Data System (ADS)

Nishio, Katsuhisa

2013-12-01

Fission fragment mass distributions were measured in heavy-ion induced fissions using 238U target nucleus. The measured mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si + 238U and 34S + 238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections for seaborgium and hassium isotopes.

In-beam fission study for Heavy Element Synthesis

NASA Astrophysics Data System (ADS)

Nishio, Katsuhisa

2013-12-01

Fission fragment mass distributions were measured in heavy-ion induced fissions using 238U target nucleus. The measured mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si + 238U and 34S + 238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections for seaborgium and hassium isotopes.

Lake bed classification using acoustic data

USGS Publications Warehouse

Yin, Karen K.; Li, Xing; Bonde, John; Richards, Carl; Cholwek, Gary

1998-01-01

As part of our effort to identify the lake bed surficial substrates using remote sensing data, this work designs pattern classifiers by multivariate statistical methods. Probability distribution of the preprocessed acoustic signal is analyzed first. A confidence region approach is then adopted to improve the design of the existing classifier. A technique for further isolation is proposed which minimizes the expected loss from misclassification. The devices constructed are applicable for real-time lake bed categorization. A mimimax approach is suggested to treat more general cases where the a priori probability distribution of the substrate types is unknown. Comparison of the suggested methods with the traditional likelihood ratio tests is discussed.

Search for Point Sources of Ultra-High-Energy Cosmic Rays above 4.0 × 1019 eV Using a Maximum Likelihood Ratio Test

NASA Astrophysics Data System (ADS)

Abbasi, R. U.; Abu-Zayyad, T.; Amann, J. F.; Archbold, G.; Atkins, R.; Bellido, J. A.; Belov, K.; Belz, J. W.; Ben-Zvi, S. Y.; Bergman, D. R.; Boyer, J. H.; Burt, G. W.; Cao, Z.; Clay, R. W.; Connolly, B. M.; Dawson, B. R.; Deng, W.; Farrar, G. R.; Fedorova, Y.; Findlay, J.; Finley, C. B.; Hanlon, W. F.; Hoffman, C. M.; Holzscheiter, M. H.; Hughes, G. A.; Hüntemeyer, P.; Jui, C. C. H.; Kim, K.; Kirn, M. A.; Knapp, B. C.; Loh, E. C.; Maestas, M. M.; Manago, N.; Mannel, E. J.; Marek, L. J.; Martens, K.; Matthews, J. A. J.; Matthews, J. N.; O'Neill, A.; Painter, C. A.; Perera, L.; Reil, K.; Riehle, R.; Roberts, M. D.; Sasaki, M.; Schnetzer, S. R.; Seman, M.; Simpson, K. M.; Sinnis, G.; Smith, J. D.; Snow, R.; Sokolsky, P.; Song, C.; Springer, R. W.; Stokes, B. T.; Thomas, J. R.; Thomas, S. B.; Thomson, G. B.; Tupa, D.; Westerhoff, S.; Wiencke, L. R.; Zech, A.

2005-04-01

We present the results of a search for cosmic-ray point sources at energies in excess of 4.0×1019 eV in the combined data sets recorded by the Akeno Giant Air Shower Array and High Resolution Fly's Eye stereo experiments. The analysis is based on a maximum likelihood ratio test using the probability density function for each event rather than requiring an a priori choice of a fixed angular bin size. No statistically significant clustering of events consistent with a point source is found.

Maximum entropy approach to statistical inference for an ocean acoustic waveguide.

PubMed

Knobles, D P; Sagers, J D; Koch, R A

2012-02-01

A conditional probability distribution suitable for estimating the statistical properties of ocean seabed parameter values inferred from acoustic measurements is derived from a maximum entropy principle. The specification of the expectation value for an error function constrains the maximization of an entropy functional. This constraint determines the sensitivity factor (β) to the error function of the resulting probability distribution, which is a canonical form that provides a conservative estimate of the uncertainty of the parameter values. From the conditional distribution, marginal distributions for individual parameters can be determined from integration over the other parameters. The approach is an alternative to obtaining the posterior probability distribution without an intermediary determination of the likelihood function followed by an application of Bayes' rule. In this paper the expectation value that specifies the constraint is determined from the values of the error function for the model solutions obtained from a sparse number of data samples. The method is applied to ocean acoustic measurements taken on the New Jersey continental shelf. The marginal probability distribution for the values of the sound speed ratio at the surface of the seabed and the source levels of a towed source are examined for different geoacoustic model representations. © 2012 Acoustical Society of America

Integrating statistical and process-based models to produce probabilistic landslide hazard at regional scale

NASA Astrophysics Data System (ADS)

Strauch, R. L.; Istanbulluoglu, E.

2017-12-01

We develop a landslide hazard modeling approach that integrates a data-driven statistical model and a probabilistic process-based shallow landslide model for mapping probability of landslide initiation, transport, and deposition at regional scales. The empirical model integrates the influence of seven site attribute (SA) classes: elevation, slope, curvature, aspect, land use-land cover, lithology, and topographic wetness index, on over 1,600 observed landslides using a frequency ratio (FR) approach. A susceptibility index is calculated by adding FRs for each SA on a grid-cell basis. Using landslide observations we relate susceptibility index to an empirically-derived probability of landslide impact. This probability is combined with results from a physically-based model to produce an integrated probabilistic map. Slope was key in landslide initiation while deposition was linked to lithology and elevation. Vegetation transition from forest to alpine vegetation and barren land cover with lower root cohesion leads to higher frequency of initiation. Aspect effects are likely linked to differences in root cohesion and moisture controlled by solar insulation and snow. We demonstrate the model in the North Cascades of Washington, USA and identify locations of high and low probability of landslide impacts that can be used by land managers in their design, planning, and maintenance.

Three methods to construct predictive models using logistic regression and likelihood ratios to facilitate adjustment for pretest probability give similar results.

PubMed

Chan, Siew Foong; Deeks, Jonathan J; Macaskill, Petra; Irwig, Les

2008-01-01

To compare three predictive models based on logistic regression to estimate adjusted likelihood ratios allowing for interdependency between diagnostic variables (tests). This study was a review of the theoretical basis, assumptions, and limitations of published models; and a statistical extension of methods and application to a case study of the diagnosis of obstructive airways disease based on history and clinical examination. Albert's method includes an offset term to estimate an adjusted likelihood ratio for combinations of tests. Spiegelhalter and Knill-Jones method uses the unadjusted likelihood ratio for each test as a predictor and computes shrinkage factors to allow for interdependence. Knottnerus' method differs from the other methods because it requires sequencing of tests, which limits its application to situations where there are few tests and substantial data. Although parameter estimates differed between the models, predicted "posttest" probabilities were generally similar. Construction of predictive models using logistic regression is preferred to the independence Bayes' approach when it is important to adjust for dependency of tests errors. Methods to estimate adjusted likelihood ratios from predictive models should be considered in preference to a standard logistic regression model to facilitate ease of interpretation and application. Albert's method provides the most straightforward approach.

What's Missing in Teaching Probability and Statistics: Building Cognitive Schema for Understanding Random Phenomena

ERIC Educational Resources Information Center

Kuzmak, Sylvia

2016-01-01

Teaching probability and statistics is more than teaching the mathematics itself. Historically, the mathematics of probability and statistics was first developed through analyzing games of chance such as the rolling of dice. This article makes the case that the understanding of probability and statistics is dependent upon building a…

Inclusion probability for DNA mixtures is a subjective one-sided match statistic unrelated to identification information

PubMed Central

Perlin, Mark William

2015-01-01

Background: DNA mixtures of two or more people are a common type of forensic crime scene evidence. A match statistic that connects the evidence to a criminal defendant is usually needed for court. Jurors rely on this strength of match to help decide guilt or innocence. However, the reliability of unsophisticated match statistics for DNA mixtures has been questioned. Materials and Methods: The most prevalent match statistic for DNA mixtures is the combined probability of inclusion (CPI), used by crime labs for over 15 years. When testing 13 short tandem repeat (STR) genetic loci, the CPI-1 value is typically around a million, regardless of DNA mixture composition. However, actual identification information, as measured by a likelihood ratio (LR), spans a much broader range. This study examined probability of inclusion (PI) mixture statistics for 517 locus experiments drawn from 16 reported cases and compared them with LR locus information calculated independently on the same data. The log(PI-1) values were examined and compared with corresponding log(LR) values. Results: The LR and CPI methods were compared in case examples of false inclusion, false exclusion, a homicide, and criminal justice outcomes. Statistical analysis of crime laboratory STR data shows that inclusion match statistics exhibit a truncated normal distribution having zero center, with little correlation to actual identification information. By the law of large numbers (LLN), CPI-1 increases with the number of tested genetic loci, regardless of DNA mixture composition or match information. These statistical findings explain why CPI is relatively constant, with implications for DNA policy, criminal justice, cost of crime, and crime prevention. Conclusions: Forensic crime laboratories have generated CPI statistics on hundreds of thousands of DNA mixture evidence items. However, this commonly used match statistic behaves like a random generator of inclusionary values, following the LLN rather than measuring identification information. A quantitative CPI number adds little meaningful information beyond the analyst's initial qualitative assessment that a person's DNA is included in a mixture. Statistical methods for reporting on DNA mixture evidence should be scientifically validated before they are relied upon by criminal justice. PMID:26605124

Inclusion probability for DNA mixtures is a subjective one-sided match statistic unrelated to identification information.

PubMed

Perlin, Mark William

2015-01-01

DNA mixtures of two or more people are a common type of forensic crime scene evidence. A match statistic that connects the evidence to a criminal defendant is usually needed for court. Jurors rely on this strength of match to help decide guilt or innocence. However, the reliability of unsophisticated match statistics for DNA mixtures has been questioned. The most prevalent match statistic for DNA mixtures is the combined probability of inclusion (CPI), used by crime labs for over 15 years. When testing 13 short tandem repeat (STR) genetic loci, the CPI(-1) value is typically around a million, regardless of DNA mixture composition. However, actual identification information, as measured by a likelihood ratio (LR), spans a much broader range. This study examined probability of inclusion (PI) mixture statistics for 517 locus experiments drawn from 16 reported cases and compared them with LR locus information calculated independently on the same data. The log(PI(-1)) values were examined and compared with corresponding log(LR) values. The LR and CPI methods were compared in case examples of false inclusion, false exclusion, a homicide, and criminal justice outcomes. Statistical analysis of crime laboratory STR data shows that inclusion match statistics exhibit a truncated normal distribution having zero center, with little correlation to actual identification information. By the law of large numbers (LLN), CPI(-1) increases with the number of tested genetic loci, regardless of DNA mixture composition or match information. These statistical findings explain why CPI is relatively constant, with implications for DNA policy, criminal justice, cost of crime, and crime prevention. Forensic crime laboratories have generated CPI statistics on hundreds of thousands of DNA mixture evidence items. However, this commonly used match statistic behaves like a random generator of inclusionary values, following the LLN rather than measuring identification information. A quantitative CPI number adds little meaningful information beyond the analyst's initial qualitative assessment that a person's DNA is included in a mixture. Statistical methods for reporting on DNA mixture evidence should be scientifically validated before they are relied upon by criminal justice.

Applying quantitative bias analysis to estimate the plausible effects of selection bias in a cluster randomised controlled trial: secondary analysis of the Primary care Osteoarthritis Screening Trial (POST).

PubMed

Barnett, L A; Lewis, M; Mallen, C D; Peat, G

2017-12-04

Selection bias is a concern when designing cluster randomised controlled trials (c-RCT). Despite addressing potential issues at the design stage, bias cannot always be eradicated from a trial design. The application of bias analysis presents an important step forward in evaluating whether trial findings are credible. The aim of this paper is to give an example of the technique to quantify potential selection bias in c-RCTs. This analysis uses data from the Primary care Osteoarthritis Screening Trial (POST). The primary aim of this trial was to test whether screening for anxiety and depression, and providing appropriate care for patients consulting their GP with osteoarthritis would improve clinical outcomes. Quantitative bias analysis is a seldom-used technique that can quantify types of bias present in studies. Due to lack of information on the selection probability, probabilistic bias analysis with a range of triangular distributions was also used, applied at all three follow-up time points; 3, 6, and 12 months post consultation. A simple bias analysis was also applied to the study. Worse pain outcomes were observed among intervention participants than control participants (crude odds ratio at 3, 6, and 12 months: 1.30 (95% CI 1.01, 1.67), 1.39 (1.07, 1.80), and 1.17 (95% CI 0.90, 1.53), respectively). Probabilistic bias analysis suggested that the observed effect became statistically non-significant if the selection probability ratio was between 1.2 and 1.4. Selection probability ratios of > 1.8 were needed to mask a statistically significant benefit of the intervention. The use of probabilistic bias analysis in this c-RCT suggested that worse outcomes observed in the intervention arm could plausibly be attributed to selection bias. A very large degree of selection of bias was needed to mask a beneficial effect of intervention making this interpretation less plausible.

Expert system for online surveillance of nuclear reactor coolant pumps

DOEpatents

Gross, Kenny C.; Singer, Ralph M.; Humenik, Keith E.

1993-01-01

An expert system for online surveillance of nuclear reactor coolant pumps. This system provides a means for early detection of pump or sensor degradation. Degradation is determined through the use of a statistical analysis technique, sequential probability ratio test, applied to information from several sensors which are responsive to differing physical parameters. The results of sequential testing of the data provide the operator with an early warning of possible sensor or pump failure.

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…

Four hundred or more participants needed for stable contingency table estimates of clinical prediction rule performance.

PubMed

Kent, Peter; Boyle, Eleanor; Keating, Jennifer L; Albert, Hanne B; Hartvigsen, Jan

2017-02-01

To quantify variability in the results of statistical analyses based on contingency tables and discuss the implications for the choice of sample size for studies that derive clinical prediction rules. An analysis of three pre-existing sets of large cohort data (n = 4,062-8,674) was performed. In each data set, repeated random sampling of various sample sizes, from n = 100 up to n = 2,000, was performed 100 times at each sample size and the variability in estimates of sensitivity, specificity, positive and negative likelihood ratios, posttest probabilities, odds ratios, and risk/prevalence ratios for each sample size was calculated. There were very wide, and statistically significant, differences in estimates derived from contingency tables from the same data set when calculated in sample sizes below 400 people, and typically, this variability stabilized in samples of 400-600 people. Although estimates of prevalence also varied significantly in samples below 600 people, that relationship only explains a small component of the variability in these statistical parameters. To reduce sample-specific variability, contingency tables should consist of 400 participants or more when used to derive clinical prediction rules or test their performance. Copyright © 2016 Elsevier Inc. All rights reserved.

The Mantel-Haenszel procedure revisited: models and generalizations.

PubMed

Fidler, Vaclav; Nagelkerke, Nico

2013-01-01

Several statistical methods have been developed for adjusting the Odds Ratio of the relation between two dichotomous variables X and Y for some confounders Z. With the exception of the Mantel-Haenszel method, commonly used methods, notably binary logistic regression, are not symmetrical in X and Y. The classical Mantel-Haenszel method however only works for confounders with a limited number of discrete strata, which limits its utility, and appears to have no basis in statistical models. Here we revisit the Mantel-Haenszel method and propose an extension to continuous and vector valued Z. The idea is to replace the observed cell entries in strata of the Mantel-Haenszel procedure by subject specific classification probabilities for the four possible values of (X,Y) predicted by a suitable statistical model. For situations where X and Y can be treated symmetrically we propose and explore the multinomial logistic model. Under the homogeneity hypothesis, which states that the odds ratio does not depend on Z, the logarithm of the odds ratio estimator can be expressed as a simple linear combination of three parameters of this model. Methods for testing the homogeneity hypothesis are proposed. The relationship between this method and binary logistic regression is explored. A numerical example using survey data is presented.

The Mantel-Haenszel Procedure Revisited: Models and Generalizations

PubMed Central

Fidler, Vaclav; Nagelkerke, Nico

2013-01-01

Several statistical methods have been developed for adjusting the Odds Ratio of the relation between two dichotomous variables X and Y for some confounders Z. With the exception of the Mantel-Haenszel method, commonly used methods, notably binary logistic regression, are not symmetrical in X and Y. The classical Mantel-Haenszel method however only works for confounders with a limited number of discrete strata, which limits its utility, and appears to have no basis in statistical models. Here we revisit the Mantel-Haenszel method and propose an extension to continuous and vector valued Z. The idea is to replace the observed cell entries in strata of the Mantel-Haenszel procedure by subject specific classification probabilities for the four possible values of (X,Y) predicted by a suitable statistical model. For situations where X and Y can be treated symmetrically we propose and explore the multinomial logistic model. Under the homogeneity hypothesis, which states that the odds ratio does not depend on Z, the logarithm of the odds ratio estimator can be expressed as a simple linear combination of three parameters of this model. Methods for testing the homogeneity hypothesis are proposed. The relationship between this method and binary logistic regression is explored. A numerical example using survey data is presented. PMID:23516463

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.

Statistically Qualified Neuro-Analytic system and Method for Process Monitoring

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

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

1998-11-04

An apparatus and method for monitoring a process involves development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two steps: deterministic model adaption and stochastic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics,augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation emor minimization technique. Stochastic model adaptation involves qualifying any remaining uncertaintymore » in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system.« less

A new method for detecting small and dim targets in starry background

NASA Astrophysics Data System (ADS)

Yao, Rui; Zhang, Yanning; Jiang, Lei

2011-08-01

Small visible optical space targets detection is one of the key issues in the research of long-range early warning and space debris surveillance. The SNR(Signal to Noise Ratio) of the target is very low because of the self influence of image device. Random noise and background movement also increase the difficulty of target detection. In order to detect small visible optical space targets effectively and rapidly, we bring up a novel detecting method based on statistic theory. Firstly, we get a reasonable statistical model of visible optical space image. Secondly, we extract SIFT(Scale-Invariant Feature Transform) feature of the image frames, and calculate the transform relationship, then use the transform relationship to compensate whole visual field's movement. Thirdly, the influence of star was wiped off by using interframe difference method. We find segmentation threshold to differentiate candidate targets and noise by using OTSU method. Finally, we calculate statistical quantity to judge whether there is the target for every pixel position in the image. Theory analysis shows the relationship of false alarm probability and detection probability at different SNR. The experiment result shows that this method could detect target efficiently, even the target passing through stars.

Index/Ring Finger Ratio, Hand and Foot Index: Gender Estimation Tools.

PubMed

Gupta, Sonia; Gupta, Vineeta; Tyagi, Nutan; Ettishree; Bhagat, Sinthia; Dadu, Mohit; Anthwal, Nishita; Ashraf, Tahira

2017-06-01

Gender estimation from dismembered human body parts and skeletal remains in cases of mass disasters, explosions, and assaults cases is an imperative element of any medico-legal investigations and has been a major challenge for forensic scientists. The aim of the present study was to estimate the gender by using index and ring finger length ratio, hand and foot index along with the correlation of both the hand and foot index to determine the vital role of all the indices in establishing gender identity. A descriptive cross-sectional study was done on 300 subjects (150 males and 150 females). Various anthropometric measurements like hand length, hand breadth and hand index, Index Finger Length (IFL), Ring Finger Length (RFL) and IFL/RFL ratio as well as foot length, foot breadth and foot index were estimated in millimeters (mm) with the help of sliding-anthropometric caliper. The data was analysed using independent t-test and Pearson correlation coefficient test. A probability value (p) of ≤ 0.05 was considered statistically significant. The index and ring finger ratio was found to be higher in females as compared to males. The hand and foot index was more in males than in females. The index and ring finger length ratio, hand and foot index between males and females was found to be statistically significant for both hands and feet. A statistically significant correlation was determined between hand indexes versus foot index. This study can be useful to establish the gender of a dismembered hand or foot when subjected for medicolegal examination.

Urban seismic risk assessment: statistical repair cost data and probable structural losses based on damage scenario—correlation analysis

NASA Astrophysics Data System (ADS)

Eleftheriadou, Anastasia K.; Baltzopoulou, Aikaterini D.; Karabinis, Athanasios I.

2016-06-01

The current seismic risk assessment is based on two discrete approaches, actual and probable, validating afterwards the produced results. In the first part of this research, the seismic risk is evaluated from the available data regarding the mean statistical repair/strengthening or replacement cost for the total number of damaged structures (180,427 buildings) after the 7/9/1999 Parnitha (Athens) earthquake. The actual evaluated seismic risk is afterwards compared to the estimated probable structural losses, which is presented in the second part of the paper, based on a damage scenario in the referring earthquake. The applied damage scenario is based on recently developed damage probability matrices (DPMs) from Athens (Greece) damage database. The seismic risk estimation refers to 750,085 buildings situated in the extended urban region of Athens. The building exposure is categorized in five typical structural types and represents 18.80 % of the entire building stock in Greece. The last information is provided by the National Statistics Service of Greece (NSSG) according to the 2000-2001 census. The seismic input is characterized by the ratio, a g/ a o, where a g is the regional peak ground acceleration (PGA) which is evaluated from the earlier estimated research macroseismic intensities, and a o is the PGA according to the hazard map of the 2003 Greek Seismic Code. Finally, the collected investigated financial data derived from different National Services responsible for the post-earthquake crisis management concerning the repair/strengthening or replacement costs or other categories of costs for the rehabilitation of earthquake victims (construction and function of settlements for earthquake homeless, rent supports, demolitions, shorings) are used to determine the final total seismic risk factor.

Optimizing exoplanet transit searches around low-mass stars with inclination constraints

NASA Astrophysics Data System (ADS)

Herrero, E.; Ribas, I.; Jordi, C.; Guinan, E. F.; Engle, S. G.

2012-01-01

Aims: We investigate a method to increase the efficiency of a targeted exoplanet search with the transit technique by preselecting a subset of candidates from large catalogs of stars. Assuming spin-orbit alignment, this can be achieved by considering stars that have a higher probability to be oriented nearly equator-on (inclination close to 90°). Methods: We used activity-rotation velocity relations for low-mass stars with a convective envelope to study the dependence of the position in the activity-vsini diagram on the stellar axis inclination. We composed a catalog of G-, K-, M-type main-sequence simulated stars using isochrones, an isotropic inclination distribution and empirical relations to obtain their rotation periods and activity indexes. Then the activity-vsini diagram was completed and statistics were applied to trace the areas containing the higher ratio of stars with inclinations above 80°. A similar statistics was applied to stars from real catalogs with log(R'HK) and vsini data to find their probability of being oriented equator-on. Results: We present our method to generate the simulated star catalog and the subsequent statistics to find the highly inclined stars from real catalogs using the activity-vsini diagram. Several catalogs from the literature are analyzed and a subsample of stars with the highest probability of being equator-on is presented. Conclusions: Assuming spin-orbit alignment, the efficiency of an exoplanet transit search in the resulting subsample of probably highly inclined stars is estimated to be two to three times higher than with a general search without preselection. Table 4 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/537/A147

Tips and Tricks for Successful Application of Statistical Methods to Biological Data.

PubMed

Schlenker, Evelyn

2016-01-01

This chapter discusses experimental design and use of statistics to describe characteristics of data (descriptive statistics) and inferential statistics that test the hypothesis posed by the investigator. Inferential statistics, based on probability distributions, depend upon the type and distribution of the data. For data that are continuous, randomly and independently selected, as well as normally distributed more powerful parametric tests such as Student's t test and analysis of variance (ANOVA) can be used. For non-normally distributed or skewed data, transformation of the data (using logarithms) may normalize the data allowing use of parametric tests. Alternatively, with skewed data nonparametric tests can be utilized, some of which rely on data that are ranked prior to statistical analysis. Experimental designs and analyses need to balance between committing type 1 errors (false positives) and type 2 errors (false negatives). For a variety of clinical studies that determine risk or benefit, relative risk ratios (random clinical trials and cohort studies) or odds ratios (case-control studies) are utilized. Although both use 2 × 2 tables, their premise and calculations differ. Finally, special statistical methods are applied to microarray and proteomics data, since the large number of genes or proteins evaluated increase the likelihood of false discoveries. Additional studies in separate samples are used to verify microarray and proteomic data. Examples in this chapter and references are available to help continued investigation of experimental designs and appropriate data analysis.

A discussion of the merits of random man not excluded and likelihood ratios.

PubMed

Buckleton, John; Curran, James

2008-09-01

DNA mixture interpretation is undertaken either by calculating a LR or an exclusion probability (RMNE or its complement CPI). Debate exists as to which has the greater claim. The merits and drawbacks of the two approaches are discussed. We conclude that the two matters that appear to have real force are: (1) LRs are more difficult to present in court and (2) the RMNE statistic wastes information that should be utilised.

Surveillance of industrial processes with correlated parameters

DOEpatents

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

1996-01-01

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

Human variability in mercury toxicokinetics and steady state biomarker ratios.

PubMed

Bartell, S M; Ponce, R A; Sanga, R N; Faustman, E M

2000-10-01

Regulatory guidelines regarding methylmercury exposure depend on dose-response models relating observed mercury concentrations in maternal blood, cord blood, and maternal hair to developmental neurobehavioral endpoints. Generalized estimates of the maternal blood-to-hair, blood-to-intake, or hair-to-intake ratios are necessary for linking exposure to biomarker-based dose-response models. Most assessments have used point estimates for these ratios; however, significant interindividual and interstudy variability has been reported. For example, a maternal ratio of 250 ppm in hair per mg/L in blood is commonly used in models, but a 1990 WHO review reports mean ratios ranging from 140 to 370 ppm per mg/L. To account for interindividual and interstudy variation in applying these ratios to risk and safety assessment, some researchers have proposed representing the ratios with probability distributions and conducting probabilistic assessments. Such assessments would allow regulators to consider the range and like-lihood of mercury exposures in a population, rather than limiting the evaluation to an estimate of the average exposure or a single conservative exposure estimate. However, no consensus exists on the most appropriate distributions for representing these parameters. We discuss published reviews of blood-to-hair and blood-to-intake steady state ratios for mercury and suggest statistical approaches for combining existing datasets to form generalized probability distributions for mercury distribution ratios. Although generalized distributions may not be applicable to all populations, they allow a more informative assessment than point estimates where individual biokinetic information is unavailable. Whereas development and use of these distributions will improve existing exposure and risk models, additional efforts in data generation and model development are required.

Automatically-generated rectal dose constraints in intensity-modulated radiation therapy for prostate cancer

NASA Astrophysics Data System (ADS)

Hwang, Taejin; Kim, Yong Nam; Kim, Soo Kon; Kang, Sei-Kwon; Cheong, Kwang-Ho; Park, Soah; Yoon, Jai-Woong; Han, Taejin; Kim, Haeyoung; Lee, Meyeon; Kim, Kyoung-Joo; Bae, Hoonsik; Suh, Tae-Suk

2015-06-01

The dose constraint during prostate intensity-modulated radiation therapy (IMRT) optimization should be patient-specific for better rectum sparing. The aims of this study are to suggest a novel method for automatically generating a patient-specific dose constraint by using an experience-based dose volume histogram (DVH) of the rectum and to evaluate the potential of such a dose constraint qualitatively. The normal tissue complication probabilities (NTCPs) of the rectum with respect to V %ratio in our study were divided into three groups, where V %ratio was defined as the percent ratio of the rectal volume overlapping the planning target volume (PTV) to the rectal volume: (1) the rectal NTCPs in the previous study (clinical data), (2) those statistically generated by using the standard normal distribution (calculated data), and (3) those generated by combining the calculated data and the clinical data (mixed data). In the calculated data, a random number whose mean value was on the fitted curve described in the clinical data and whose standard deviation was 1% was generated by using the `randn' function in the MATLAB program and was used. For each group, we validated whether the probability density function (PDF) of the rectal NTCP could be automatically generated with the density estimation method by using a Gaussian kernel. The results revealed that the rectal NTCP probability increased in proportion to V %ratio , that the predictive rectal NTCP was patient-specific, and that the starting point of IMRT optimization for the given patient might be different. The PDF of the rectal NTCP was obtained automatically for each group except that the smoothness of the probability distribution increased with increasing number of data and with increasing window width. We showed that during the prostate IMRT optimization, the patient-specific dose constraints could be automatically generated and that our method could reduce the IMRT optimization time as well as maintain the IMRT plan quality.

Two-step estimation in ratio-of-mediator-probability weighted causal mediation analysis.

PubMed

Bein, Edward; Deutsch, Jonah; Hong, Guanglei; Porter, Kristin E; Qin, Xu; Yang, Cheng

2018-04-15

This study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score-based weighting. Such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator. Ratio-of-mediator-probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score-based weighting. In step 1, a propensity score model is estimated. In step 2, the causal effects of interest are estimated using weights derived from the prior step's regression coefficient estimates. Statistical inferences obtained from this 2-step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights. This study extends to ratio-of-mediator-probability weighting analysis a solution to the 2-step estimation problem by stacking the score functions from both steps. We derive the asymptotic variance-covariance matrix for the indirect effect and direct effect 2-step estimators, provide simulation results, and illustrate with an application study. Our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored. The standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation. We discuss broad implications of this approach for causal analysis involving propensity score-based weighting. Copyright © 2018 John Wiley & Sons, Ltd.

Performance of mixed RF/FSO systems in exponentiated Weibull distributed channels

NASA Astrophysics Data System (ADS)

Zhao, Jing; Zhao, Shang-Hong; Zhao, Wei-Hu; Liu, Yun; Li, Xuan

2017-12-01

This paper presented the performances of asymmetric mixed radio frequency (RF)/free-space optical (FSO) system with the amplify-and-forward relaying scheme. The RF channel undergoes Nakagami- m channel, and the Exponentiated Weibull distribution is adopted for the FSO component. The mathematical formulas for cumulative distribution function (CDF), probability density function (PDF) and moment generating function (MGF) of equivalent signal-to-noise ratio (SNR) are achieved. According to the end-to-end statistical characteristics, the new analytical expressions of outage probability are obtained. Under various modulation techniques, we derive the average bit-error-rate (BER) based on the Meijer's G function. The evaluation and simulation are provided for the system performance, and the aperture average effect is discussed as well.

Leads Detection Using Mixture Statistical Distribution Based CRF Algorithm from Sentinel-1 Dual Polarization SAR Imagery

NASA Astrophysics Data System (ADS)

Zhang, Yu; Li, Fei; Zhang, Shengkai; Zhu, Tingting

2017-04-01

Synthetic Aperture Radar (SAR) is significantly important for polar remote sensing since it can provide continuous observations in all days and all weather. SAR can be used for extracting the surface roughness information characterized by the variance of dielectric properties and different polarization channels, which make it possible to observe different ice types and surface structure for deformation analysis. In November, 2016, Chinese National Antarctic Research Expedition (CHINARE) 33rd cruise has set sails in sea ice zone in Antarctic. Accurate leads spatial distribution in sea ice zone for routine planning of ship navigation is essential. In this study, the semantic relationship between leads and sea ice categories has been described by the Conditional Random Fields (CRF) model, and leads characteristics have been modeled by statistical distributions in SAR imagery. In the proposed algorithm, a mixture statistical distribution based CRF is developed by considering the contexture information and the statistical characteristics of sea ice for improving leads detection in Sentinel-1A dual polarization SAR imagery. The unary potential and pairwise potential in CRF model is constructed by integrating the posteriori probability estimated from statistical distributions. For mixture statistical distribution parameter estimation, Method of Logarithmic Cumulants (MoLC) is exploited for single statistical distribution parameters estimation. The iteration based Expectation Maximal (EM) algorithm is investigated to calculate the parameters in mixture statistical distribution based CRF model. In the posteriori probability inference, graph-cut energy minimization method is adopted in the initial leads detection. The post-processing procedures including aspect ratio constrain and spatial smoothing approaches are utilized to improve the visual result. The proposed method is validated on Sentinel-1A SAR C-band Extra Wide Swath (EW) Ground Range Detected (GRD) imagery with a pixel spacing of 40 meters near Prydz Bay area, East Antarctica. Main work is listed as follows: 1) A mixture statistical distribution based CRF algorithm has been developed for leads detection from Sentinel-1A dual polarization images. 2) The assessment of the proposed mixture statistical distribution based CRF method and single distribution based CRF algorithm has been presented. 3) The preferable parameters sets including statistical distributions, the aspect ratio threshold and spatial smoothing window size have been provided. In the future, the proposed algorithm will be developed for the operational Sentinel series data sets processing due to its less time consuming cost and high accuracy in leads detection.

Economic and statistical analysis of time limitations for spotting fluids and fishing operations

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

Keller, P.S.; Brinkmann, P.E.; Taneja, P.K.

1984-05-01

This paper reviews the statistics of ''Spotting Fluids'' to free stuck drill pipe as well as the economics and statistics of drill string fishing operations. Data were taken from Mobil Oil Exploration and Producing Southeast Inc.'s (MOEPSI) records from 1970-1981. Only those events which occur after a drill string becomes stuck are discussed. The data collected were categorized as Directional Wells and Straight Wells. Bar diagrams are presented to show the Success Ratio vs. Soaking Time for each of the two categories. An analysis was made to identify the elapsed time limit to place the spotting fluid for maximum probabilitymore » of success. Also determined was the statistical minimum soaking time and the maximum soaking time. For determining the time limit for fishing operations, the following criteria were used: 1. The Risked ''Economic Breakeven Analysis'' concept was developed based on the work of Harrison. 2. Statistical Probability of Success based on MOEPSI's records from 1970-1981.« less

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…

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.

No compelling positive association between ovarian hormones and wearing red clothing when using multinomial analyses.

PubMed

Blake, Khandis R; Dixson, Barnaby J W; O'Dean, Siobhan M; Denson, Thomas F

2017-04-01

Several studies report that wearing red clothing enhances women's attractiveness and signals sexual proceptivity to men. The associated hypothesis that women will choose to wear red clothing when fertility is highest, however, has received mixed support from empirical studies. One possible cause of these mixed findings may be methodological. The current study aimed to replicate recent findings suggesting a positive association between hormonal profiles associated with high fertility (high estradiol to progesterone ratios) and the likelihood of wearing red. We compared the effect of the estradiol to progesterone ratio on the probability of wearing: red versus non-red (binary logistic regression); red versus neutral, black, blue, green, orange, multi-color, and gray (multinomial logistic regression); and each of these same colors in separate binary models (e.g., green versus non-green). Red versus non-red analyses showed a positive trend between a high estradiol to progesterone ratio and wearing red, but the effect only arose for younger women and was not robust across samples. We found no compelling evidence for ovarian hormones increasing the probability of wearing red in the other analyses. However, we did find that the probability of wearing neutral was positively associated with the estradiol to progesterone ratio, though the effect did not reach conventional levels of statistical significance. Findings suggest that although ovarian hormones may affect younger women's preference for red clothing under some conditions, the effect is not robust when differentiating amongst other colors of clothing. In addition, the effect of ovarian hormones on clothing color preference may not be specific to the color red. Copyright © 2017 Elsevier Inc. All rights reserved.

Statistical Optimality in Multipartite Ranking and Ordinal Regression.

PubMed

Uematsu, Kazuki; Lee, Yoonkyung

2015-05-01

Statistical optimality in multipartite ranking is investigated as an extension of bipartite ranking. We consider the optimality of ranking algorithms through minimization of the theoretical risk which combines pairwise ranking errors of ordinal categories with differential ranking costs. The extension shows that for a certain class of convex loss functions including exponential loss, the optimal ranking function can be represented as a ratio of weighted conditional probability of upper categories to lower categories, where the weights are given by the misranking costs. This result also bridges traditional ranking methods such as proportional odds model in statistics with various ranking algorithms in machine learning. Further, the analysis of multipartite ranking with different costs provides a new perspective on non-smooth list-wise ranking measures such as the discounted cumulative gain and preference learning. We illustrate our findings with simulation study and real data analysis.

Asymptotically optimum multialternative sequential procedures for discernment of processes minimizing average length of observations

NASA Astrophysics Data System (ADS)

Fishman, M. M.

1985-01-01

The problem of multialternative sequential discernment of processes is formulated in terms of conditionally optimum procedures minimizing the average length of observations, without any probabilistic assumptions about any one occurring process, rather than in terms of Bayes procedures minimizing the average risk. The problem is to find the procedure that will transform inequalities into equalities. The problem is formulated for various models of signal observation and data processing: (1) discernment of signals from background interference by a multichannel system; (2) discernment of pulse sequences with unknown time delay; (3) discernment of harmonic signals with unknown frequency. An asymptotically optimum sequential procedure is constructed which compares the statistics of the likelihood ratio with the mean-weighted likelihood ratio and estimates the upper bound for conditional average lengths of observations. This procedure is shown to remain valid as the upper bound for the probability of erroneous partial solutions decreases approaching zero and the number of hypotheses increases approaching infinity. It also remains valid under certain special constraints on the probability such as a threshold. A comparison with a fixed-length procedure reveals that this sequential procedure decreases the length of observations to one quarter, on the average, when the probability of erroneous partial solutions is low.

Statistical characteristics of the sequential detection of signals in correlated noise

NASA Astrophysics Data System (ADS)

Averochkin, V. A.; Baranov, P. E.

1985-10-01

A solution is given to the problem of determining the distribution of the duration of the sequential two-threshold Wald rule for the time-discrete detection of determinate and Gaussian correlated signals on a background of Gaussian correlated noise. Expressions are obtained for the joint probability densities of the likelihood ratio logarithms, and an analysis is made of the effect of correlation and SNR on the duration distribution and the detection efficiency. Comparison is made with Neumann-Pearson detection.

Simple and flexible SAS and SPSS programs for analyzing lag-sequential categorical data.

PubMed

O'Connor, B P

1999-11-01

This paper describes simple and flexible programs for analyzing lag-sequential categorical data, using SAS and SPSS. The programs read a stream of codes and produce a variety of lag-sequential statistics, including transitional frequencies, expected transitional frequencies, transitional probabilities, adjusted residuals, z values, Yule's Q values, likelihood ratio tests of stationarity across time and homogeneity across groups or segments, transformed kappas for unidirectional dependence, bidirectional dependence, parallel and nonparallel dominance, and significance levels based on both parametric and randomization tests.

Surveillance of industrial processes with correlated parameters

DOEpatents

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

1996-12-17

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

Stochastic demographic forecasting.

PubMed

Lee, R D

1992-11-01

"This paper describes a particular approach to stochastic population forecasting, which is implemented for the U.S.A. through 2065. Statistical time series methods are combined with demographic models to produce plausible long run forecasts of vital rates, with probability distributions. The resulting mortality forecasts imply gains in future life expectancy that are roughly twice as large as those forecast by the Office of the Social Security Actuary.... Resulting stochastic forecasts of the elderly population, elderly dependency ratios, and payroll tax rates for health, education and pensions are presented." excerpt

The intriguing evolution of effect sizes in biomedical research over time: smaller but more often statistically significant.

PubMed

Monsarrat, Paul; Vergnes, Jean-Noel

2018-01-01

In medicine, effect sizes (ESs) allow the effects of independent variables (including risk/protective factors or treatment interventions) on dependent variables (e.g., health outcomes) to be quantified. Given that many public health decisions and health care policies are based on ES estimates, it is important to assess how ESs are used in the biomedical literature and to investigate potential trends in their reporting over time. Through a big data approach, the text mining process automatically extracted 814 120 ESs from 13 322 754 PubMed abstracts. Eligible ESs were risk ratio, odds ratio, and hazard ratio, along with their confidence intervals. Here we show a remarkable decrease of ES values in PubMed abstracts between 1990 and 2015 while, concomitantly, results become more often statistically significant. Medians of ES values have decreased over time for both "risk" and "protective" values. This trend was found in nearly all fields of biomedical research, with the most marked downward tendency in genetics. Over the same period, the proportion of statistically significant ESs increased regularly: among the abstracts with at least 1 ES, 74% were statistically significant in 1990-1995, vs 85% in 2010-2015. whereas decreasing ESs could be an intrinsic evolution in biomedical research, the concomitant increase of statistically significant results is more intriguing. Although it is likely that growing sample sizes in biomedical research could explain these results, another explanation may lie in the "publish or perish" context of scientific research, with the probability of a growing orientation toward sensationalism in research reports. Important provisions must be made to improve the credibility of biomedical research and limit waste of resources. © The Authors 2017. Published by Oxford University Press.

Evidence-Based Medicine as a Tool for Undergraduate Probability and Statistics Education

PubMed Central

Masel, J.; Humphrey, P. T.; Blackburn, B.; Levine, J. A.

2015-01-01

Most students have difficulty reasoning about chance events, and misconceptions regarding probability can persist or even strengthen following traditional instruction. Many biostatistics classes sidestep this problem by prioritizing exploratory data analysis over probability. However, probability itself, in addition to statistics, is essential both to the biology curriculum and to informed decision making in daily life. One area in which probability is particularly important is medicine. Given the preponderance of pre health students, in addition to more general interest in medicine, we capitalized on students’ intrinsic motivation in this area to teach both probability and statistics. We use the randomized controlled trial as the centerpiece of the course, because it exemplifies the most salient features of the scientific method, and the application of critical thinking to medicine. The other two pillars of the course are biomedical applications of Bayes’ theorem and science and society content. Backward design from these three overarching aims was used to select appropriate probability and statistics content, with a focus on eliciting and countering previously documented misconceptions in their medical context. Pretest/posttest assessments using the Quantitative Reasoning Quotient and Attitudes Toward Statistics instruments are positive, bucking several negative trends previously reported in statistics education. PMID:26582236

75 FR 53925 - Sea Turtle Conservation; Shrimp and Summer Flounder Trawling Requirements

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-02

... because of the statistical probability the candidate TED may not achieve the standard (i.e., control TED... the test with 4 turtle captures because of the statistical probability the candidate TED may not... because of the statistical probability the candidate TED may not achieve the standard (i.e., [[Page 53930...

Statistically qualified neuro-analytic failure detection method and system

DOEpatents

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

2002-03-02

An apparatus and method for monitoring a process involve development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two stages: deterministic model adaption and stochastic model modification of the deterministic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics, augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation error minimization technique. Stochastic model modification involves qualifying any remaining uncertainty in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system. Illustrative of the method and apparatus, the method is applied to a peristaltic pump system.

Real-time Mainshock Forecast by Statistical Discrimination of Foreshock Clusters

NASA Astrophysics Data System (ADS)

Nomura, S.; Ogata, Y.

2016-12-01

Foreshock discremination is one of the most effective ways for short-time forecast of large main shocks. Though many large earthquakes accompany their foreshocks, discreminating them from enormous small earthquakes is difficult and only probabilistic evaluation from their spatio-temporal features and magnitude evolution may be available. Logistic regression is the statistical learning method best suited to such binary pattern recognition problems where estimates of a-posteriori probability of class membership are required. Statistical learning methods can keep learning discreminating features from updating catalog and give probabilistic recognition of forecast in real time. We estimated a non-linear function of foreshock proportion by smooth spline bases and evaluate the possibility of foreshocks by the logit function. In this study, we classified foreshocks from earthquake catalog by the Japan Meteorological Agency by single-link clustering methods and learned spatial and temporal features of foreshocks by the probability density ratio estimation. We use the epicentral locations, time spans and difference in magnitudes for learning and forecasting. Magnitudes of main shocks are also predicted our method by incorporating b-values into our method. We discuss the spatial pattern of foreshocks from the classifier composed by our model. We also implement a back test to validate predictive performance of the model by this catalog.

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

PubMed

Allen, Jeff; Ghattas, Andrew

2016-06-01

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

A Multidisciplinary Approach for Teaching Statistics and Probability

ERIC Educational Resources Information Center

Rao, C. Radhakrishna

1971-01-01

The author presents a syllabus for an introductory (first year after high school) course in statistics and probability and some methods of teaching statistical techniques. The description comes basically from the procedures used at the Indian Statistical Institute, Calcutta. (JG)

Diversity of Poissonian populations.

PubMed

Eliazar, Iddo I; Sokolov, Igor M

2010-01-01

Populations represented by collections of points scattered randomly on the real line are ubiquitous in science and engineering. The statistical modeling of such populations leads naturally to Poissonian populations-Poisson processes on the real line with a distinguished maximal point. Poissonian populations are infinite objects underlying key issues in statistical physics, probability theory, and random fractals. Due to their infiniteness, measuring the diversity of Poissonian populations depends on the lower-bound cut-off applied. This research characterizes the classes of Poissonian populations whose diversities are invariant with respect to the cut-off level applied and establishes an elemental connection between these classes and extreme-value theory. The measures of diversity considered are variance and dispersion, Simpson's index and inverse participation ratio, Shannon's entropy and Rényi's entropy, and Gini's index.

Regional statistics in confined two-dimensional decaying turbulence.

PubMed

Házi, Gábor; Tóth, Gábor

2011-06-28

Two-dimensional decaying turbulence in a square container has been simulated using the lattice Boltzmann method. The probability density function (PDF) of the vorticity and the particle distribution functions have been determined at various regions of the domain. It is shown that, after the initial stage of decay, the regional area averaged enstrophy fluctuates strongly around a mean value in time. The ratio of the regional mean and the overall enstrophies increases monotonously with increasing distance from the wall. This function shows a similar shape to the axial mean velocity profile of turbulent channel flows. The PDF of the vorticity peaks at zero and is nearly symmetric considering the statistics in the overall domain. Approaching the wall, the PDFs become skewed owing to the boundary layer.

Investigating the collision energy dependence of η /s in the beam energy scan at the BNL Relativistic Heavy Ion Collider using Bayesian statistics

NASA Astrophysics Data System (ADS)

Auvinen, Jussi; Bernhard, Jonah E.; Bass, Steffen A.; Karpenko, Iurii

2018-04-01

We determine the probability distributions of the shear viscosity over the entropy density ratio η /s in the quark-gluon plasma formed in Au + Au collisions at √{sN N}=19.6 ,39 , and 62.4 GeV , using Bayesian inference and Gaussian process emulators for a model-to-data statistical analysis that probes the full input parameter space of a transport + viscous hydrodynamics hybrid model. We find the most likely value of η /s to be larger at smaller √{sN N}, although the uncertainties still allow for a constant value between 0.10 and 0.15 for the investigated collision energy range.

Sets, Probability and Statistics: The Mathematics of Life Insurance. [Computer Program.] Second Edition.

ERIC Educational Resources Information Center

King, James M.; And Others

The materials described here represent the conversion of a highly popular student workbook "Sets, Probability and Statistics: The Mathematics of Life Insurance" into a computer program. The program is designed to familiarize students with the concepts of sets, probability, and statistics, and to provide practice using real life examples. It also…

Controlling for Frailty in Pharmacoepidemiologic Studies of Older Adults: Validation of an Existing Medicare Claims-based Algorithm.

PubMed

Cuthbertson, Carmen C; Kucharska-Newton, Anna; Faurot, Keturah R; Stürmer, Til; Jonsson Funk, Michele; Palta, Priya; Windham, B Gwen; Thai, Sydney; Lund, Jennifer L

2018-07-01

Frailty is a geriatric syndrome characterized by weakness and weight loss and is associated with adverse health outcomes. It is often an unmeasured confounder in pharmacoepidemiologic and comparative effectiveness studies using administrative claims data. Among the Atherosclerosis Risk in Communities (ARIC) Study Visit 5 participants (2011-2013; n = 3,146), we conducted a validation study to compare a Medicare claims-based algorithm of dependency in activities of daily living (or dependency) developed as a proxy for frailty with a reference standard measure of phenotypic frailty. We applied the algorithm to the ARIC participants' claims data to generate a predicted probability of dependency. Using the claims-based algorithm, we estimated the C-statistic for predicting phenotypic frailty. We further categorized participants by their predicted probability of dependency (<5%, 5% to <20%, and ≥20%) and estimated associations with difficulties in physical abilities, falls, and mortality. The claims-based algorithm showed good discrimination of phenotypic frailty (C-statistic = 0.71; 95% confidence interval [CI] = 0.67, 0.74). Participants classified with a high predicted probability of dependency (≥20%) had higher prevalence of falls and difficulty in physical ability, and a greater risk of 1-year all-cause mortality (hazard ratio = 5.7 [95% CI = 2.5, 13]) than participants classified with a low predicted probability (<5%). Sensitivity and specificity varied across predicted probability of dependency thresholds. The Medicare claims-based algorithm showed good discrimination of phenotypic frailty and high predictive ability with adverse health outcomes. This algorithm can be used in future Medicare claims analyses to reduce confounding by frailty and improve study validity.

Validation of use of the International Consultation on Incontinence Questionnaire-Urinary Incontinence-Short Form (ICIQ-UI-SF) for impairment rating: a transversal retrospective study of 120 patients.

PubMed

Timmermans, Luc; Falez, Freddy; Mélot, Christian; Wespes, Eric

2013-09-01

A urinary incontinence impairment rating must be a highly accurate, non-invasive exploration of the condition using International Classification of Functioning (ICF)-based assessment tools. The objective of this study was to identify the best evaluation test and to determine an impairment rating model of urinary incontinence. In performing a cross-sectional study comparing successive urodynamic tests using both the International Consultation on Incontinence Questionnaire-Urinary Incontinence-Short Form (ICIQ-UI-SF) and the 1-hr pad-weighing test in 120 patients, we performed statistical likelihood ratio analysis and used logistic regression to calculate the probability of urodynamic incontinence using the most significant independent predictors. Subsequently, we created a template that was based on the significant predictors and the probability of urodynamic incontinence. The mean ICIQ-UI-SF score was 13.5 ± 4.6, and the median pad test value was 8 g. The discrimination statistic (receiver operating characteristic) described how well the urodynamic observations matched the ICIQ-UI-SF scores (under curve area (UDA):0.689) and the pad test data (UDA: 0.693). Using logistic regression analysis, we demonstrated that the best independent predictors of urodynamic incontinence were the patient's age and the ICIQ-UI-SF score. The logistic regression model permitted us to construct an equation to determine the probability of urodynamic incontinence. Using these tools, we created a template to generate a probability index of urodynamic urinary incontinence. Using this probability index, relative to the patient and to the maximum impairment of the whole person (MIWP) relative to urinary incontinence, we were able to calculate a patient's permanent impairment. Copyright © 2012 Wiley Periodicals, Inc.

Mental health difficulties in children with developmental coordination disorder.

PubMed

Lingam, Raghu; Jongmans, Marian J; Ellis, Matthew; Hunt, Linda P; Golding, Jean; Emond, Alan

2012-04-01

To explore the associations between probable developmental coordination disorder (DCD) defined at age 7 years and mental health difficulties at age 9 to 10 years. We analyzed of prospectively collected data (N = 6902) from the Avon Longitudinal Study of Parents and Children. "Probable" DCD was defined by using Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision criteria as those children below the 15th centile of the Avon Longitudinal Study of Parents and Children Coordination Test, with functional limitations in activities of daily living or handwriting, excluding children with neurologic difficulties or an IQ <70. Mental health was measured by using the child-reported Short Moods and Feelings Questionnaire and the parent-reported Strengths and Difficulties Questionnaire. Multiple logistic regression models, with the use of multiple imputation to account for missing data, assessed the associations between probable DCD and mental health difficulties. Adjustments were made for environmental confounding factors, and potential mediating factors such as verbal IQ, associated developmental traits, bullying, self-esteem, and friendships. Children with probable DCD (N = 346) had an increased odds of self-reported depression, odds ratio: 2.08 (95% confidence interval: 1.36-3.19) and parent-reported mental health difficulties odds ratio: 4.23 (95% confidence interval: 3.10-5.77). The odds of mental health difficulties significantly decreased after accounting for verbal IQ, social communication, bullying, and self-esteem. Children with probable DCD had an increased risk of mental health difficulties that, in part, were mediated through associated developmental difficulties, low verbal IQ, poor self-esteem, and bullying. Prevention and treatment of mental health difficulties should be a key element of intervention for children with DCD.

Evaluating the statistical power of DNA-based identification, exemplified by 'The missing grandchildren of Argentina'.

PubMed

Kling, Daniel; Egeland, Thore; Piñero, Mariana Herrera; Vigeland, Magnus Dehli

2017-11-01

Methods and implementations of DNA-based identification are well established in several forensic contexts. However, assessing the statistical power of these methods has been largely overlooked, except in the simplest cases. In this paper we outline general methods for such power evaluation, and apply them to a large set of family reunification cases, where the objective is to decide whether a person of interest (POI) is identical to the missing person (MP) in a family, based on the DNA profile of the POI and available family members. As such, this application closely resembles database searching and disaster victim identification (DVI). If parents or children of the MP are available, they will typically provide sufficient statistical evidence to settle the case. However, if one must resort to more distant relatives, it is not a priori obvious that a reliable conclusion is likely to be reached. In these cases power evaluation can be highly valuable, for instance in the recruitment of additional family members. To assess the power in an identification case, we advocate the combined use of two statistics: the Probability of Exclusion, and the Probability of Exceedance. The former is the probability that the genotypes of a random, unrelated person are incompatible with the available family data. If this is close to 1, it is likely that a conclusion will be achieved regarding general relatedness, but not necessarily the specific relationship. To evaluate the ability to recognize a true match, we use simulations to estimate exceedance probabilities, i.e. the probability that the likelihood ratio will exceed a given threshold, assuming that the POI is indeed the MP. All simulations are done conditionally on available family data. Such conditional simulations have a long history in medical linkage analysis, but to our knowledge this is the first systematic forensic genetics application. Also, for forensic markers mutations cannot be ignored and therefore current models and implementations must be extended. All the tools are freely available in Familias (http://www.familias.no) empowered by the R library paramlink. The above approach is applied to a large and important data set: 'The missing grandchildren of Argentina'. We evaluate the power of 196 families from the DNA reference databank (Banco Nacional de Datos Genéticos, http://www.bndg.gob.ar. As a result we show that 58 of the families have poor statistical power and require additional genetic data to enable a positive identification. Copyright © 2017 Elsevier B.V. All rights reserved.

Evaluating statistical cloud schemes: What can we gain from ground-based remote sensing?

NASA Astrophysics Data System (ADS)

Grützun, V.; Quaas, J.; Morcrette, C. J.; Ament, F.

2013-09-01

Statistical cloud schemes with prognostic probability distribution functions have become more important in atmospheric modeling, especially since they are in principle scale adaptive and capture cloud physics in more detail. While in theory the schemes have a great potential, their accuracy is still questionable. High-resolution three-dimensional observational data of water vapor and cloud water, which could be used for testing them, are missing. We explore the potential of ground-based remote sensing such as lidar, microwave, and radar to evaluate prognostic distribution moments using the "perfect model approach." This means that we employ a high-resolution weather model as virtual reality and retrieve full three-dimensional atmospheric quantities and virtual ground-based observations. We then use statistics from the virtual observation to validate the modeled 3-D statistics. Since the data are entirely consistent, any discrepancy occurring is due to the method. Focusing on total water mixing ratio, we find that the mean ratio can be evaluated decently but that it strongly depends on the meteorological conditions as to whether the variance and skewness are reliable. Using some simple schematic description of different synoptic conditions, we show how statistics obtained from point or line measurements can be poor at representing the full three-dimensional distribution of water in the atmosphere. We argue that a careful analysis of measurement data and detailed knowledge of the meteorological situation is necessary to judge whether we can use the data for an evaluation of higher moments of the humidity distribution used by a statistical cloud scheme.

Operational foreshock forecasting: Fifteen years after

NASA Astrophysics Data System (ADS)

Ogata, Y.

2010-12-01

We are concerned with operational forecasting of the probability that events are foreshocks of a forthcoming earthquake that is significantly larger (mainshock). Specifically, we define foreshocks as the preshocks substantially smaller than the mainshock by a magnitude gap of 0.5 or larger. The probability gain of foreshock forecast is extremely high compare to long-term forecast by renewal processes or various alarm-based intermediate-term forecasts because of a large event’s low occurrence rate in a short period and a narrow target region. Thus, it is desired to establish operational foreshock probability forecasting as seismologists have done for aftershocks. When a series of earthquakes occurs in a region, we attempt to discriminate foreshocks from a swarm or mainshock-aftershock sequence. Namely, after real time identification of an earthquake cluster using methods such as the single-link algorithm, the probability is calculated by applying statistical features that discriminate foreshocks from other types of clusters, by considering the events' stronger proximity in time and space and tendency towards chronologically increasing magnitudes. These features were modeled for probability forecasting and the coefficients of the model were estimated in Ogata et al. (1996) for the JMA hypocenter data (M≧4, 1926-1993). Currently, fifteen years has passed since the publication of the above-stated work so that we are able to present the performance and validation of the forecasts (1994-2009) by using the same model. Taking isolated events into consideration, the probability of the first events in a potential cluster being a foreshock vary in a range between 0+% and 10+% depending on their locations. This conditional forecasting performs significantly better than the unconditional (average) foreshock probability of 3.7% throughout Japan region. Furthermore, when we have the additional events in a cluster, the forecast probabilities range more widely from nearly 0% to about 40% depending on the discrimination features among the events in the cluster. This conditional forecasting further performs significantly better than the unconditional foreshock probability of 7.3%, which is the average probability of the plural events in the earthquake clusters. Indeed, the frequency ratios of the actual foreshocks are consistent with the forecasted probabilities. Reference: Ogata, Y., Utsu, T. and Katsura, K. (1996). Statistical discrimination of foreshocks from other earthquake clusters, Geophys. J. Int. 127, 17-30.

Optimizing exoplanet transit searches

NASA Astrophysics Data System (ADS)

Herrero, E.; Ribas, I.; Jordi, C.

2013-05-01

Exoplanet searches using the transit technique are nowadays providing a great number of findings. Most exoplanet transit detection programs that are currently underway are focused on large catalogs of stars with no pre-selection. This necessarily makes such surveys quite inefficient, because huge amounts of data are processed for a relatively low transiting planet yield. In this work we investigate a method to increase the efficiency of a targeted exoplanet search with the transit technique by preselecting a subset of candidates from large catalogs of stars. Assuming spin-orbit alignment, this can be done by considering stars that have higher probability to be oriented nearly equator-on (inclination close to 90°). We use activity-rotation velocity relations for low-mass stars to study the dependence of the position in the activity - v sin(i) diagram on the stellar axis inclination. We compose a catalog of G-, K-, M-type main sequence simulated stars using isochrones, an isotropic inclination distribution and empirical relations to obtain their rotation periods and activity indexes. Then the activity-vsini diagram is filled and statistics are applied to trace the areas containing the higher ratio of stars with inclinations above 80°. A similar statistics is applied to stars from real catalogs with log(R'_{HK}) and v sin(i) data to find their probability of being equator-on. We present the method used to generate the simulated star catalog and the subsequent statistics to find the highly inclined stars from real catalogs using the activity-v sin(i) diagram. Several catalogs from the literature are analysed and a subsample of stars with the highest probability of being equator-on is presented. Assuming spin-orbit alignment, the efficiency of an exoplanet transit search in the resulting subsample of probably highly inclined stars is estimated to be two to three times higher than with a global search with no pre-selection.

Statistical Significance of Periodicity and Log-Periodicity with Heavy-Tailed Correlated Noise

NASA Astrophysics Data System (ADS)

Zhou, Wei-Xing; Sornette, Didier

We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or log-periodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with non-Gaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis, which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the false-alarm probability of the largest spectral peak of the Lomb periodogram in the presence of power-law distributed noises, of short-range and of long-range fractional-Gaussian noises. Increasing heavy-tailness (respectively correlations describing persistence) tends to decrease (respectively increase) the false-alarm probability of finding a large spurious Lomb peak. Increasing anti-persistence tends to decrease the false-alarm probability. We also study the interplay between heavy-tailness and long-range correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should in principle characterize the Lomb peak height, its width and its relations to other peaks in the complete spectrum. As a step towards this full characterization, we construct the joint-distribution of the frequency position (relative to other peaks) and of the height of the highest peak of the power spectrum. We also provide the distributions of the ratio of the highest Lomb peak to the second highest one. Using the insight obtained by the present statistical study, we re-examine previously reported claims of ``log-periodicity'' and find that the credibility for log-periodicity in 2D-freely decaying turbulence is weakened while it is strengthened for fracture, for the ion-signature prior to the Kobe earthquake and for financial markets.

Probability workshop to be better in probability topic

NASA Astrophysics Data System (ADS)

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

2015-02-01

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

Dangerous "spin": the probability myth of evidence-based prescribing - a Merleau-Pontyian approach.

PubMed

Morstyn, Ron

2011-08-01

The aim of this study was to examine logical positivist statistical probability statements used to support and justify "evidence-based" prescribing rules in psychiatry when viewed from the major philosophical theories of probability, and to propose "phenomenological probability" based on Maurice Merleau-Ponty's philosophy of "phenomenological positivism" as a better clinical and ethical basis for psychiatric prescribing. The logical positivist statistical probability statements which are currently used to support "evidence-based" prescribing rules in psychiatry have little clinical or ethical justification when subjected to critical analysis from any of the major theories of probability and represent dangerous "spin" because they necessarily exclude the individual , intersubjective and ambiguous meaning of mental illness. A concept of "phenomenological probability" founded on Merleau-Ponty's philosophy of "phenomenological positivism" overcomes the clinically destructive "objectivist" and "subjectivist" consequences of logical positivist statistical probability and allows psychopharmacological treatments to be appropriately integrated into psychiatric treatment.

Constructing diagnostic likelihood: clinical decisions using subjective versus statistical probability.

PubMed

Kinnear, John; Jackson, Ruth

2017-07-01

Although physicians are highly trained in the application of evidence-based medicine, and are assumed to make rational decisions, there is evidence that their decision making is prone to biases. One of the biases that has been shown to affect accuracy of judgements is that of representativeness and base-rate neglect, where the saliency of a person's features leads to overestimation of their likelihood of belonging to a group. This results in the substitution of 'subjective' probability for statistical probability. This study examines clinicians' propensity to make estimations of subjective probability when presented with clinical information that is considered typical of a medical condition. The strength of the representativeness bias is tested by presenting choices in textual and graphic form. Understanding of statistical probability is also tested by omitting all clinical information. For the questions that included clinical information, 46.7% and 45.5% of clinicians made judgements of statistical probability, respectively. Where the question omitted clinical information, 79.9% of clinicians made a judgement consistent with statistical probability. There was a statistically significant difference in responses to the questions with and without representativeness information (χ2 (1, n=254)=54.45, p<0.0001). Physicians are strongly influenced by a representativeness bias, leading to base-rate neglect, even though they understand the application of statistical probability. One of the causes for this representativeness bias may be the way clinical medicine is taught where stereotypic presentations are emphasised in diagnostic decision making. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Incompressible variable-density turbulence in an external acceleration field

DOE PAGES

Gat, Ilana; Matheou, Georgios; Chung, Daniel; ...

2017-08-24

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range ofmore » $$1.05\\leqslant R\\equiv \\unicode[STIX]{x1D70C}_{1}/\\unicode[STIX]{x1D70C}_{2}\\leqslant 10$$are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate$${\\sim}t^{1/2}$$followed by a turbulence-dominated regime with a growth rate$${\\sim}t^{3}$$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.« less

Incompressible variable-density turbulence in an external acceleration field

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

Gat, Ilana; Matheou, Georgios; Chung, Daniel

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range ofmore » $$1.05\\leqslant R\\equiv \\unicode[STIX]{x1D70C}_{1}/\\unicode[STIX]{x1D70C}_{2}\\leqslant 10$$are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate$${\\sim}t^{1/2}$$followed by a turbulence-dominated regime with a growth rate$${\\sim}t^{3}$$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. In conclusion, the shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.« less

Statistical learning of action: the role of conditional probability.

PubMed

Meyer, Meredith; Baldwin, Dare

2011-12-01

Identification of distinct units within a continuous flow of human action is fundamental to action processing. Such segmentation may rest in part on statistical learning. In a series of four experiments, we examined what types of statistics people can use to segment a continuous stream involving many brief, goal-directed action elements. The results of Experiment 1 showed no evidence for sensitivity to conditional probability, whereas Experiment 2 displayed learning based on joint probability. In Experiment 3, we demonstrated that additional exposure to the input failed to engender sensitivity to conditional probability. However, the results of Experiment 4 showed that a subset of adults-namely, those more successful at identifying actions that had been seen more frequently than comparison sequences-were also successful at learning conditional-probability statistics. These experiments help to clarify the mechanisms subserving processing of intentional action, and they highlight important differences from, as well as similarities to, prior studies of statistical learning in other domains, including language.

Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

PubMed

Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie

2016-01-01

The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.

Interpretation of the results of statistical measurements. [search for basic probability model

NASA Technical Reports Server (NTRS)

Olshevskiy, V. V.

1973-01-01

For random processes, the calculated probability characteristic, and the measured statistical estimate are used in a quality functional, which defines the difference between the two functions. Based on the assumption that the statistical measurement procedure is organized so that the parameters for a selected model are optimized, it is shown that the interpretation of experimental research is a search for a basic probability model.

Study of Heavy-ion Induced Fission for Heavy Element Synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.; Ikezoe, H.; Hofmann, S.; Ackermann, D.; Aritomo, Y.; Comas, V. F.; Düllmann, Ch. E.; Heinz, S.; Heredia, J. A.; Heßberger, F. P.; Hirose, K.; Khuyagbaatar, J.; Kindler, B.; Kojouharov, I.; Lommel, B.; Makii, M.; Mann, R.; Mitsuoka, S.; Nishinaka, I.; Ohtsuki, T.; Saro, S.; Schädel, M.; Popeko, A. G.; Türler, A.; Wakabayashi, Y.; Watanabe, Y.; Yakushev, A.; Yeremin, A.

2014-05-01

Fission fragment mass distributions were measured in heavy-ion induced fission of 238U. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and quasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model for the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that sub-barrier energies can be used for heavy element synthesis.

Defensive efficacy interim design: Dynamic benefit/risk ratio view using probability of success.

PubMed

Tang, Zhongwen

2017-01-01

Traditional efficacy interim design is based on alpha spending which does not have intuitive interpretation and hence is difficult to communicate with non-statistician colleagues. The alpha-spending approach is based on efficacy alone and hence does not have the flexibility to incorporate newly emerged safety signal. Newly emerged safety signal may nullify the originally set efficacy boundary. In contrast, the probability of success (POS) concept has intuitive interpretation and hence can facilitate our communication with non-statistician colleagues and help to obtain health authority (HA) buying. The success criteria of POS are not restricted to statistical significance. Hence, POS has the capability to incorporate both efficacy and safety information. We propose to use POS and its credible interval to design efficacy interim. In the proposed method, the efficacy boundary is adjustable to offset newly emerged safety signal.

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.

Toward "Constructing" the Concept of Statistical Power: An Optical Analogy.

ERIC Educational Resources Information Center

Rogers, Bruce G.

This paper presents a visual analogy that may be used by instructors to teach the concept of statistical power in statistical courses. Statistical power is mathematically defined as the probability of rejecting a null hypothesis when that null is false, or, equivalently, the probability of detecting a relationship when it exists. The analogy…

A method for developing design diagrams for ceramic and glass materials using fatigue data

NASA Technical Reports Server (NTRS)

Heslin, T. M.; Magida, M. B.; Forrest, K. A.

1986-01-01

The service lifetime of glass and ceramic materials can be expressed as a plot of time-to-failure versus applied stress whose plot is parametric in percent probability of failure. This type of plot is called a design diagram. Confidence interval estimates for such plots depend on the type of test that is used to generate the data, on assumptions made concerning the statistical distribution of the test results, and on the type of analysis used. This report outlines the development of design diagrams for glass and ceramic materials in engineering terms using static or dynamic fatigue tests, assuming either no particular statistical distribution of test results or a Weibull distribution and using either median value or homologous ratio analysis of the test results.

Underprotection of unpredictable statistical lives compared to predictable ones

PubMed Central

Evans, Nicholas G.; Cotton-Barratt, Owen

2016-01-01

Existing ethical discussion considers the differences in care for identified versus statistical lives. However there has been little attention to the different degrees of care that are taken for different kinds of statistical lives. Here we argue that for a given number of statistical lives at stake, there will sometimes be different, and usually greater care taken to protect predictable statistical lives, in which the number of lives that will be lost can be predicted fairly accurately, than for unpredictable statistical lives, where the lives are at stake because of a low-probability event, such that most likely no one will be affected by the decision but with low probability some lives will be at stake. One reason for this difference is the statistical challenge of estimating low probabilities, and in particular the tendency of common approaches to underestimate these probabilities. Another is the existence of rational incentives to treat unpredictable risks as if the probabilities were lower than they are. Some of these factors apply outside the pure economic context, to institutions, individuals, and governments. We argue that there is no ethical reason to treat unpredictable statistical lives differently from predictable statistical lives. Moreover, lives that are unpredictable from the perspective of an individual agent may become predictable when aggregated to the level of a societal decision. Underprotection of unpredictable statistical lives is a form of market failure that may need to be corrected by altering regulation, introducing compulsory liability insurance, or other social policies. PMID:27393181

Negative values of quasidistributions and quantum wave and number statistics

NASA Astrophysics Data System (ADS)

Peřina, J.; Křepelka, J.

2018-04-01

We consider nonclassical wave and number quantum statistics, and perform a decomposition of quasidistributions for nonlinear optical down-conversion processes using Bessel functions. We show that negative values of the quasidistribution do not directly represent probabilities; however, they directly influence measurable number statistics. Negative terms in the decomposition related to the nonclassical behavior with negative amplitudes of probability can be interpreted as positive amplitudes of probability in the negative orthogonal Bessel basis, whereas positive amplitudes of probability in the positive basis describe classical cases. However, probabilities are positive in all cases, including negative values of quasidistributions. Negative and positive contributions of decompositions to quasidistributions are estimated. The approach can be adapted to quantum coherence functions.

Detection performance in clutter with variable resolution

NASA Astrophysics Data System (ADS)

Schmieder, D. E.; Weathersby, M. R.

1983-07-01

Experiments were conducted to determine the influence of background clutter on target detection criteria. The experiment consisted of placing observers in front of displayed images on a TV monitor. Observer ability to detect military targets embedded in simulated natural and manmade background clutter was measured when there was unlimited viewing time. Results were described in terms of detection probability versus target resolution for various signal to clutter ratios (SCR). The experiments were preceded by a search for a meaningful clutter definition. The selected definition was a statistical measure computed by averaging the standard deviation of contiguous scene cells over the whole scene. The cell size was comparable to the target size. Observer test results confirmed the expectation that the resolution required for a given detection probability was a continuum function of the clutter level. At the lower SCRs the resolution required for a high probability of detection was near 6 line pairs per target (LP/TGT), while at the higher SCRs it was found that a resoluton of less than 0.25 LP/TGT would yield a high probability of detection. These results are expected to aid in target acquisition performance modeling and to lead to improved specifications for imaging automatic target screeners.

An Experiment Quantifying The Effect Of Clutter On Target Detection

NASA Astrophysics Data System (ADS)

Weathersby, Marshall R.; Schmieder, David E.

1985-01-01

Experiments were conducted to determine the influence of background clutter on target detection criteria. The experiment consisted of placing observers in front of displayed images on a TV monitor. Observer ability to detect military targets embedded in simulated natural and manmade background clutter was measured when there was unlimited viewing time. Results were described in terms of detection probability versus target resolution for various signal to clutter ratios (SCR). The experiments were preceded by a search for a meaningful clutter definition. The selected definition was a statistical measure computed by averaging the standard deviation of contiguous scene cells over the whole scene. The cell size was comparable to the target size. Observer test results confirmed the expectation that the resolution required for a given detection probability was a continuum function of the clutter level. At the lower SCRs the resolution required for a high probability of detection was near 6 lines pairs per target (LP/TGT), while at the higher SCRs it was found that a resolution of less than 0.25 LP/TGT would yield a high probability of detection. These results are expected to aid in target acquisition performance modeling and to lead to improved specifications for imaging automatic target screeners.

Quantifying Treatment Benefit in Molecular Subgroups to Assess a Predictive Biomarker

PubMed Central

Iasonos, Alexia; Chapman, Paul B.; Satagopan, Jaya M.

2016-01-01

There is an increased interest in finding predictive biomarkers that can guide treatment options for both mutation carriers and non-carriers. The statistical assessment of variation in treatment benefit (TB) according to the biomarker carrier status plays an important role in evaluating predictive biomarkers. For time to event endpoints, the hazard ratio (HR) for interaction between treatment and a biomarker from a Proportional Hazards regression model is commonly used as a measure of variation in treatment benefit. While this can be easily obtained using available statistical software packages, the interpretation of HR is not straightforward. In this article, we propose different summary measures of variation in TB on the scale of survival probabilities for evaluating a predictive biomarker. The proposed summary measures can be easily interpreted as quantifying differential in TB in terms of relative risk or excess absolute risk due to treatment in carriers versus non-carriers. We illustrate the use and interpretation of the proposed measures using data from completed clinical trials. We encourage clinical practitioners to interpret variation in TB in terms of measures based on survival probabilities, particularly in terms of excess absolute risk, as opposed to HR. PMID:27141007

Empirical likelihood method for non-ignorable missing data problems.

PubMed

Guan, Zhong; Qin, Jing

2017-01-01

Missing response problem is ubiquitous in survey sampling, medical, social science and epidemiology studies. It is well known that non-ignorable missing is the most difficult missing data problem where the missing of a response depends on its own value. In statistical literature, unlike the ignorable missing data problem, not many papers on non-ignorable missing data are available except for the full parametric model based approach. In this paper we study a semiparametric model for non-ignorable missing data in which the missing probability is known up to some parameters, but the underlying distributions are not specified. By employing Owen (1988)'s empirical likelihood method we can obtain the constrained maximum empirical likelihood estimators of the parameters in the missing probability and the mean response which are shown to be asymptotically normal. Moreover the likelihood ratio statistic can be used to test whether the missing of the responses is non-ignorable or completely at random. The theoretical results are confirmed by a simulation study. As an illustration, the analysis of a real AIDS trial data shows that the missing of CD4 counts around two years are non-ignorable and the sample mean based on observed data only is biased.

Molecular dynamics study of the conformational properties of cyclohexadecane

NASA Astrophysics Data System (ADS)

Zhang, Renshi; Mattice, Wayne L.

1993-06-01

Molecular dynamics has been used for the first time for the study of the conformational properties of cyclohexadecane, c-C16H32. By analyzing a long molecular dynamics trajectory (14.5 ns) at 450 K, equilibrium statistics such as the relative populations of different isomeric conformers and the probability ratios, p(gt)/p(tt), p(gg)/p(tt), and p(gg)/p(gtg), of different conformational segments, have been studied. The dynamic properties including the transition modes of gauche migration and gauche-pair creation, which have been reported before in n-alkanes, and the auto- and cross-correlations of the bond dihedral angles, have also been obtained. It was possible to make direct comparisons on some of the statistics with theory and experiment. Most of the results extracted from the molecular dynamics trajectory lie in between previously reported experimental and theoretical values. Many previously predicted conformers have been confirmed by our simulations. The results of the population probability of the most populated conformer seems to suggest that an earlier discrepancy between the theoretical works and an experimental work originates from insufficient samplings in earlier theoretical works, rather than from their inaccurate force field.

Liquisolid technique: a promising alternative to conventional coating for improvement of drug photostability in solid dosage forms.

PubMed

Khames, Ahmed

2013-10-01

The objective of this study was to investigate the photoprotective effect of liquisolid technique on amlodipine, a calcium channel blocker antihypertensive drug, representing a photosensitive drug model. Several liquisolid formulations were prepared using propylene glycol as a water-miscible nonvolatile vehicle at drug/solvent ratio (1:1), Avicel PH 102 as a carrier, nanometer-sized amorphous silicon and titanium dioxide either alone or in combination as coating materials. The carrier/coat ratio (R) was varied from 5 to 50. The prepared liquisolids, coated, noncoated tablets and drug substance were irradiated with a light dose of 0.5 W/m(2)/h visible light, 55.1 W/m(2)/h UVA, and 0.247 W/m(2)/h UVB for 8 h. The effect of coating material type and (R) value on the drug dissolution rate and photostability was studied. Results were statistically analyzed by post hoc two-way ANOVA at a probability level (α = 0.05). The results indicated that liquisolid technique not only improved the dissolution rate, but also significantly inhibited the photodegradative effect of different light energies in all prepared liquisolid formulations. The residual drug percentage reached 97.37% in comparison to 73.8% for the drug substance after 8 h of irradiation. The residual drug percentage was affected by the (R) value. Statistically; the detected difference was significant at the selected probability level (α = 0.05). It can thus be concluded that this liquisolid technique is a promising alternative to conventional coating procedures in formulations containing photosensitive drugs.

Know the risk, take the win: how executive functions and probability processing influence advantageous decision making under risk conditions.

PubMed

Brand, Matthias; Schiebener, Johannes; Pertl, Marie-Theres; Delazer, Margarete

2014-01-01

Recent models on decision making under risk conditions have suggested that numerical abilities are important ingredients of advantageous decision-making performance, but empirical evidence is still limited. The results of our first study show that logical reasoning and basic mental calculation capacities predict ratio processing and that ratio processing predicts decision making under risk. In the second study, logical reasoning together with executive functions predicted probability processing (numeracy and probability knowledge), and probability processing predicted decision making under risk. These findings suggest that increasing an individual's understanding of ratios and probabilities should lead to more advantageous decisions under risk conditions.

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

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…

Wald Sequential Probability Ratio Test for Analysis of Orbital Conjunction Data

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis; Gold, Dara

2013-01-01

We propose a Wald Sequential Probability Ratio Test for analysis of commonly available predictions associated with spacecraft conjunctions. Such predictions generally consist of a relative state and relative state error covariance at the time of closest approach, under the assumption that prediction errors are Gaussian. We show that under these circumstances, the likelihood ratio of the Wald test reduces to an especially simple form, involving the current best estimate of collision probability, and a similar estimate of collision probability that is based on prior assumptions about the likelihood of collision.

Multiple statistical tests: Lessons from a d20.

PubMed

Madan, Christopher R

2016-01-01

Statistical analyses are often conducted with α= .05. When multiple statistical tests are conducted, this procedure needs to be adjusted to compensate for the otherwise inflated Type I error. In some instances in tabletop gaming, sometimes it is desired to roll a 20-sided die (or 'd20') twice and take the greater outcome. Here I draw from probability theory and the case of a d20, where the probability of obtaining any specific outcome is (1)/ 20, to determine the probability of obtaining a specific outcome (Type-I error) at least once across repeated, independent statistical tests.

Meteor trail footprint statistics

NASA Astrophysics Data System (ADS)

Mui, S. Y.; Ellicott, R. C.

Footprint statistics derived from field-test data are presented. The statistics are the probability that two receivers will lie in the same footprint. The dependence of the footprint statistics on the transmitter range, link orientation, and antenna polarization are examined. Empirical expressions for the footprint statistics are presented. The need to distinguish the instantaneous footprint, which is the area illuminated at a particular instant, from the composite footprint, which is the total area illuminated during the lifetime of the meteor trail, is explained. The statistics for the instantaneous and composite footprints have been found to be similar. The only significant difference lies in the parameter that represents the probability of two colocated receivers being in the same footprint. The composite footprint statistics can be used to calculate the space diversity gain of a multiple-receiver system. The instantaneous footprint statistics are useful in the evaluation of the interference probability in a network of meteor burst communication nodes.

Characterisation of seasonal flood types according to timescales in mixed probability distributions

NASA Astrophysics Data System (ADS)

Fischer, Svenja; Schumann, Andreas; Schulte, Markus

2016-08-01

When flood statistics are based on annual maximum series (AMS), the sample often contains flood peaks, which differ in their genesis. If the ratios among event types change over the range of observations, the extrapolation of a probability distribution function (pdf) can be dominated by a majority of events that belong to a certain flood type. If this type is not typical for extraordinarily large extremes, such an extrapolation of the pdf is misleading. To avoid this breach of the assumption of homogeneity, seasonal models were developed that differ between winter and summer floods. We show that a distinction between summer and winter floods is not always sufficient if seasonal series include events with different geneses. Here, we differentiate floods by their timescales into groups of long and short events. A statistical method for such a distinction of events is presented. To demonstrate their applicability, timescales for winter and summer floods in a German river basin were estimated. It is shown that summer floods can be separated into two main groups, but in our study region, the sample of winter floods consists of at least three different flood types. The pdfs of the two groups of summer floods are combined via a new mixing model. This model considers that information about parallel events that uses their maximum values only is incomplete because some of the realisations are overlaid. A statistical method resulting in an amendment of statistical parameters is proposed. The application in a German case study demonstrates the advantages of the new model, with specific emphasis on flood types.

Interaction between body mass index and central adiposity and risk of incident cognitive impairment and dementia: results from the Women's Health Initiative Memory Study.

PubMed

Kerwin, Diana R; Gaussoin, Sarah A; Chlebowski, Rowan T; Kuller, Lewis H; Vitolins, Mara; Coker, Laura H; Kotchen, Jane M; Nicklas, Barbara J; Wassertheil-Smoller, Sylvia; Hoffmann, Raymond G; Espeland, Mark A

2011-01-01

To assess the relationship between body mass index (BMI) and waist-hip ratio (WHR) and the clinical end points of cognitive impairment and probable dementia in a cohort of older women enrolled in the Women's Health Initiative Memory Study (WHIMS). Prospective, randomized clinical trial of hormone therapies with annual cognitive assessments and anthropometrics. Fourteen U.S. clinical sites of the WHIMS. Seven thousand one hundred sixty-three postmenopausal women aged 65 to 80 without dementia. Annual cognitive assessments, average follow-up of 4.4 years, including classification of incident cognitive impairment and probable dementia. Height, weight, waist, and hip measurements were assessed at baseline, and a waist-hip ratio (WHR) of 0.8 or greater was used as a marker of central adiposity. There were statistically significant interactions between BMI and WHR and incident cognitive impairment and probable dementia with and without adjustment for a panel of cognitive risk factors. Women with a WHR of 0.80 or greater with a BMI of 20.0 to 24.9 kg/m² had a greater risk of cognitive impairment and probable dementia than more-obese women or women with a WHR less than 0.80, although women with a WHR less than 0.80 and a BMI of 20.0 to 24.9 kg/m² had poorer scores on cognitive assessments. WHR affects the relationship between BMI and risk of cognitive impairment and probable dementia in older women. Underweight women (BMI < 20.0 kg/m²) with a WHR less than 0.80 had a greater risk than those with higher BMIs. In normal-weight to obese women (20.0-29.9 kg/m², central adiposity (WHR ≥ 0.80) is associated with greater risk of cognitive impairment and probable dementia than in women with higher BMI. These data suggest that central adiposity as a risk factor for cognitive impairment and probable dementia in normal-weight women. © 2011, Copyright the Authors. Journal compilation © 2011, The American Geriatrics Society.

Bivariate categorical data analysis using normal linear conditional multinomial probability model.

PubMed

Sun, Bingrui; Sutradhar, Brajendra

2015-02-10

Bivariate multinomial data such as the left and right eyes retinopathy status data are analyzed either by using a joint bivariate probability model or by exploiting certain odds ratio-based association models. However, the joint bivariate probability model yields marginal probabilities, which are complicated functions of marginal and association parameters for both variables, and the odds ratio-based association model treats the odds ratios involved in the joint probabilities as 'working' parameters, which are consequently estimated through certain arbitrary 'working' regression models. Also, this later odds ratio-based model does not provide any easy interpretations of the correlations between two categorical variables. On the basis of pre-specified marginal probabilities, in this paper, we develop a bivariate normal type linear conditional multinomial probability model to understand the correlations between two categorical variables. The parameters involved in the model are consistently estimated using the optimal likelihood and generalized quasi-likelihood approaches. The proposed model and the inferences are illustrated through an intensive simulation study as well as an analysis of the well-known Wisconsin Diabetic Retinopathy status data. Copyright © 2014 John Wiley & Sons, Ltd.

Teaching Basic Probability in Undergraduate Statistics or Management Science Courses

ERIC Educational Resources Information Center

Naidu, Jaideep T.; Sanford, John F.

2017-01-01

Standard textbooks in core Statistics and Management Science classes present various examples to introduce basic probability concepts to undergraduate business students. These include tossing of a coin, throwing a die, and examples of that nature. While these are good examples to introduce basic probability, we use improvised versions of Russian…

Evidence-Based Medicine as a Tool for Undergraduate Probability and Statistics Education.

PubMed

Masel, J; Humphrey, P T; Blackburn, B; Levine, J A

2015-01-01

Most students have difficulty reasoning about chance events, and misconceptions regarding probability can persist or even strengthen following traditional instruction. Many biostatistics classes sidestep this problem by prioritizing exploratory data analysis over probability. However, probability itself, in addition to statistics, is essential both to the biology curriculum and to informed decision making in daily life. One area in which probability is particularly important is medicine. Given the preponderance of pre health students, in addition to more general interest in medicine, we capitalized on students' intrinsic motivation in this area to teach both probability and statistics. We use the randomized controlled trial as the centerpiece of the course, because it exemplifies the most salient features of the scientific method, and the application of critical thinking to medicine. The other two pillars of the course are biomedical applications of Bayes' theorem and science and society content. Backward design from these three overarching aims was used to select appropriate probability and statistics content, with a focus on eliciting and countering previously documented misconceptions in their medical context. Pretest/posttest assessments using the Quantitative Reasoning Quotient and Attitudes Toward Statistics instruments are positive, bucking several negative trends previously reported in statistics education. © 2015 J. Masel et al. CBE—Life Sciences Education © 2015 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

The exact probability distribution of the rank product statistics for replicated experiments.

PubMed

Eisinga, Rob; Breitling, Rainer; Heskes, Tom

2013-03-18

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Evaluation of trace analyte identification in complex matrices by low-resolution gas chromatography--Mass spectrometry through signal simulation.

PubMed

Bettencourt da Silva, Ricardo J N

2016-04-01

The identification of trace levels of compounds in complex matrices by conventional low-resolution gas chromatography hyphenated with mass spectrometry is based in the comparison of retention times and abundance ratios of characteristic mass spectrum fragments of analyte peaks from calibrators with sample peaks. Statistically sound criteria for the comparison of these parameters were developed based on the normal distribution of retention times and the simulation of possible non-normal distribution of correlated abundances ratios. The confidence level used to set the statistical maximum and minimum limits of parameters defines the true positive rates of identifications. The false positive rate of identification was estimated from worst-case signal noise models. The estimated true and false positive identifications rate from one retention time and two correlated ratios of three fragments abundances were combined using simple Bayes' statistics to estimate the probability of compound identification being correct designated examination uncertainty. Models of the variation of examination uncertainty with analyte quantity allowed the estimation of the Limit of Examination as the lowest quantity that produced "Extremely strong" evidences of compound presence. User friendly MS-Excel files are made available to allow the easy application of developed approach in routine and research laboratories. The developed approach was successfully applied to the identification of chlorpyrifos-methyl and malathion in QuEChERS method extracts of vegetables with high water content for which the estimated Limit of Examination is 0.14 mg kg(-1) and 0.23 mg kg(-1) respectively. Copyright © 2015 Elsevier B.V. All rights reserved.

Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

DOE PAGES

Zhu, Lin; Dai, Zhenxue; Gong, Huili; ...

2015-06-12

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less

Log-Linear Models for Gene Association

PubMed Central

Hu, Jianhua; Joshi, Adarsh; Johnson, Valen E.

2009-01-01

We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data that have been reduced to contingency tables using ranks of observations within subjects, and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens’ sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in a microarray study for which it was possible to obtain biological confirmation of detected interactions. PMID:19655032

Fusion-fission Study at JAEA for Heavy-element Synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.

Fission fragment mass distributions were measured in the heavy-ion induced fission using 238U target nucleus. The mass distribu- tions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their inci- dent energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that the sub-barrier energies can be used for heavy element synthesis.

In-beam fissio study at JAEA for heavy element synthesis

NASA Astrophysics Data System (ADS)

Nishio, K.; Ikezoe, H.; Hofmann, S.; Ackermann, D.; Aritomo, Y.; Comas, V. F.; Düllmann, Ch. E.; Heinz, S.; Heredia, J. A.; Heßberger, F. P.; Hirose, K.; Khuyagbaatar, J.; Kindler, B.; Kojouharov, I.; Lommel, B.; Makii, M.; Mann, R.; Mitsuoka, S.; Nishinaka, I.; Ohtsuki, T.; Saro, S.; Schädel, M.; Popeko, A. G.; Türler, A.; Wakabayashi, Y.; Watanabe, Y.; Yakushev, A.; Yeremin, A.

2013-04-01

Fission fragment mass distributions were measured in the heavy-ion induced fission using 238U target nucleus. The mass distributions changed drastically with incident energy. The results are explained by a change of the ratio between fusion and qasifission with nuclear orientation. A calculation based on a fluctuation dissipation model reproduced the mass distributions and their incident energy dependence. Fusion probability was determined in the analysis. Evaporation residue cross sections were calculated with a statistical model in the reactions of 30Si+238U and 34S+238U using the obtained fusion probability in the entrance channel. The results agree with the measured cross sections of 263,264Sg and 267,268Hs, produced by 30Si+238U and 34S+238U, respectively. It is also suggested that the sub-barrier energies can be used for heavy element synthesis.

Too True to be Bad: When Sets of Studies With Significant and Nonsignificant Findings Are Probably True.

PubMed

Lakens, Daniël; Etz, Alexander J

2017-11-01

Psychology journals rarely publish nonsignificant results. At the same time, it is often very unlikely (or "too good to be true") that a set of studies yields exclusively significant results. Here, we use likelihood ratios to explain when sets of studies that contain a mix of significant and nonsignificant results are likely to be true or "too true to be bad." As we show, mixed results are not only likely to be observed in lines of research but also, when observed, often provide evidence for the alternative hypothesis, given reasonable levels of statistical power and an adequately controlled low Type 1 error rate. Researchers should feel comfortable submitting such lines of research with an internal meta-analysis for publication. A better understanding of probabilities, accompanied by more realistic expectations of what real sets of studies look like, might be an important step in mitigating publication bias in the scientific literature.

Muscle contraction and the elasticity-mediated crosstalk effect

NASA Astrophysics Data System (ADS)

Dharan, Nadiv; Farago, Oded

2013-05-01

Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively generate in actin filaments. Here, we use a statistical mechanical analysis to investigate the influence of the EMC effect on the sarcomere — the basic contractile unit of skeletal muscles. We demonstrate that the EMC effect leads to an increase in the attachment probability of motors located near the end of the sarcomere while simultaneously decreasing the attachment probability of the motors in the central part. Such a polarized attachment probability would impair the motors' ability to cooperate efficiently. Interestingly, this undesired phenomenon becomes significant only when the system size exceeds that of the sarcomere in skeletal muscles, which provides an explanation for the remarkable lack of sarcomere variability in vertebrates. Another phenomenon that we investigate is the recently observed increase in the duty ratio of the motors with the tension in muscle. We reveal that the celebrated Hill's equation for muscle contraction is very closely related to this observation.

Heterogeneities in the case fatality ratio in the West African Ebola outbreak 2013–2016

PubMed Central

Ariyarajah, Archchun; Blake, Isobel M.; Dorigatti, Ilaria; Eckmanns, Tim; Fraser, Christophe; Hinsley, Wes; Jombart, Thibaut; Mills, Harriet L.; Newton, Emily; Nouvellet, Pierre; Perkins, Devin; Riley, Steven; Schumacher, Dirk; Shah, Anita; Van Kerkhove, Maria D.; Dye, Christopher; Ferguson, Neil M.

2017-01-01

The 2013–2016 Ebola outbreak in West Africa is the largest on record with 28 616 confirmed, probable and suspected cases and 11 310 deaths officially recorded by 10 June 2016, the true burden probably considerably higher. The case fatality ratio (CFR: proportion of cases that are fatal) is a key indicator of disease severity useful for gauging the appropriate public health response and for evaluating treatment benefits, if estimated accurately. We analysed individual-level clinical outcome data from Guinea, Liberia and Sierra Leone officially reported to the World Health Organization. The overall mean CFR was 62.9% (95% CI: 61.9% to 64.0%) among confirmed cases with recorded clinical outcomes. Age was the most important modifier of survival probabilities, but country, stage of the epidemic and whether patients were hospitalized also played roles. We developed a statistical analysis to detect outliers in CFR between districts of residence and treatment centres (TCs), adjusting for known factors influencing survival and identified eight districts and three TCs with a CFR significantly different from the average. From the current dataset, we cannot determine whether the observed variation in CFR seen by district or treatment centre reflects real differences in survival, related to the quality of care or other factors or was caused by differences in reporting practices or case ascertainment. This article is part of the themed issue ‘The 2013–2016 West African Ebola epidemic: data, decision-making and disease control’. PMID:28396479

Does Breast Cancer Drive the Building of Survival Probability Models among States? An Assessment of Goodness of Fit for Patient Data from SEER Registries

PubMed

Khan, Hafiz; Saxena, Anshul; Perisetti, Abhilash; Rafiq, Aamrin; Gabbidon, Kemesha; Mende, Sarah; Lyuksyutova, Maria; Quesada, Kandi; Blakely, Summre; Torres, Tiffany; Afesse, Mahlet

2016-12-01

Background: Breast cancer is a worldwide public health concern and is the most prevalent type of cancer in women in the United States. This study concerned the best fit of statistical probability models on the basis of survival times for nine state cancer registries: California, Connecticut, Georgia, Hawaii, Iowa, Michigan, New Mexico, Utah, and Washington. Materials and Methods: A probability random sampling method was applied to select and extract records of 2,000 breast cancer patients from the Surveillance Epidemiology and End Results (SEER) database for each of the nine state cancer registries used in this study. EasyFit software was utilized to identify the best probability models by using goodness of fit tests, and to estimate parameters for various statistical probability distributions that fit survival data. Results: Statistical analysis for the summary of statistics is reported for each of the states for the years 1973 to 2012. Kolmogorov-Smirnov, Anderson-Darling, and Chi-squared goodness of fit test values were used for survival data, the highest values of goodness of fit statistics being considered indicative of the best fit survival model for each state. Conclusions: It was found that California, Connecticut, Georgia, Iowa, New Mexico, and Washington followed the Burr probability distribution, while the Dagum probability distribution gave the best fit for Michigan and Utah, and Hawaii followed the Gamma probability distribution. These findings highlight differences between states through selected sociodemographic variables and also demonstrate probability modeling differences in breast cancer survival times. The results of this study can be used to guide healthcare providers and researchers for further investigations into social and environmental factors in order to reduce the occurrence of and mortality due to breast cancer. Creative Commons Attribution License

A Computer-Aided Diagnosis System for Breast Cancer Combining Mammography and Proteomics

DTIC Science & Technology

2007-05-01

findings in both Data sets C and M. The likelihood ratio is the probability of the features un- der the malignant case divided by the probability of...likelihood ratio value as a classification decision variable, the probabilities of detection and false alarm are calculated as follows: Pdfusion...lowered the fused classifier’s performance to near chance levels. A genetic algorithm searched over the likelihood- ratio thresh- old values for each

CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

PubMed

Hansen, John P

2003-01-01

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.

Anisotropy, size, and aspect ratio effects on micropillar compression of Al-SiC nanolaminate composites

DOE PAGES

Mayer, C. R.; Yang, L. W.; Singh, S. S.; ...

2016-05-20

Metal-ceramic nanolaminate composites show promise as high strength and toughness materials. Micropillar compression was used to characterize the mechanical behavior of AlSiC multilayers in different orientations including loading at 0°, 45° and 90° with respect to the direction of the layers. The 0° orientation showed the highest strength while the 45° orientation showed the lowest strength. Each orientation showed unique deformation behavior. Effects of pillar size and aspect ratio were also studied. Higher compressive strengths were observed in smaller pillars for all orientations. This effect was shown to be due to a lower probability of flaws using Weibull statistics. Additionally,more » changes in the aspect ratio was shown to have no significant effect on the behavior except an increase in the strain to failure in the 0° orientation. In conclusion, finite element analysis (FEA) was used to simulate and understand the effect of these parameters on the deformation behavior.« less

Hereditary hemochromatosis is characterized by a clinically definable arthropathy that correlates with iron load.

PubMed

Carroll, G J; Breidahl, W H; Bulsara, M K; Olynyk, J K

2011-01-01

To determine the frequency and character of arthropathy in hereditary hemochromatosis (HH) and to investigate the relationship between this arthropathy, nodal interphalangeal osteoarthritis, and iron load. Participants were recruited from the community by newspaper advertisement and assigned to diagnostic confidence categories for HH (definite/probable or possible/unlikely). Arthropathy was determined by use of a predetermined clinical protocol, radiographs of the hands of all participants, and radiographs of other joints in which clinical criteria were met. An arthropathy considered typical for HH, involving metacarpophalangeal joints 2-5 and bilateral specified large joints, was observed in 10 of 41 patients with definite or probable HH (24%), all of whom were homozygous for the C282Y mutation in the HFE gene, while only 2 of 62 patients with possible/unlikely HH had such an arthropathy (P=0.0024). Arthropathy in definite/probable HH was more common with increasing age and was associated with ferritin concentrations>1,000 μg/liter at the time of diagnosis (odds ratio 14.0 [95% confidence interval 1.30-150.89], P=0.03). A trend toward more episodes requiring phlebotomy was also observed among those with arthropathy, but this was not statistically significant (odds ratio 1.03 [95% confidence interval 0.99-1.06], P=0.097). There was no significant association between arthropathy in definite/probable HH and a history of intensive physical labor (P=0.12). An arthropathy consistent with that commonly attributed to HH was found to occur in 24% of patients with definite/probable HH. The association observed between this arthropathy, homozygosity for C282Y, and serum ferritin concentrations at the time of diagnosis suggests that iron load is likely to be a major determinant of arthropathy in HH and to be more important than occupational factors. Copyright © 2011 by the American College of Rheumatology.

Quantifying Safety Margin Using the Risk-Informed Safety Margin Characterization (RISMC)

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

Grabaskas, David; Bucknor, Matthew; Brunett, Acacia

2015-04-26

The Risk-Informed Safety Margin Characterization (RISMC), developed by Idaho National Laboratory as part of the Light-Water Reactor Sustainability Project, utilizes a probabilistic safety margin comparison between a load and capacity distribution, rather than a deterministic comparison between two values, as is usually done in best-estimate plus uncertainty analyses. The goal is to determine the failure probability, or in other words, the probability of the system load equaling or exceeding the system capacity. While this method has been used in pilot studies, there has been little work conducted investigating the statistical significance of the resulting failure probability. In particular, it ismore » difficult to determine how many simulations are necessary to properly characterize the failure probability. This work uses classical (frequentist) statistics and confidence intervals to examine the impact in statistical accuracy when the number of simulations is varied. Two methods are proposed to establish confidence intervals related to the failure probability established using a RISMC analysis. The confidence interval provides information about the statistical accuracy of the method utilized to explore the uncertainty space, and offers a quantitative method to gauge the increase in statistical accuracy due to performing additional simulations.« less

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

PubMed

Miller, Jeff; Schwarz, Wolf

2011-09-01

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

Probability of identification: a statistical model for the validation of qualitative botanical identification methods.

PubMed

LaBudde, Robert A; Harnly, James M

2012-01-01

A qualitative botanical identification method (BIM) is an analytical procedure that returns a binary result (1 = Identified, 0 = Not Identified). A BIM may be used by a buyer, manufacturer, or regulator to determine whether a botanical material being tested is the same as the target (desired) material, or whether it contains excessive nontarget (undesirable) material. The report describes the development and validation of studies for a BIM based on the proportion of replicates identified, or probability of identification (POI), as the basic observed statistic. The statistical procedures proposed for data analysis follow closely those of the probability of detection, and harmonize the statistical concepts and parameters between quantitative and qualitative method validation. Use of POI statistics also harmonizes statistical concepts for botanical, microbiological, toxin, and other analyte identification methods that produce binary results. The POI statistical model provides a tool for graphical representation of response curves for qualitative methods, reporting of descriptive statistics, and application of performance requirements. Single collaborator and multicollaborative study examples are given.

Statistical deprojection of galaxy pairs

NASA Astrophysics Data System (ADS)

Nottale, Laurent; Chamaraux, Pierre

2018-06-01

Aims: The purpose of the present paper is to provide methods of statistical analysis of the physical properties of galaxy pairs. We perform this study to apply it later to catalogs of isolated pairs of galaxies, especially two new catalogs we recently constructed that contain ≈1000 and ≈13 000 pairs, respectively. We are particularly interested by the dynamics of those pairs, including the determination of their masses. Methods: We could not compute the dynamical parameters directly since the necessary data are incomplete. Indeed, we only have at our disposal one component of the intervelocity between the members, namely along the line of sight, and two components of their interdistance, i.e., the projection on the sky-plane. Moreover, we know only one point of each galaxy orbit. Hence we need statistical methods to find the probability distribution of 3D interdistances and 3D intervelocities from their projections; we designed those methods under the term deprojection. Results: We proceed in two steps to determine and use the deprojection methods. First we derive the probability distributions expected for the various relevant projected quantities, namely intervelocity vz, interdistance rp, their ratio, and the product rp v_z^2, which is involved in mass determination. In a second step, we propose various methods of deprojection of those parameters based on the previous analysis. We start from a histogram of the projected data and we apply inversion formulae to obtain the deprojected distributions; lastly, we test the methods by numerical simulations, which also allow us to determine the uncertainties involved.

Do doctors need statistics? Doctors' use of and attitudes to probability and statistics.

PubMed

Swift, Louise; Miles, Susan; Price, Gill M; Shepstone, Lee; Leinster, Sam J

2009-07-10

There is little published evidence on what doctors do in their work that requires probability and statistics, yet the General Medical Council (GMC) requires new doctors to have these skills. This study investigated doctors' use of and attitudes to probability and statistics with a view to informing undergraduate teaching.An email questionnaire was sent to 473 clinicians with an affiliation to the University of East Anglia's Medical School.Of 130 respondents approximately 90 per cent of doctors who performed each of the following activities found probability and statistics useful for that activity: accessing clinical guidelines and evidence summaries, explaining levels of risk to patients, assessing medical marketing and advertising material, interpreting the results of a screening test, reading research publications for general professional interest, and using research publications to explore non-standard treatment and management options.Seventy-nine per cent (103/130, 95 per cent CI 71 per cent, 86 per cent) of participants considered probability and statistics important in their work. Sixty-three per cent (78/124, 95 per cent CI 54 per cent, 71 per cent) said that there were activities that they could do better or start doing if they had an improved understanding of these areas and 74 of these participants elaborated on this. Themes highlighted by participants included: being better able to critically evaluate other people's research; becoming more research-active, having a better understanding of risk; and being better able to explain things to, or teach, other people.Our results can be used to inform how probability and statistics should be taught to medical undergraduates and should encourage today's medical students of the subjects' relevance to their future careers. Copyright 2009 John Wiley & Sons, Ltd.

Pre-Service Mathematics Teachers' Use of Probability Models in Making Informal Inferences about a Chance Game

ERIC Educational Resources Information Center

Kazak, Sibel; Pratt, Dave

2017-01-01

This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers' use of probability models for a chance game, where the sum of two dice matters in…

PROBABILITY SAMPLING AND POPULATION INFERENCE IN MONITORING PROGRAMS

EPA Science Inventory

A fundamental difference between probability sampling and conventional statistics is that "sampling" deals with real, tangible populations, whereas "conventional statistics" usually deals with hypothetical populations that have no real-world realization. he focus here is on real ...

Age estimation by pulp-to-tooth area ratio using cone-beam computed tomography: A preliminary analysis

PubMed Central

Rai, Arpita; Acharya, Ashith B.; Naikmasur, Venkatesh G.

2016-01-01

Background: Age estimation of living or deceased individuals is an important aspect of forensic sciences. Conventionally, pulp-to-tooth area ratio (PTR) measured from periapical radiographs have been utilized as a nondestructive method of age estimation. Cone-beam computed tomography (CBCT) is a new method to acquire three-dimensional images of the teeth in living individuals. Aims: The present study investigated age estimation based on PTR of the maxillary canines measured in three planes obtained from CBCT image data. Settings and Design: Sixty subjects aged 20–85 years were included in the study. Materials and Methods: For each tooth, mid-sagittal, mid-coronal, and three axial sections—cementoenamel junction (CEJ), one-fourth root level from CEJ, and mid-root—were assessed. PTR was calculated using AutoCAD software after outlining the pulp and tooth. Statistical Analysis Used: All statistical analyses were performed using an SPSS 17.0 software program. Results and Conclusions: Linear regression analysis showed that only PTR in axial plane at CEJ had significant age correlation (r = 0.32; P < 0.05). This is probably because of clearer demarcation of pulp and tooth outline at this level. PMID:28123269

The synthesis and cell interaction of statistical L-arginine - glycine - L-aspartic acid terpolypeptides.

PubMed

Mbizana, Siyasanga; Hlalele, Lebohang; Pfukwa, Rueben; du Toit, Andre; Lumkwana, Dumisile; Loos, Benjamin; Klumperman, Bert

2018-05-01

Copolymerizations and terpolymerizations of N-carboxyanhydrides (NCAs) of glycine (Gly), Nδ-carbobenzyloxy-L-ornithine ((Z)-Orn) and β-benzyl-L-aspartate ((Bz)-Asp) were investigated. In situ 1H NMR spectroscopy was used to monitor individual comonomer consumptions during binary and ternary copolymerizations. The six relevant reactivity ratios were determined from copolymerizations of the NCAs of amino acids via nonlinear least squares curve fitting. The reactivity ratios were subsequently used to maximize the occurrence of the Asp-Gly-Orn (DGR') sequence in the terpolymers. Terpolymers with variable probability of occurrence of DGR' were prepared in the lab. Subsequently, the ornithine residues on the terpolymers were converted to L-arginine (R) residues via guanidination reaction after removal of the protecting groups. The resulting DGR terpolymers translate to traditional peptides and proteins with variable RGD content, due to the convention in nomenclature that peptides are depicted from N- to C-terminus, whereas the NCA ring-opening polymerization is conducted from C- to N-terminus. The L-arginine containing terpolymers were evaluated for cell interaction, where it was found that neuronal cells display enhanced adhesion and process formation when plated in the presence of statistical DGR terpolymers.

The Soil Moisture Dependence of TRMM Microwave Imager Rainfall Estimates

NASA Astrophysics Data System (ADS)

Seyyedi, H.; Anagnostou, E. N.

2011-12-01

This study presents an in-depth analysis of the dependence of overland rainfall estimates from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) on the soil moisture conditions at the land surface. TMI retrievals are verified against rainfall fields derived from a high resolution rain-gauge network (MESONET) covering Oklahoma. Soil moisture (SOM) patterns are extracted based on recorded data from 2000-2007 with 30 minutes temporal resolution. The area is divided into wet and dry regions based on normalized SOM (Nsom) values. Statistical comparison between two groups is conducted based on recorded ground station measurements and the corresponding passive microwave retrievals from TMI overpasses at the respective MESONET station location and time. The zero order error statistics show that the Probability of Detection (POD) for the wet regions (higher Nsom values) is higher than the dry regions. The Falls Alarm Ratio (FAR) and volumetric FAR is lower for the wet regions. The volumetric missed rain for the wet region is lower than dry region. Analysis of the MESONET-to-TMI ratio values shows that TMI tends to overestimate for surface rainfall intensities less than 12 (mm/h), however the magnitude of the overestimation over the wet regions is lower than the dry regions.

12 CFR 700.2 - Definitions.

Code of Federal Regulations, 2010 CFR

2010-01-01

... that the facts that caused the deficient share-asset ratio no longer exist; and (ii) The likelihood of further depreciation of the share-asset ratio is not probable; and (iii) The return of the share-asset ratio to its normal limits within a reasonable time for the credit union concerned is probable; and (iv...

Concurrent progressive ratio schedules: Effects of reinforcer probability on breakpoint and response allocation.

PubMed

Jarmolowicz, David P; Sofis, Michael J; Darden, Alexandria C

2016-07-01

Although progressive ratio (PR) schedules have been used to explore effects of a range of reinforcer parameters (e.g., magnitude, delay), effects of reinforcer probability remain underexplored. The present project used independently progressing concurrent PR PR schedules to examine effects of reinforcer probability on PR breakpoint (highest completed ratio prior to a session terminating 300s pause) and response allocation. The probability of reinforcement on one lever remained at 100% across all conditions while the probability of reinforcement on the other lever was systematically manipulated (i.e., 100%, 50%, 25%, 12.5%, and a replication of 25%). Breakpoints systematically decreased with decreasing reinforcer probabilities while breakpoints on the control lever remained unchanged. Patterns of switching between the two levers were well described by a choice-by-choice unit price model that accounted for the hyperbolic discounting of the value of probabilistic reinforcers. Copyright © 2016 Elsevier B.V. All rights reserved.

Inferring relationships between pairs of individuals from locus heterozygosities

PubMed Central

Presciuttini, Silvano; Toni, Chiara; Tempestini, Elena; Verdiani, Simonetta; Casarino, Lucia; Spinetti, Isabella; Stefano, Francesco De; Domenici, Ranieri; Bailey-Wilson, Joan E

2002-01-01

Background The traditional exact method for inferring relationships between individuals from genetic data is not easily applicable in all situations that may be encountered in several fields of applied genetics. This study describes an approach that gives affordable results and is easily applicable; it is based on the probabilities that two individuals share 0, 1 or both alleles at a locus identical by state. Results We show that these probabilities (zi) depend on locus heterozygosity (H), and are scarcely affected by variation of the distribution of allele frequencies. This allows us to obtain empirical curves relating zi's to H for a series of common relationships, so that the likelihood ratio of a pair of relationships between any two individuals, given their genotypes at a locus, is a function of a single parameter, H. Application to large samples of mother-child and full-sib pairs shows that the statistical power of this method to infer the correct relationship is not much lower than the exact method. Analysis of a large database of STR data proves that locus heterozygosity does not vary significantly among Caucasian populations, apart from special cases, so that the likelihood ratio of the more common relationships between pairs of individuals may be obtained by looking at tabulated zi values. Conclusions A simple method is provided, which may be used by any scientist with the help of a calculator or a spreadsheet to compute the likelihood ratios of common alternative relationships between pairs of individuals. PMID:12441003

M≥7 Earthquake rupture forecast and time-dependent probability for the Sea of Marmara region, Turkey

USGS Publications Warehouse

Murru, Maura; Akinci, Aybige; Falcone, Guiseppe; Pucci, Stefano; Console, Rodolfo; Parsons, Thomas E.

2016-01-01

We forecast time-independent and time-dependent earthquake ruptures in the Marmara region of Turkey for the next 30 years using a new fault-segmentation model. We also augment time-dependent Brownian Passage Time (BPT) probability with static Coulomb stress changes (ΔCFF) from interacting faults. We calculate Mw > 6.5 probability from 26 individual fault sources in the Marmara region. We also consider a multisegment rupture model that allows higher-magnitude ruptures over some segments of the Northern branch of the North Anatolian Fault Zone (NNAF) beneath the Marmara Sea. A total of 10 different Mw=7.0 to Mw=8.0 multisegment ruptures are combined with the other regional faults at rates that balance the overall moment accumulation. We use Gaussian random distributions to treat parameter uncertainties (e.g., aperiodicity, maximum expected magnitude, slip rate, and consequently mean recurrence time) of the statistical distributions associated with each fault source. We then estimate uncertainties of the 30-year probability values for the next characteristic event obtained from three different models (Poisson, BPT, and BPT+ΔCFF) using a Monte Carlo procedure. The Gerede fault segment located at the eastern end of the Marmara region shows the highest 30-yr probability, with a Poisson value of 29%, and a time-dependent interaction probability of 48%. We find an aggregated 30-yr Poisson probability of M >7.3 earthquakes at Istanbul of 35%, which increases to 47% if time dependence and stress transfer are considered. We calculate a 2-fold probability gain (ratio time-dependent to time-independent) on the southern strands of the North Anatolian Fault Zone.

The Probability of Neonatal Respiratory Distress Syndrome as a Function of Gestational Age and Lecithin/Sphingomyelin Ratio

PubMed Central

St. Clair, Caryn; Norwitz, Errol R.; Woensdregt, Karlijn; Cackovic, Michael; Shaw, Julia A.; Malkus, Herbert; Ehrenkranz, Richard A.; Illuzzi, Jessica L.

2011-01-01

We sought to define the risk of neonatal respiratory distress syndrome (RDS) as a function of both lecithin/sphingomyelin (L/S) ratio and gestational age. Amniotic fluid L/S ratio data were collected from consecutive women undergoing amniocentesis for fetal lung maturity at Yale-New Haven Hospital from January 1998 to December 2004. Women were included in the study if they delivered a live-born, singleton, nonanomalous infant within 72 hours of amniocentesis. The probability of RDS was modeled using multivariate logistic regression with L/S ratio and gestational age as predictors. A total of 210 mother-neonate pairs (8 RDS, 202 non-RDS) met criteria for analysis. Both gestational age and L/S ratio were independent predictors of RDS. A probability of RDS of 3% or less was noted at an L/S ratio cutoff of ≥3.4 at 34 weeks, ≥2.6 at 36 weeks, ≥1.6 at 38 weeks, and ≥1.2 at term. Under 34 weeks of gestation, the prevalence of RDS was so high that a probability of 3% or less was not observed by this model. These data describe a means of stratifying the probability of neonatal RDS using both gestational age and the L/S ratio and may aid in clinical decision making concerning the timing of delivery. PMID:18773379

An Efficient Algorithm for the Detection of Infrequent Rapid Bursts in Time Series Data

NASA Astrophysics Data System (ADS)

Giles, A. B.

1997-01-01

Searching through data for infrequent rapid bursts is a common requirement in many areas of scientific research. In this paper, we present a powerful and flexible analysis method that, in a single pass through the data, searches for statistically significant bursts on a set of specified short timescales. The input data are binned, if necessary, and then quantified in terms of probabilities rather than rates or ratios. Using a measure-like probability makes the method relatively count rate independent. The method has been made computationally efficient by the use of lookup tables and cyclic buffers, and it is therefore particularly well suited to real-time applications. The technique has been developed specifically for use in an X-ray astronomy application to search for millisecond bursts from black hole candidates such as Cyg X-1. We briefly review the few observations of these types of features reported in the literature, as well as the variety of ways in which their statistical reliability was challenged. The developed technique, termed the burst expectation search (BES) method, is illustrated using some data simulations and archived data obtained during ground testing of the proportional counter array (PCA) experiment detectors on the Rossi X-Ray Timing Explorer (RXTE). A potential application for a real-time BES method on board RXTE is also examined.

Quantifying Treatment Benefit in Molecular Subgroups to Assess a Predictive Biomarker.

PubMed

Iasonos, Alexia; Chapman, Paul B; Satagopan, Jaya M

2016-05-01

An increased interest has been expressed in finding predictive biomarkers that can guide treatment options for both mutation carriers and noncarriers. The statistical assessment of variation in treatment benefit (TB) according to the biomarker carrier status plays an important role in evaluating predictive biomarkers. For time-to-event endpoints, the hazard ratio (HR) for interaction between treatment and a biomarker from a proportional hazards regression model is commonly used as a measure of variation in TB. Although this can be easily obtained using available statistical software packages, the interpretation of HR is not straightforward. In this article, we propose different summary measures of variation in TB on the scale of survival probabilities for evaluating a predictive biomarker. The proposed summary measures can be easily interpreted as quantifying differential in TB in terms of relative risk or excess absolute risk due to treatment in carriers versus noncarriers. We illustrate the use and interpretation of the proposed measures with data from completed clinical trials. We encourage clinical practitioners to interpret variation in TB in terms of measures based on survival probabilities, particularly in terms of excess absolute risk, as opposed to HR. Clin Cancer Res; 22(9); 2114-20. ©2016 AACR. ©2016 American Association for Cancer Research.

Multipactor threshold calculation of coaxial transmission lines in microwave applications with nonstationary statistical theory

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

Lin, S.; Li, Y.; Liu, C.

2015-08-15

This paper presents a statistical theory for the initial onset of multipactor breakdown in coaxial transmission lines, taking both the nonuniform electric field and random electron emission velocity into account. A general numerical method is first developed to construct the joint probability density function based on the approximate equation of the electron trajectory. The nonstationary dynamics of the multipactor process on both surfaces of coaxial lines are modelled based on the probability of various impacts and their corresponding secondary emission. The resonant assumption of the classical theory on the independent double-sided and single-sided impacts is replaced by the consideration ofmore » their interaction. As a result, the time evolutions of the electron population for exponential growth and absorption on both inner and outer conductor, in response to the applied voltage above and below the multipactor breakdown level, are obtained to investigate the exact mechanism of multipactor discharge in coaxial lines. Furthermore, the multipactor threshold predictions of the presented model are compared with experimental results using measured secondary emission yield of the tested samples which shows reasonable agreement. Finally, the detailed impact scenario reveals that single-surface multipactor is more likely to occur with a higher outer to inner conductor radius ratio.« less

A potential risk of overestimating apparent diffusion coefficient in parotid glands.

PubMed

Liu, Yi-Jui; Lee, Yi-Hsiung; Chang, Hing-Chiu; Huang, Teng-Yi; Chiu, Hui-Chu; Wang, Chih-Wei; Chiou, Ta-Wei; Hsu, Kang; Juan, Chun-Jung; Huang, Guo-Shu; Hsu, Hsian-He

2015-01-01

To investigate transient signal loss on diffusion weighted images (DWI) and overestimation of apparent diffusion coefficient (ADC) in parotid glands using single shot echoplanar DWI (EPDWI). This study enrolled 6 healthy subjects and 7 patients receiving radiotherapy. All participants received dynamic EPDWI with a total of 8 repetitions. Imaging quality of DWI was evaluated. Probability of severe overestimation of ADC (soADC), defined by an ADC ratio more than 1.2, was calculated. Error on T2WI, DWI, and ADC was computed. Statistical analysis included paired Student t testing and Mann-Whitney U test. A P value less than 0.05 was considered statistically significant. Transient signal loss was visually detected on some excitations of DWI but not on T2WI or mean DWI. soADC occurred randomly among 8 excitations and 3 directions of diffusion encoding gradients. Probability of soADC was significantly higher in radiotherapy group (42.86%) than in healthy group (24.39%). The mean error percentage decreased as the number of excitations increased on all images, and, it was smallest on T2WI, followed by DWI and ADC in an increasing order. Transient signal loss on DWI was successfully detected by dynamic EPDWI. The signal loss on DWI and overestimation of ADC could be partially remedied by increasing the number of excitations.

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.

Quantum probability, choice in large worlds, and the statistical structure of reality.

PubMed

Ross, Don; Ladyman, James

2013-06-01

Classical probability models of incentive response are inadequate in "large worlds," where the dimensions of relative risk and the dimensions of similarity in outcome comparisons typically differ. Quantum probability models for choice in large worlds may be motivated pragmatically - there is no third theory - or metaphysically: statistical processing in the brain adapts to the true scale-relative structure of the universe.

When Is Statistical Evidence Superior to Anecdotal Evidence in Supporting Probability Claims? The Role of Argument Type

ERIC Educational Resources Information Center

Hoeken, Hans; Hustinx, Lettica

2009-01-01

Under certain conditions, statistical evidence is more persuasive than anecdotal evidence in supporting a claim about the probability that a certain event will occur. In three experiments, it is shown that the type of argument is an important condition in this respect. If the evidence is part of an argument by generalization, statistical evidence…

Scan statistics with local vote for target detection in distributed system

NASA Astrophysics Data System (ADS)

Luo, Junhai; Wu, Qi

2017-12-01

Target detection has occupied a pivotal position in distributed system. Scan statistics, as one of the most efficient detection methods, has been applied to a variety of anomaly detection problems and significantly improves the probability of detection. However, scan statistics cannot achieve the expected performance when the noise intensity is strong, or the signal emitted by the target is weak. The local vote algorithm can also achieve higher target detection rate. After the local vote, the counting rule is always adopted for decision fusion. The counting rule does not use the information about the contiguity of sensors but takes all sensors' data into consideration, which makes the result undesirable. In this paper, we propose a scan statistics with local vote (SSLV) method. This method combines scan statistics with local vote decision. Before scan statistics, each sensor executes local vote decision according to the data of its neighbors and its own. By combining the advantages of both, our method can obtain higher detection rate in low signal-to-noise ratio environment than the scan statistics. After the local vote decision, the distribution of sensors which have detected the target becomes more intensive. To make full use of local vote decision, we introduce a variable-step-parameter for the SSLV. It significantly shortens the scan period especially when the target is absent. Analysis and simulations are presented to demonstrate the performance of our method.

Numeracy moderates the influence of task-irrelevant affect on probability weighting.

PubMed

Traczyk, Jakub; Fulawka, Kamil

2016-06-01

Statistical numeracy, defined as the ability to understand and process statistical and probability information, plays a significant role in superior decision making. However, recent research has demonstrated that statistical numeracy goes beyond simple comprehension of numbers and mathematical operations. On the contrary to previous studies that were focused on emotions integral to risky prospects, we hypothesized that highly numerate individuals would exhibit more linear probability weighting because they would be less biased by incidental and decision-irrelevant affect. Participants were instructed to make a series of insurance decisions preceded by negative (i.e., fear-inducing) or neutral stimuli. We found that incidental negative affect increased the curvature of the probability weighting function (PWF). Interestingly, this effect was significant only for less numerate individuals, while probability weighting in more numerate people was not altered by decision-irrelevant affect. We propose two candidate mechanisms for the observed effect. Copyright © 2016 Elsevier B.V. All rights reserved.

The Sequential Probability Ratio Test and Binary Item Response Models

ERIC Educational Resources Information Center

Nydick, Steven W.

2014-01-01

The sequential probability ratio test (SPRT) is a common method for terminating item response theory (IRT)-based adaptive classification tests. To decide whether a classification test should stop, the SPRT compares a simple log-likelihood ratio, based on the classification bound separating two categories, to prespecified critical values. As has…

Testing manifest monotonicity using order-constrained statistical inference.

PubMed

Tijmstra, Jesper; Hessen, David J; van der Heijden, Peter G M; Sijtsma, Klaas

2013-01-01

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.

Development of damage probability matrices based on Greek earthquake damage data

NASA Astrophysics Data System (ADS)

Eleftheriadou, Anastasia K.; Karabinis, Athanasios I.

2011-03-01

A comprehensive study is presented for empirical seismic vulnerability assessment of typical structural types, representative of the building stock of Southern Europe, based on a large set of damage statistics. The observational database was obtained from post-earthquake surveys carried out in the area struck by the September 7, 1999 Athens earthquake. After analysis of the collected observational data, a unified damage database has been created which comprises 180,945 damaged buildings from/after the near-field area of the earthquake. The damaged buildings are classified in specific structural types, according to the materials, seismic codes and construction techniques in Southern Europe. The seismic demand is described in terms of both the regional macroseismic intensity and the ratio α g/ a o, where α g is the maximum peak ground acceleration (PGA) of the earthquake event and a o is the unique value PGA that characterizes each municipality shown on the Greek hazard map. The relative and cumulative frequencies of the different damage states for each structural type and each intensity level are computed in terms of damage ratio. Damage probability matrices (DPMs) and vulnerability curves are obtained for specific structural types. A comparison analysis is fulfilled between the produced and the existing vulnerability models.

Bayesian statistics in radionuclide metrology: measurement of a decaying source

NASA Astrophysics Data System (ADS)

Bochud, François O.; Bailat, Claude J.; Laedermann, Jean-Pascal

2007-08-01

The most intuitive way of defining a probability is perhaps through the frequency at which it appears when a large number of trials are realized in identical conditions. The probability derived from the obtained histogram characterizes the so-called frequentist or conventional statistical approach. In this sense, probability is defined as a physical property of the observed system. By contrast, in Bayesian statistics, a probability is not a physical property or a directly observable quantity, but a degree of belief or an element of inference. The goal of this paper is to show how Bayesian statistics can be used in radionuclide metrology and what its advantages and disadvantages are compared with conventional statistics. This is performed through the example of an yttrium-90 source typically encountered in environmental surveillance measurement. Because of the very low activity of this kind of source and the small half-life of the radionuclide, this measurement takes several days, during which the source decays significantly. Several methods are proposed to compute simultaneously the number of unstable nuclei at a given reference time, the decay constant and the background. Asymptotically, all approaches give the same result. However, Bayesian statistics produces coherent estimates and confidence intervals in a much smaller number of measurements. Apart from the conceptual understanding of statistics, the main difficulty that could deter radionuclide metrologists from using Bayesian statistics is the complexity of the computation.

Energy transfer mechanism and probability analysis of submarine pipe laterally impacted by dropped objects

NASA Astrophysics Data System (ADS)

Liang, Jing; Yu, Jian-xing; Yu, Yang; Lam, W.; Zhao, Yi-yu; Duan, Jing-hui

2016-06-01

Energy transfer ratio is the basic-factor affecting the level of pipe damage during the impact between dropped object and submarine pipe. For the purpose of studying energy transfer and damage mechanism of submarine pipe impacted by dropped objects, series of experiments are designed and carried out. The effective yield strength is deduced to make the quasi-static analysis more reliable, and the normal distribution of energy transfer ratio caused by lateral impact on pipes is presented by statistic analysis of experimental results based on the effective yield strength, which provides experimental and theoretical basis for the risk analysis of submarine pipe system impacted by dropped objects. Failure strains of pipe material are confirmed by comparing experimental results with finite element simulation. In addition, impact contact area and impact time are proved to be the major influence factors of energy transfer by sensitivity analysis of the finite element simulation.

Recent results on heavy flavor physics from LEP experiments using 1990-92 data

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

Gasparini, U.

1994-12-01

After three years of data taking, the four LEP experiments collected a total of about four million Z{sup 0} hadronic decays, in which a heavy quark pair (either b{bar b} or c{bar c}) is produced with 40% probability. Results are presented both in the sector of the electroweak precision measurements, with particular emphasis on the beauty quark, and in the determination of the beauty decay properties, where lifetimes and branching ratio measurements take advantage of the large statistics now available and of the recent improvements in the analysis based on microvertex detectors and particle identification devices.

Statistical context shapes stimulus-specific adaptation in human auditory cortex

PubMed Central

Henry, Molly J.; Fromboluti, Elisa Kim; McAuley, J. Devin

2015-01-01

Stimulus-specific adaptation is the phenomenon whereby neural response magnitude decreases with repeated stimulation. Inconsistencies between recent nonhuman animal recordings and computational modeling suggest dynamic influences on stimulus-specific adaptation. The present human electroencephalography (EEG) study investigates the potential role of statistical context in dynamically modulating stimulus-specific adaptation by examining the auditory cortex-generated N1 and P2 components. As in previous studies of stimulus-specific adaptation, listeners were presented with oddball sequences in which the presentation of a repeated tone was infrequently interrupted by rare spectral changes taking on three different magnitudes. Critically, the statistical context varied with respect to the probability of small versus large spectral changes within oddball sequences (half of the time a small change was most probable; in the other half a large change was most probable). We observed larger N1 and P2 amplitudes (i.e., release from adaptation) for all spectral changes in the small-change compared with the large-change statistical context. The increase in response magnitude also held for responses to tones presented with high probability, indicating that statistical adaptation can overrule stimulus probability per se in its influence on neural responses. Computational modeling showed that the degree of coadaptation in auditory cortex changed depending on the statistical context, which in turn affected stimulus-specific adaptation. Thus the present data demonstrate that stimulus-specific adaptation in human auditory cortex critically depends on statistical context. Finally, the present results challenge the implicit assumption of stationarity of neural response magnitudes that governs the practice of isolating established deviant-detection responses such as the mismatch negativity. PMID:25652920

Leptospirosis and Human Immunodeficiency Virus Co-Infection Among Febrile Inpatients in Northern Tanzania

PubMed Central

Biggs, Holly M.; Galloway, Renee L.; Bui, Duy M.; Morrissey, Annie B.; Maro, Venance P.

2013-01-01

Abstract Background Leptospirosis and human immunodeficiency virus (HIV) infection are prevalent in many areas, including northern Tanzania, yet little is known about their interaction. Methods We enrolled febrile inpatients at two hospitals in Moshi, Tanzania, over 1 year and performed HIV antibody testing and the microscopic agglutination test (MAT) for leptospirosis. Confirmed leptospirosis was defined as ≥four-fold rise in MAT titer between acute and convalescent serum samples, and probable leptospirosis was defined as any reciprocal MAT titer ≥800. Results Confirmed or probable leptospirosis was found in 70 (8.4%) of 831 participants with at least one serum sample tested. At total of 823 (99.0%) of 831 participants had HIV testing performed, and 203 (24.7%) were HIV infected. Among HIV-infected participants, 9 (4.4%) of 203 had confirmed or probable leptospirosis, whereas among HIV-uninfected participants 61 (9.8%) of 620 had leptospirosis. Leptospirosis was less prevalent among HIV-infected as compared to HIV-uninfected participants [odds ratio (OR) 0.43, p=0.019]. Among those with leptospirosis, HIV-infected patients more commonly presented with features of severe sepsis syndrome than HIV-uninfected patients, but differences were not statistically significant. Among HIV-infected patients, severe immunosuppression was not significantly different between those with and without leptospirosis (p=0.476). Among HIV-infected adolescents and adults, median CD4 percent and median CD4 count were higher among those with leptospirosis as compared to those with other etiologies of febrile illness, but differences in CD4 count did not reach statistical significance (p=0.015 and p=0.089, respectively). Conclusions Among febrile inpatients in northern Tanzania, leptospirosis was not more prevalent among HIV-infected patients. Although some indicators of leptospirosis severity were more common among HIV-infected patients, a statistically significant difference was not demonstrated. Among HIV-infected patients, those with leptospirosis were not more immunosuppressed relative to those with other etiologies of febrile illness. PMID:23663165

Wald Sequential Probability Ratio Test for Space Object Conjunction Assessment

NASA Technical Reports Server (NTRS)

Carpenter, James R.; Markley, F Landis

2014-01-01

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

Using effort information with change-in-ratio data for population estimation

USGS Publications Warehouse

Udevitz, Mark S.; Pollock, Kenneth H.

1995-01-01

Most change-in-ratio (CIR) methods for estimating fish and wildlife population sizes have been based only on assumptions about how encounter probabilities vary among population subclasses. When information on sampling effort is available, it is also possible to derive CIR estimators based on assumptions about how encounter probabilities vary over time. This paper presents a generalization of previous CIR models that allows explicit consideration of a range of assumptions about the variation of encounter probabilities among subclasses and over time. Explicit estimators are derived under this model for specific sets of assumptions about the encounter probabilities. Numerical methods are presented for obtaining estimators under the full range of possible assumptions. Likelihood ratio tests for these assumptions are described. Emphasis is on obtaining estimators based on assumptions about variation of encounter probabilities over time.

[Gender based violence in the Spanish Parliamentary Agenda (1979-2004)].

PubMed

Vives-Cases, Carmen; Gil-González, Diana; Carrasco-Portiño, Mercedes; Alvarez-Dardet, Carlos

2006-01-01

To systematically examine the characteristics of the processes of formulating and taking decisions on gender-based violence in the Spanish Parliament. A search was performed for all parliamentary initiatives on gender-based violence in the Spanish parliament (1979-2004) and their qualitative content was analyzed. The ratio between initiatives on gender-based violence and those on other issues was calculated by years and legislatures. The probability of presenting initiatives on gender-based violence was analyzed by sex and political group (government vs. opposition) (odds ratio, 95% CI and statistical significance using the Mantel-Haenszel method). In the 26 years studied, there were 322,187 initiatives, of which 569 concerned gender-based violence. Initiatives on this issue increased in 1998 (4.12 per 1,000), 2001 (4.49 per 1,000) and 2004 (9.19 per 1,000). Sixty-seven percent were questions to the government. The majority of the initiatives were registered without agreement or decision (81%). Men had a higher probability of asking questions (OR = 17.08; 95%CI, 5.91-55.62), but women instigated 60% of the initiatives. Parliamentary groups in government showed a higher probability of asking questions (OR = 2.63; 95%CI, 1.32-5.31), but 88% of the initiatives were promoted by the opposition. The process of policy construction has been started in Spain, which could lead to the development of true policies on gender-based violence in the future. Parliamentary activity on this issue should be maintained in the long-term, as the problem shows no sign of abating.

Factors influencing the probability of a diagnosis of autism spectrum disorder in girls versus boys.

PubMed

Duvekot, Jorieke; van der Ende, Jan; Verhulst, Frank C; Slappendel, Geerte; van Daalen, Emma; Maras, Athanasios; Greaves-Lord, Kirstin

2017-08-01

In order to shed more light on why referred girls are less likely to be diagnosed with autism spectrum disorder than boys, this study examined whether behavioral characteristics influence the probability of an autism spectrum disorder diagnosis differently in girls versus boys derived from a multicenter sample of consecutively referred children aged 2.5-10 years. Based on information from the short version of the Developmental, Dimensional and Diagnostic Interview and the Autism Diagnostic Observation Schedule, 130 children (106 boys and 24 girls) received a diagnosis of autism spectrum disorder according to Diagnostic and Statistical Manual of Mental Disorders (4th ed., text rev.) criteria and 101 children (61 boys and 40 girls) did not. Higher overall levels of parent-reported repetitive and restricted behavior symptoms were less predictive of an autism spectrum disorder diagnosis in girls than in boys (odds ratio interaction = 0.41, 95% confidence interval = 0.18-0.92, p = 0.03). In contrast, higher overall levels of parent-reported emotional and behavioral problems increased the probability of an autism spectrum disorder diagnosis more in girls than in boys (odds ratio interaction = 2.44, 95% confidence interval = 1.13-5.29, p = 0.02). No differences were found between girls and boys in the prediction of an autism spectrum disorder diagnosis by overall autistic impairment, sensory symptoms, and cognitive functioning. These findings provide insight into possible explanations for the assumed underidentification of autism spectrum disorder in girls in the clinic.

Estimated Accuracy of Three Common Trajectory Statistical Methods

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

Comparison of sticking probabilities of metal atoms in magnetron sputtering deposition of CuZnSnS films

NASA Astrophysics Data System (ADS)

Sasaki, K.; Kikuchi, S.

2014-10-01

In this work, we compared the sticking probabilities of Cu, Zn, and Sn atoms in magnetron sputtering deposition of CZTS films. The evaluations of the sticking probabilities were based on the temporal decays of the Cu, Zn, and Sn densities in the afterglow, which were measured by laser-induced fluorescence spectroscopy. Linear relationships were found between the discharge pressure and the lifetimes of the atom densities. According to Chantry, the sticking probability is evaluated from the extrapolated lifetime at the zero pressure, which is given by 2l0 (2 - α) / (v α) with α, l0, and v being the sticking probability, the ratio between the volume and the surface area of the chamber, and the mean velocity, respectively. The ratio of the extrapolated lifetimes observed experimentally was τCu :τSn :τZn = 1 : 1 . 3 : 1 . This ratio coincides well with the ratio of the reciprocals of their mean velocities (1 /vCu : 1 /vSn : 1 /vZn = 1 . 00 : 1 . 37 : 1 . 01). Therefore, the present experimental result suggests that the sticking probabilities of Cu, Sn, and Zn are roughly the same.

Spatial correlations and probability density function of the phase difference in a developed speckle-field: numerical and natural experiments

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

Mysina, N Yu; Maksimova, L A; Ryabukho, V P

Investigated are statistical properties of the phase difference of oscillations in speckle-fields at two points in the far-field diffraction region, with different shapes of the scatterer aperture. Statistical and spatial nonuniformity of the probability density function of the field phase difference is established. Numerical experiments show that, for the speckle-fields with an oscillating alternating-sign transverse correlation function, a significant nonuniformity of the probability density function of the phase difference in the correlation region of the field complex amplitude, with the most probable values 0 and p, is observed. A natural statistical interference experiment using Young diagrams has confirmed the resultsmore » of numerical experiments. (laser applications and other topics in quantum electronics)« less

Health Professionals Prefer to Communicate Risk-Related Numerical Information Using "1-in-X" Ratios.

PubMed

Sirota, Miroslav; Juanchich, Marie; Petrova, Dafina; Garcia-Retamero, Rocio; Walasek, Lukasz; Bhatia, Sudeep

2018-04-01

Previous research has shown that format effects, such as the "1-in-X" effect-whereby "1-in-X" ratios lead to a higher perceived probability than "N-in-N*X" ratios-alter perceptions of medical probabilities. We do not know, however, how prevalent this effect is in practice; i.e., how often health professionals use the "1-in-X" ratio. We assembled 4 different sources of evidence, involving experimental work and corpus studies, to examine the use of "1-in-X" and other numerical formats quantifying probability. Our results revealed that the use of the "1-in-X" ratio is prevalent and that health professionals prefer this format compared with other numerical formats (i.e., the "N-in-N*X", %, and decimal formats). In Study 1, UK family physicians preferred to communicate prenatal risk using a "1-in-X" ratio (80.4%, n = 131) across different risk levels and regardless of patients' numeracy levels. In Study 2, a sample from the UK adult population ( n = 203) reported that most GPs (60.6%) preferred to use "1-in-X" ratios compared with other formats. In Study 3, "1-in-X" ratios were the most commonly used format in a set of randomly sampled drug leaflets describing the risk of side effects (100%, n = 94). In Study 4, the "1-in-X" format was the most commonly used numerical expression of medical probabilities or frequencies on the UK's NHS website (45.7%, n = 2,469 sentences). The prevalent use of "1-in-X" ratios magnifies the chances of increased subjective probability. Further research should establish clinical significance of the "1-in-X" effect.

Promise and problems in using stress triggering models for time-dependent earthquake hazard assessment

NASA Astrophysics Data System (ADS)

Cocco, M.

2001-12-01

Earthquake stress changes can promote failures on favorably oriented faults and modify the seismicity pattern over broad regions around the causative faults. Because the induced stress perturbations modify the rate of production of earthquakes, they alter the probability of seismic events in a specified time window. Comparing the Coulomb stress changes with the seismicity rate changes and aftershock patterns can statistically test the role of stress transfer in earthquake occurrence. The interaction probability may represent a further tool to test the stress trigger or shadow model. The probability model, which incorporate stress transfer, has the main advantage to include the contributions of the induced stress perturbation (a static step in its present formulation), the loading rate and the fault constitutive properties. Because the mechanical conditions of the secondary faults at the time of application of the induced load are largely unkown, stress triggering can only be tested on fault populations and not on single earthquake pairs with a specified time delay. The interaction probability can represent the most suitable tool to test the interaction between large magnitude earthquakes. Despite these important implications and the stimulating perspectives, there exist problems in understanding earthquake interaction that should motivate future research but at the same time limit its immediate social applications. One major limitation is that we are unable to predict how and if the induced stress perturbations modify the ratio between small versus large magnitude earthquakes. In other words, we cannot distinguish between a change in this ratio in favor of small events or of large magnitude earthquakes, because the interaction probability is independent of magnitude. Another problem concerns the reconstruction of the stressing history. The interaction probability model is based on the response to a static step; however, we know that other processes contribute to the stressing history perturbing the faults (such as dynamic stress changes, post-seismic stress changes caused by viscolelastic relaxation or fluid flow). If, for instance, we believe that dynamic stress changes can trigger aftershocks or earthquakes years after the passing of the seismic waves through the fault, the perspective of calculating interaction probability is untenable. It is therefore clear we have learned a lot on earthquake interaction incorporating fault constitutive properties, allowing to solve existing controversy, but leaving open questions for future research.

Maternal Upward Socioeconomic Mobility and Black–White Disparities in Infant Birthweight

PubMed Central

Colen, Cynthia G.; Geronimus, Arline T.; Bound, John; James, Sherman A.

2006-01-01

Objectives. We estimate the extent to which upward socioeconomic mobility limits the probability that Black and White women who spent their childhoods in or near poverty will give birth to a low-birthweight baby. Methods. Data from the National Longitudinal Survey of Youth 1979 and the 1970 US Census were used to complete a series of logistic regression models. We restricted multivariate analyses to female survey respondents who, at 14 years of age, were living in households in which the income-to-needs ratio did not exceed 200% of poverty. Results. For White women, the probability of giving birth to a low-birthweight baby decreases by 48% for every 1 unit increase in the natural logarithm of adult family income, once the effects of all other covariates are taken into account. For Black women, the relation between adult family income and the probability of low birthweight is also negative; however, this association fails to reach statistical significance. Conclusions. Upward socioeconomic mobility contributes to improved birth outcomes among infants born to White women who were poor as children, but the same does not hold true for their Black counterparts. PMID:17018818

[Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

PubMed

He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

2013-09-01

The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents with various solvent extracts. The TQSMSS can characterize the sample similarity, by which we can quantitate the correct probability with the test of power under to make positive and negative conclusions no matter the samples come from same population under confident coefficient a or not, by which we can realize an analysis at both macroscopic and microcosmic levels, as an important similar analytical method for medical theoretical research.

The Dependence Structure of Conditional Probabilities in a Contingency Table

ERIC Educational Resources Information Center

Joarder, Anwar H.; Al-Sabah, Walid S.

2002-01-01

Conditional probability and statistical independence can be better explained with contingency tables. In this note some special cases of 2 x 2 contingency tables are considered. In turn an interesting insight into statistical dependence as well as independence of events is obtained.

Local and global approaches to the problem of Poincaré recurrences. Applications in nonlinear dynamics

NASA Astrophysics Data System (ADS)

Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.

2015-07-01

We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how the fractal dimension of chaotic attractors can be estimated using the Poincaré recurrence statistics.

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.

Exploration in free word association networks: models and experiment.

PubMed

Ludueña, Guillermo A; Behzad, Mehran Djalali; Gros, Claudius

2014-05-01

Free association is a task that requires a subject to express the first word to come to their mind when presented with a certain cue. It is a task which can be used to expose the basic mechanisms by which humans connect memories. In this work, we have made use of a publicly available database of free associations to model the exploration of the averaged network of associations using a statistical and the adaptive control of thought-rational (ACT-R) model. We performed, in addition, an online experiment asking participants to navigate the averaged network using their individual preferences for word associations. We have investigated the statistics of word repetitions in this guided association task. We find that the considered models mimic some of the statistical properties, viz the probability of word repetitions, the distance between repetitions and the distribution of association chain lengths, of the experiment, with the ACT-R model showing a particularly good fit to the experimental data for the more intricate properties as, for instance, the ratio of repetitions per length of association chains.

A Monte Carlo study of Weibull reliability analysis for space shuttle main engine components

NASA Technical Reports Server (NTRS)

Abernethy, K.

1986-01-01

The incorporation of a number of additional capabilities into an existing Weibull analysis computer program and the results of Monte Carlo computer simulation study to evaluate the usefulness of the Weibull methods using samples with a very small number of failures and extensive censoring are discussed. Since the censoring mechanism inherent in the Space Shuttle Main Engine (SSME) data is hard to analyze, it was decided to use a random censoring model, generating censoring times from a uniform probability distribution. Some of the statistical techniques and computer programs that are used in the SSME Weibull analysis are described. The methods documented in were supplemented by adding computer calculations of approximate (using iteractive methods) confidence intervals for several parameters of interest. These calculations are based on a likelihood ratio statistic which is asymptotically a chisquared statistic with one degree of freedom. The assumptions built into the computer simulations are described. The simulation program and the techniques used in it are described there also. Simulation results are tabulated for various combinations of Weibull shape parameters and the numbers of failures in the samples.

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

Zhu, Lin; Dai, Zhenxue; Gong, Huili

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less

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

Multiple-solution problems in a statistics classroom: an example

NASA Astrophysics Data System (ADS)

Chu, Chi Wing; Chan, Kevin L. T.; Chan, Wai-Sum; Kwong, Koon-Shing

2017-11-01

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students' understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact probability mass distribution for the sum of face values. Four different ways of solving the problem are discussed. The solutions span various basic concepts in different mathematical disciplines (sample space in probability theory, the probability generating function in statistics, integer partition in basic combinatorics and individual risk model in actuarial science) and thus promotes upper undergraduate students' awareness of knowledge connections between their courses. All solutions of the example are implemented using the R statistical software package.

Statistical hydrodynamics and related problems in spaces of probability measures

NASA Astrophysics Data System (ADS)

Dostoglou, Stamatios

2017-11-01

A rigorous theory of statistical solutions of the Navier-Stokes equations, suitable for exploring Kolmogorov's ideas, has been developed by M.I. Vishik and A.V. Fursikov, culminating in their monograph "Mathematical problems of Statistical Hydromechanics." We review some progress made in recent years following this approach, with emphasis on problems concerning the correlation of velocities and corresponding questions in the space of probability measures on Hilbert spaces.

Teaching Elementary Probability and Statistics: Some Applications in Epidemiology.

ERIC Educational Resources Information Center

Sahai, Hardeo; Reesal, Michael R.

1992-01-01

Illustrates some applications of elementary probability and statistics to epidemiology, the branch of medical science that attempts to discover associations between events, patterns, and the cause of disease in human populations. Uses real-life examples involving cancer's link to smoking and the AIDS virus. (MDH)

Inference Control Mechanism for Statistical Database: Frequency-Imposed Data Distortions.

ERIC Educational Resources Information Center

Liew, Chong K.; And Others

1985-01-01

Introduces two data distortion methods (Frequency-Imposed Distortion, Frequency-Imposed Probability Distortion) and uses a Monte Carlo study to compare their performance with that of other distortion methods (Point Distortion, Probability Distortion). Indications that data generated by these two methods produce accurate statistics and protect…

A Vehicle for Bivariate Data Analysis

ERIC Educational Resources Information Center

Roscoe, Matt B.

2016-01-01

Instead of reserving the study of probability and statistics for special fourth-year high school courses, the Common Core State Standards for Mathematics (CCSSM) takes a "statistics for all" approach. The standards recommend that students in grades 6-8 learn to summarize and describe data distributions, understand probability, draw…

Dynamic Graphics in Excel for Teaching Statistics: Understanding the Probability Density Function

ERIC Educational Resources Information Center

Coll-Serrano, Vicente; Blasco-Blasco, Olga; Alvarez-Jareno, Jose A.

2011-01-01

In this article, we show a dynamic graphic in Excel that is used to introduce an important concept in our subject, Statistics I: the probability density function. This interactive graphic seeks to facilitate conceptual understanding of the main aspects analysed by the learners.

Statistical complexity without explicit reference to underlying probabilities

NASA Astrophysics Data System (ADS)

Pennini, F.; Plastino, A.

2018-06-01

We show that extremely simple systems of a not too large number of particles can be simultaneously thermally stable and complex. To such an end, we extend the statistical complexity's notion to simple configurations of non-interacting particles, without appeal to probabilities, and discuss configurational properties.

A scan statistic for binary outcome based on hypergeometric probability model, with an application to detecting spatial clusters of Japanese encephalitis.

PubMed

Zhao, Xing; Zhou, Xiao-Hua; Feng, Zijian; Guo, Pengfei; He, Hongyan; Zhang, Tao; Duan, Lei; Li, Xiaosong

2013-01-01

As a useful tool for geographical cluster detection of events, the spatial scan statistic is widely applied in many fields and plays an increasingly important role. The classic version of the spatial scan statistic for the binary outcome is developed by Kulldorff, based on the Bernoulli or the Poisson probability model. In this paper, we apply the Hypergeometric probability model to construct the likelihood function under the null hypothesis. Compared with existing methods, the likelihood function under the null hypothesis is an alternative and indirect method to identify the potential cluster, and the test statistic is the extreme value of the likelihood function. Similar with Kulldorff's methods, we adopt Monte Carlo test for the test of significance. Both methods are applied for detecting spatial clusters of Japanese encephalitis in Sichuan province, China, in 2009, and the detected clusters are identical. Through a simulation to independent benchmark data, it is indicated that the test statistic based on the Hypergeometric model outweighs Kulldorff's statistics for clusters of high population density or large size; otherwise Kulldorff's statistics are superior.

Peripheral vascular damage in systemic lupus erythematosus: data from LUMINA, a large multi-ethnic U.S. cohort (LXIX).

PubMed

Burgos, P I; Vilá, L M; Reveille, J D; Alarcón, G S

2009-12-01

To determine the factors associated with peripheral vascular damage in systemic lupus erythematosus patients and its impact on survival from Lupus in Minorities, Nature versus Nurture, a longitudinal US multi-ethnic cohort. Peripheral vascular damage was defined by the Systemic Lupus International Collaborating Clinics Damage Index (SDI). Factors associated with peripheral vascular damage were examined by univariable and multi-variable logistic regression models and its impact on survival by a Cox multi-variable regression. Thirty-four (5.3%) of 637 patients (90% women, mean [SD] age 36.5 [12.6] [16-87] years) developed peripheral vascular damage. Age and the SDI (without peripheral vascular damage) were statistically significant (odds ratio [OR] = 1.05, 95% confidence interval [CI] 1.01-1.08; P = 0.0107 and OR = 1.30, 95% CI 0.09-1.56; P = 0.0043, respectively) in multi-variable analyses. Azathioprine, warfarin and statins were also statistically significant, and glucocorticoid use was borderline statistically significant (OR = 1.03, 95% CI 0.10-1.06; P = 0.0975). In the survival analysis, peripheral vascular damage was independently associated with a diminished survival (hazard ratio = 2.36; 95% CI 1.07-5.19; P = 0.0334). In short, age was independently associated with peripheral vascular damage, but so was the presence of damage in other organs (ocular, neuropsychiatric, renal, cardiovascular, pulmonary, musculoskeletal and integument) and some medications (probably reflecting more severe disease). Peripheral vascular damage also negatively affected survival.

Affordability and cost-effectiveness: decision-making on the cost-effectiveness plane.

PubMed

Sendi, P P; Briggs, A H

2001-10-01

Much recent research interest has focused on handling uncertainty in cost-effectiveness analysis and in particular the calculation of confidence intervals for incremental cost-effectiveness ratios (ICERs). Problems of interpretation when ICERs are negative have led to two important and related developments: the use of the net-benefit statistic and the presentation of uncertainty in cost-effectiveness analysis using acceptability curves. However, neither of these developments directly addresses the problem that decision-makers are constrained by a fixed-budget and may not be able to fund new, more expensive interventions, even if they have been shown to represent good value for money. In response to this limitation, the authors introduce the 'affordability curve' which reflects the probability that a programme is affordable for a wide range of threshold budgets. The authors argue that the joint probability an intervention is affordable and cost-effective is more useful for decision-making since it captures both dimensions of the decision problem faced by those responsible for health service budgets. Copyright 2001 John Wiley & Sons, Ltd.

[Analysis and experimental verification of sensitivity and SNR of laser warning receiver].

PubMed

Zhang, Ji-Long; Wang, Ming; Tian, Er-Ming; Li, Xiao; Wang, Zhi-Bin; Zhang, Yue

2009-01-01

In order to countermeasure increasingly serious threat from hostile laser in modern war, it is urgent to do research on laser warning technology and system, and the sensitivity and signal to noise ratio (SNR) are two important performance parameters in laser warning system. In the present paper, based on the signal statistical detection theory, a method for calculation of the sensitivity and SNR in coherent detection laser warning receiver (LWR) has been proposed. Firstly, the probabilities of the laser signal and receiver noise were analyzed. Secondly, based on the threshold detection theory and Neyman-Pearson criteria, the signal current equation was established by introducing detection probability factor and false alarm rate factor, then, the mathematical expressions of sensitivity and SNR were deduced. Finally, by using method, the sensitivity and SNR of the sinusoidal grating laser warning receiver developed by our group were analyzed, and the theoretic calculation and experimental results indicate that the SNR analysis method is feasible, and can be used in performance analysis of LWR.

Noise deconvolution based on the L1-metric and decomposition of discrete distributions of postsynaptic responses.

PubMed

Astrelin, A V; Sokolov, M V; Behnisch, T; Reymann, K G; Voronin, L L

1997-04-25

A statistical approach to analysis of amplitude fluctuations of postsynaptic responses is described. This includes (1) using a L1-metric in the space of distribution functions for minimisation with application of linear programming methods to decompose amplitude distributions into a convolution of Gaussian and discrete distributions; (2) deconvolution of the resulting discrete distribution with determination of the release probabilities and the quantal amplitude for cases with a small number (< 5) of discrete components. The methods were tested against simulated data over a range of sample sizes and signal-to-noise ratios which mimicked those observed in physiological experiments. In computer simulation experiments, comparisons were made with other methods of 'unconstrained' (generalized) and constrained reconstruction of discrete components from convolutions. The simulation results provided additional criteria for improving the solutions to overcome 'over-fitting phenomena' and to constrain the number of components with small probabilities. Application of the programme to recordings from hippocampal neurones demonstrated its usefulness for the analysis of amplitude distributions of postsynaptic responses.

The Efficiency of Solar Flares With Gamma-ray Emission of Solar Cosmic Rays Production.

NASA Astrophysics Data System (ADS)

Belov, A. V.; Kurt, V. G.; Mavromichalaki, H.

A statistical analysis of solar flares with gamma-ray emission measured by SMM (W.T. Westrand, at al.,1999, Ap.J, Suppl. Series, 409) and proton events occurrence based on the proton events catalog (A.Belov, at al.2001, Proc. 27th ICRC 2001, Ham- burg, 3465) was performed. We obtained the probabilities of the appearence of pro- ton fluxes near the Earth from the different fluence values of gamma-line emission, bremsstrahlung emissions and soft X-ray emission of the parent flares. This statisti- cal approach allows us to obtain if not precise than at least proper quantitative ratios than relate the flares with obvious evidences for proton production with the escaped from the Sun viciniy. We than look at the available data of soft X-ray flares time behaviour and show the exact timing of proton acceleration and probably shock for- mation comparing the soft X-ray injection function. The shock wave influence on the proton escaping process is shortly discussed.

On the probability of violations of Fourier's law for heat flow in small systems observed for short times

NASA Astrophysics Data System (ADS)

Evans, Denis J.; Searles, Debra J.; Williams, Stephen R.

2010-01-01

We study the statistical mechanics of thermal conduction in a classical many-body system that is in contact with two thermal reservoirs maintained at different temperatures. The ratio of the probabilities, that when observed for a finite time, the time averaged heat flux flows in and against the direction required by Fourier's Law for heat flow, is derived from first principles. This result is obtained using the transient fluctuation theorem. We show that the argument of that theorem, namely, the dissipation function is, close to equilibrium, equal to a microscopic expression for the entropy production. We also prove that if transient time correlation functions of smooth zero mean variables decay to zero at long times, the system will relax to a unique nonequilibrium steady state, and for this state, the thermal conductivity must be positive. Our expressions are tested using nonequilibrium molecular dynamics simulations of heat flow between thermostated walls.

Patterns of a spatial exploration under time evolution of the attractiveness: Persistent nodes, degree distribution, and spectral properties

NASA Astrophysics Data System (ADS)

da Silva, Roberto

2018-06-01

This work explores the features of a graph generated by agents that hop from one node to another node, where the nodes have evolutionary attractiveness. The jumps are governed by Boltzmann-like transition probabilities that depend both on the euclidean distance between the nodes and on the ratio (β) of the attractiveness between them. It is shown that persistent nodes, i.e., nodes that never been reached by this special random walk are possible in the stationary limit differently from the case where the attractiveness is fixed and equal to one for all nodes (β = 1). Simultaneously, one also investigates the spectral properties and statistics related to the attractiveness and degree distribution of the evolutionary network. Finally, a study of the crossover between persistent phase and no persistent phase was performed and it was also observed the existence of a special type of transition probability which leads to a power law behaviour for the time evolution of the persistence.

Reconstructing missing information on precipitation datasets: impact of tails on adopted statistical distributions.

NASA Astrophysics Data System (ADS)

Pedretti, Daniele; Beckie, Roger Daniel

2014-05-01

Missing data in hydrological time-series databases are ubiquitous in practical applications, yet it is of fundamental importance to make educated decisions in problems involving exhaustive time-series knowledge. This includes precipitation datasets, since recording or human failures can produce gaps in these time series. For some applications, directly involving the ratio between precipitation and some other quantity, lack of complete information can result in poor understanding of basic physical and chemical dynamics involving precipitated water. For instance, the ratio between precipitation (recharge) and outflow rates at a discharge point of an aquifer (e.g. rivers, pumping wells, lysimeters) can be used to obtain aquifer parameters and thus to constrain model-based predictions. We tested a suite of methodologies to reconstruct missing information in rainfall datasets. The goal was to obtain a suitable and versatile method to reduce the errors given by the lack of data in specific time windows. Our analyses included both a classical chronologically-pairing approach between rainfall stations and a probability-based approached, which accounted for the probability of exceedence of rain depths measured at two or multiple stations. Our analyses proved that it is not clear a priori which method delivers the best methodology. Rather, this selection should be based considering the specific statistical properties of the rainfall dataset. In this presentation, our emphasis is to discuss the effects of a few typical parametric distributions used to model the behavior of rainfall. Specifically, we analyzed the role of distributional "tails", which have an important control on the occurrence of extreme rainfall events. The latter strongly affect several hydrological applications, including recharge-discharge relationships. The heavy-tailed distributions we considered were parametric Log-Normal, Generalized Pareto, Generalized Extreme and Gamma distributions. The methods were first tested on synthetic examples, to have a complete control of the impact of several variables such as minimum amount of data required to obtain reliable statistical distributions from the selected parametric functions. Then, we applied the methodology to precipitation datasets collected in the Vancouver area and on a mining site in Peru.

Statistical context shapes stimulus-specific adaptation in human auditory cortex.

PubMed

Herrmann, Björn; Henry, Molly J; Fromboluti, Elisa Kim; McAuley, J Devin; Obleser, Jonas

2015-04-01

Stimulus-specific adaptation is the phenomenon whereby neural response magnitude decreases with repeated stimulation. Inconsistencies between recent nonhuman animal recordings and computational modeling suggest dynamic influences on stimulus-specific adaptation. The present human electroencephalography (EEG) study investigates the potential role of statistical context in dynamically modulating stimulus-specific adaptation by examining the auditory cortex-generated N1 and P2 components. As in previous studies of stimulus-specific adaptation, listeners were presented with oddball sequences in which the presentation of a repeated tone was infrequently interrupted by rare spectral changes taking on three different magnitudes. Critically, the statistical context varied with respect to the probability of small versus large spectral changes within oddball sequences (half of the time a small change was most probable; in the other half a large change was most probable). We observed larger N1 and P2 amplitudes (i.e., release from adaptation) for all spectral changes in the small-change compared with the large-change statistical context. The increase in response magnitude also held for responses to tones presented with high probability, indicating that statistical adaptation can overrule stimulus probability per se in its influence on neural responses. Computational modeling showed that the degree of coadaptation in auditory cortex changed depending on the statistical context, which in turn affected stimulus-specific adaptation. Thus the present data demonstrate that stimulus-specific adaptation in human auditory cortex critically depends on statistical context. Finally, the present results challenge the implicit assumption of stationarity of neural response magnitudes that governs the practice of isolating established deviant-detection responses such as the mismatch negativity. Copyright © 2015 the American Physiological Society.

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

Boundary Layer Effect on Behavior of Discrete Models.

PubMed

Eliáš, Jan

2017-02-10

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

Predictive landslide susceptibility mapping using spatial information in the Pechabun area of Thailand

NASA Astrophysics Data System (ADS)

Oh, Hyun-Joo; Lee, Saro; Chotikasathien, Wisut; Kim, Chang Hwan; Kwon, Ju Hyoung

2009-04-01

For predictive landslide susceptibility mapping, this study applied and verified probability model, the frequency ratio and statistical model, logistic regression at Pechabun, Thailand, using a geographic information system (GIS) and remote sensing. Landslide locations were identified in the study area from interpretation of aerial photographs and field surveys, and maps of the topography, geology and land cover were constructed to spatial database. The factors that influence landslide occurrence, such as slope gradient, slope aspect and curvature of topography and distance from drainage were calculated from the topographic database. Lithology and distance from fault were extracted and calculated from the geology database. Land cover was classified from Landsat TM satellite image. The frequency ratio and logistic regression coefficient were overlaid for landslide susceptibility mapping as each factor’s ratings. Then the landslide susceptibility map was verified and compared using the existing landslide location. As the verification results, the frequency ratio model showed 76.39% and logistic regression model showed 70.42% in prediction accuracy. The method can be used to reduce hazards associated with landslides and to plan land cover.

Outflow and clogging of shape-anisotropic grains in hoppers with small apertures.

PubMed

Ashour, A; Wegner, S; Trittel, T; Börzsönyi, T; Stannarius, R

2017-01-04

Outflow of granular material through a small orifice is a fundamental process in many industrial fields, for example in silo discharge, and in everyday's life. Most experimental studies of the dynamics have been performed so far with monodisperse disks in two-dimensional (2D) hoppers or spherical grains in 3D. We investigate this process for shape-anisotropic grains in 3D hoppers and discuss the role of size and shape parameters on avalanche statistics, clogging states, and mean flow velocities. It is shown that an increasing aspect ratio of the grains leads to lower flow rates and higher clogging probabilities compared to spherical grains. On the other hand, the number of grains forming the clog is larger for elongated grains of comparable volumes, and the long axis of these blocking grains is preferentially aligned towards the center of the orifice. We find a qualitative transition in the hopper discharge behavior for aspect ratios larger than ≈6. At still higher aspect ratios >8-12, the outflowing material leaves long vertical holes in the hopper that penetrate the complete granular bed. This changes the discharge characteristics qualitatively.

Variance in age-specific sex composition of Pacific halibut catches, and comparison of statistical and genetic methods for reconstructing sex ratios

NASA Astrophysics Data System (ADS)

Loher, Timothy; Woods, Monica A.; Jimenez-Hidalgo, Isadora; Hauser, Lorenz

2016-01-01

Declines in size at age of Pacific halibut Hippoglossus stenolepis, in concert with sexually-dimorphic growth and a constant minimum commercial size limit, have led to the expectation that the sex composition of commercial catches should be increasingly female-biased. Sensitivity analyses suggest that variance in sex composition of landings may be the most influential source of uncertainty affecting current understanding of spawning stock biomass. However, there is no reliable way to determine sex at landing because all halibut are eviscerated at sea. In 2014, a statistical method based on survey data was developed to estimate the probability that fish of any given length at age (LAA) would be female, derived from the fundamental observation that large, young fish are likely female whereas small, old fish have a high probability of being male. Here, we examine variability in age-specific sex composition using at-sea commercial and closed-season survey catches, and compare the accuracy of the survey-based LAA technique to genetic markers for reconstructing the sex composition of catches. Sexing by LAA performed best for summer-collected samples, consistent with the hypothesis that the ability to characterize catches can be influenced by seasonal demographic shifts. Additionally, differences between survey and commercial selectivity that allow fishers to harvest larger fish within cohorts may generate important mismatch between survey and commercial datasets. Length-at-age-based estimates ranged from 4.7% underestimation of female proportion to 12.0% overestimation, with mean error of 5.8 ± 1.5%. Ratios determined by genetics were closer to true sample proportions and displayed less variability; estimation to within < 1% of true ratios was limited to genetics. Genetic estimation of female proportions ranged from 4.9% underestimation to 2.5% overestimation, with a mean absolute error of 1.2 ± 1.2%. Males were generally more difficult to assign than females: 6.7% of males and 3.4% of females were incorrectly assigned. Although nuclear microsatellites proved more consistent at partitioning catches by sex, we recommend that SNP assays be developed to allow for rapid, cost-effective, and accurate sex identification.

Predictive criteria for prostate cancer detection in men with serum PSA concentration of 2.0 to 4.0 ng/mL.

PubMed

Kravchick, Sergey; Peled, Ronit; Dorfman, Dov; Agulansky, Leonid; Ben-Dor, David; Cytron, Shmuel

2005-09-01

To assess the usefulness of measuring testosterone, free testosterone, and the free/total (f/t) prostate-specific antigen (PSA) ratio with the intention of reducing the number of unnecessary biopsies in the patients with PSA values between 2.0 and 4.0 ng/mL. Cancer detection is not rare among patients with PSA values between 2.0 and 4.0 ng/mL. A total of 171 men with serum PSA levels of 2.0 to 4.0 ng/mL were enrolled in this study. The f/t PSA ratio and total and free testosterone levels were quantified. All patients underwent transrectal ultrasound-guided biopsy. The cancer detection rate, clinical and pathologic features of the cancers detected, and the probability of cancer detection in relation to the f/t PSA ratio and total and free testosterone levels were estimated. Two-step statistical analysis was used for descriptive purposes and in the detection of cancer predictors. Statistical significance was set at P < or = 0.05. The mean patient age was 63.3 years. Cancer was detected in 39 (22.8%) of the 171 patients. Only 15.4% of our patients had insignificant cancer. The f/t PSA ratio and total and free testosterone levels were significantly lower in the patients with prostate cancer (19.3%, 13.68 nmol/L, and 28.4 pmol/L, respectively; P < 0.001). The f/t PSA ratio and free testosterone were the strongest predictors of cancer detection (P < 0.001). The results of our study have shown that an important number of cancers could be detected in the PSA range of 2.0 to 4.0 ng/mL. The great majority of cancers detected have the features of medically significant tumors. The combination of the f/t PSA ratio and free testosterone measurements may reveal those patients who require biopsy.

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

What Is the Probability You Are a Bayesian?

ERIC Educational Resources Information Center

Wulff, Shaun S.; Robinson, Timothy J.

2014-01-01

Bayesian methodology continues to be widely used in statistical applications. As a result, it is increasingly important to introduce students to Bayesian thinking at early stages in their mathematics and statistics education. While many students in upper level probability courses can recite the differences in the Frequentist and Bayesian…

Statistics concerning the Apollo command module water landing, including the probability of occurrence of various impact conditions, sucessful impact, and body X-axis loads

NASA Technical Reports Server (NTRS)

Whitnah, A. M.; Howes, D. B.

1971-01-01

Statistical information for the Apollo command module water landings is presented. This information includes the probability of occurrence of various impact conditions, a successful impact, and body X-axis loads of various magnitudes.

A Brief Look at the History of Probability and Statistics.

ERIC Educational Resources Information Center

Lightner, James E.

1991-01-01

The historical development of probability theory is traced from its early origins in games of chance through its mathematical foundations in the work of Pascal and Fermat. The roots of statistics are also presented beginning with early actuarial developments through the work of Laplace, Gauss, and others. (MDH)

Focus in High School Mathematics: Statistics and Probability

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2009

2009-01-01

Reasoning about and making sense of statistics and probability are essential to students' future success. This volume belongs to a series that supports National Council of Teachers of Mathematics' (NCTM's) "Focus in High School Mathematics: Reasoning and Sense Making" by providing additional guidance for making reasoning and sense making part of…

A Study of Strengthening Secondary Mathematics Teachers' Knowledge of Statistics and Probability via Professional Development

ERIC Educational Resources Information Center

DeVaul, Lina

2017-01-01

A professional development program (PSPD) was implemented to improve in-service secondary mathematics teachers' content knowledge, pedagogical knowledge, and self-efficacy in teaching secondary school statistics and probability. Participants generated a teaching resource website at the conclusion of the PSPD program. Participants' content…

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…

Specifying the Probability Characteristics of Funnel Plot Control Limits: An Investigation of Three Approaches

PubMed Central

Manktelow, Bradley N.; Seaton, Sarah E.

2012-01-01

Background Emphasis is increasingly being placed on the monitoring and comparison of clinical outcomes between healthcare providers. Funnel plots have become a standard graphical methodology to identify outliers and comprise plotting an outcome summary statistic from each provider against a specified ‘target’ together with upper and lower control limits. With discrete probability distributions it is not possible to specify the exact probability that an observation from an ‘in-control’ provider will fall outside the control limits. However, general probability characteristics can be set and specified using interpolation methods. Guidelines recommend that providers falling outside such control limits should be investigated, potentially with significant consequences, so it is important that the properties of the limits are understood. Methods Control limits for funnel plots for the Standardised Mortality Ratio (SMR) based on the Poisson distribution were calculated using three proposed interpolation methods and the probability calculated of an ‘in-control’ provider falling outside of the limits. Examples using published data were shown to demonstrate the potential differences in the identification of outliers. Results The first interpolation method ensured that the probability of an observation of an ‘in control’ provider falling outside either limit was always less than a specified nominal probability (p). The second method resulted in such an observation falling outside either limit with a probability that could be either greater or less than p, depending on the expected number of events. The third method led to a probability that was always greater than, or equal to, p. Conclusion The use of different interpolation methods can lead to differences in the identification of outliers. This is particularly important when the expected number of events is small. We recommend that users of these methods be aware of the differences, and specify which interpolation method is to be used prior to any analysis. PMID:23029202

Diagnostic accuracy of FEV1/forced vital capacity ratio z scores in asthmatic patients.

PubMed

Lambert, Allison; Drummond, M Bradley; Wei, Christine; Irvin, Charles; Kaminsky, David; McCormack, Meredith; Wise, Robert

2015-09-01

The FEV1/forced vital capacity (FVC) ratio is used as a criterion for airflow obstruction; however, the test characteristics of spirometry in the diagnosis of asthma are not well established. The accuracy of a test depends on the pretest probability of disease. We wanted to estimate the FEV1/FVC ratio z score threshold with optimal accuracy for the diagnosis of asthma for different pretest probabilities. Asthmatic patients enrolled in 4 trials from the Asthma Clinical Research Centers were included in this analysis. Measured and predicted FEV1/FVC ratios were obtained, with calculation of z scores for each participant. Across a range of asthma prevalences and z score thresholds, the overall diagnostic accuracy was calculated. One thousand six hundred eight participants were included (mean age, 39 years; 71% female; 61% white). The mean FEV1 percent predicted value was 83% (SD, 15%). In a symptomatic population with 50% pretest probability of asthma, optimal accuracy (68%) is achieved with a z score threshold of -1.0 (16th percentile), corresponding to a 6 percentage point reduction from the predicted ratio. However, in a screening population with a 5% pretest probability of asthma, the optimum z score is -2.0 (second percentile), corresponding to a 12 percentage point reduction from the predicted ratio. These findings were not altered by markers of disease control. Reduction of the FEV1/FVC ratio can support the diagnosis of asthma; however, the ratio is neither sensitive nor specific enough for diagnostic accuracy. When interpreting spirometric results, consideration of the pretest probability is an important consideration in the diagnosis of asthma based on airflow limitation. Copyright © 2015 American Academy of Allergy, Asthma & Immunology. Published by Elsevier Inc. All rights reserved.

Statistical theory of dynamo

NASA Astrophysics Data System (ADS)

Kim, E.; Newton, A. P.

2012-04-01

One major problem in dynamo theory is the multi-scale nature of the MHD turbulence, which requires statistical theory in terms of probability distribution functions. In this contribution, we present the statistical theory of magnetic fields in a simplified mean field α-Ω dynamo model by varying the statistical property of alpha, including marginal stability and intermittency, and then utilize observational data of solar activity to fine-tune the mean field dynamo model. Specifically, we first present a comprehensive investigation into the effect of the stochastic parameters in a simplified α-Ω dynamo model. Through considering the manifold of marginal stability (the region of parameter space where the mean growth rate is zero), we show that stochastic fluctuations are conductive to dynamo. Furthermore, by considering the cases of fluctuating alpha that are periodic and Gaussian coloured random noise with identical characteristic time-scales and fluctuating amplitudes, we show that the transition to dynamo is significantly facilitated for stochastic alpha with random noise. Furthermore, we show that probability density functions (PDFs) of the growth-rate, magnetic field and magnetic energy can provide a wealth of useful information regarding the dynamo behaviour/intermittency. Finally, the precise statistical property of the dynamo such as temporal correlation and fluctuating amplitude is found to be dependent on the distribution the fluctuations of stochastic parameters. We then use observations of solar activity to constrain parameters relating to the effect in stochastic α-Ω nonlinear dynamo models. This is achieved through performing a comprehensive statistical comparison by computing PDFs of solar activity from observations and from our simulation of mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain PDFs of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α-Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. By varying the correlation time of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha <α'2>/α02 (where angular brackets <> denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity on both long and short time scales. In particular, a good agreement is obtained when the fluctuation in alpha is roughly equal to the mean part with a correlation time shorter than the solar period.

Applied Problems and Use of Technology in an Aligned Way in Basic Courses in Probability and Statistics for Engineering Students--A Way to Enhance Understanding and Increase Motivation

ERIC Educational Resources Information Center

Zetterqvist, Lena

2017-01-01

Researchers and teachers often recommend motivating exercises and use of mathematics or statistics software for the teaching of basic courses in probability and statistics. Our courses are given to large groups of engineering students at Lund Institute of Technology. We found that the mere existence of real-life data and technology in a course…

Assessment of Three Flood Hazard Mapping Methods: A Case Study of Perlis

NASA Astrophysics Data System (ADS)

Azizat, Nazirah; Omar, Wan Mohd Sabki Wan

2018-03-01

Flood is a common natural disaster and also affect the all state in Malaysia. Regarding to Drainage and Irrigation Department (DID) in 2007, about 29, 270 km2 or 9 percent of region of the country is prone to flooding. Flood can be such devastating catastrophic which can effected to people, economy and environment. Flood hazard mapping can be used is an important part in flood assessment to define those high risk area prone to flooding. The purposes of this study are to prepare a flood hazard mapping in Perlis and to evaluate flood hazard using frequency ratio, statistical index and Poisson method. The six factors affecting the occurrence of flood including elevation, distance from the drainage network, rainfall, soil texture, geology and erosion were created using ArcGIS 10.1 software. Flood location map in this study has been generated based on flooded area in year 2010 from DID. These parameters and flood location map were analysed to prepare flood hazard mapping in representing the probability of flood area. The results of the analysis were verified using flood location data in year 2013, 2014, 2015. The comparison result showed statistical index method is better in prediction of flood area rather than frequency ratio and Poisson method.

Brick tunnel randomization and the momentum of the probability mass.

PubMed

Kuznetsova, Olga M

2015-12-30

The allocation space of an unequal-allocation permuted block randomization can be quite wide. The development of unequal-allocation procedures with a narrower allocation space, however, is complicated by the need to preserve the unconditional allocation ratio at every step (the allocation ratio preserving (ARP) property). When the allocation paths are depicted on the K-dimensional unitary grid, where allocation to the l-th treatment is represented by a step along the l-th axis, l = 1 to K, the ARP property can be expressed in terms of the center of the probability mass after i allocations. Specifically, for an ARP allocation procedure that randomizes subjects to K treatment groups in w1 :⋯:wK ratio, w1 +⋯+wK =1, the coordinates of the center of the mass are (w1 i,…,wK i). In this paper, the momentum with respect to the center of the probability mass (expected imbalance in treatment assignments) is used to compare ARP procedures in how closely they approximate the target allocation ratio. It is shown that the two-arm and three-arm brick tunnel randomizations (BTR) are the ARP allocation procedures with the tightest allocation space among all allocation procedures with the same allocation ratio; the two-arm BTR is the minimum-momentum two-arm ARP allocation procedure. Resident probabilities of two-arm and three-arm BTR are analytically derived from the coordinates of the center of the probability mass; the existence of the respective transition probabilities is proven. Probability of deterministic assignments with BTR is found generally acceptable. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Why Current Statistics of Complementary Alternative Medicine Clinical Trials is Invalid.

PubMed

Pandolfi, Maurizio; Carreras, Giulia

2018-06-07

It is not sufficiently known that frequentist statistics cannot provide direct information on the probability that the research hypothesis tested is correct. The error resulting from this misunderstanding is compounded when the hypotheses under scrutiny have precarious scientific bases, which, generally, those of complementary alternative medicine (CAM) are. In such cases, it is mandatory to use inferential statistics, considering the prior probability that the hypothesis tested is true, such as the Bayesian statistics. The authors show that, under such circumstances, no real statistical significance can be achieved in CAM clinical trials. In this respect, CAM trials involving human material are also hardly defensible from an ethical viewpoint.

Conditional Probabilities and Collapse in Quantum Measurements

NASA Astrophysics Data System (ADS)

Laura, Roberto; Vanni, Leonardo

2008-09-01

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

Data Analysis Techniques for Physical Scientists

NASA Astrophysics Data System (ADS)

Pruneau, Claude A.

2017-10-01

Preface; How to read this book; 1. The scientific method; Part I. Foundation in Probability and Statistics: 2. Probability; 3. Probability models; 4. Classical inference I: estimators; 5. Classical inference II: optimization; 6. Classical inference III: confidence intervals and statistical tests; 7. Bayesian inference; Part II. Measurement Techniques: 8. Basic measurements; 9. Event reconstruction; 10. Correlation functions; 11. The multiple facets of correlation functions; 12. Data correction methods; Part III. Simulation Techniques: 13. Monte Carlo methods; 14. Collision and detector modeling; List of references; Index.

A Meta-Analysis and Multisite Time-Series Analysis of the Differential Toxicity of Major Fine Particulate Matter Constituents

PubMed Central

Levy, Jonathan I.; Diez, David; Dou, Yiping; Barr, Christopher D.; Dominici, Francesca

2012-01-01

Health risk assessments of particulate matter less than 2.5 μm in diameter (PM2.5) often assume that all constituents of PM2.5 are equally toxic. While investigators in previous epidemiologic studies have evaluated health risks from various PM2.5 constituents, few have conducted the analyses needed to directly inform risk assessments. In this study, the authors performed a literature review and conducted a multisite time-series analysis of hospital admissions and exposure to PM2.5 constituents (elemental carbon, organic carbon matter, sulfate, and nitrate) in a population of 12 million US Medicare enrollees for the period 2000–2008. The literature review illustrated a general lack of multiconstituent models or insight about probabilities of differential impacts per unit of concentration change. Consistent with previous results, the multisite time-series analysis found statistically significant associations between short-term changes in elemental carbon and cardiovascular hospital admissions. Posterior probabilities from multiconstituent models provided evidence that some individual constituents were more toxic than others, and posterior parameter estimates coupled with correlations among these estimates provided necessary information for risk assessment. Ratios of constituent toxicities, commonly used in risk assessment to describe differential toxicity, were extremely uncertain for all comparisons. These analyses emphasize the subtlety of the statistical techniques and epidemiologic studies necessary to inform risk assessments of particle constituents. PMID:22510275

Combining and comparing neutrinoless double beta decay experiments using different nuclei

NASA Astrophysics Data System (ADS)

Bergström, Johannes

2013-02-01

We perform a global fit of the most relevant neutrinoless double beta decay experiments within the standard model with massive Majorana neutrinos. Using Bayesian inference makes it possible to take into account the theoretical uncertainties on the nuclear matrix elements in a fully consistent way. First, we analyze the data used to claim the observation of neutrinoless double beta decay in 76Ge, and find strong evidence (according to Jeffrey's scale) for a peak in the spectrum and moderate evidence for that the peak is actually close to the energy expected for the neutrinoless decay. We also find a significantly larger statistical error than the original analysis, which we include in the comparison with other data. Then, we statistically test the consistency between this claim with that of recent measurements using 136Xe. We find that the two data sets are about 40 to 80 times more probable under the assumption that they are inconsistent, depending on the nuclear matrix element uncertainties and the prior on the smallest neutrino mass. Hence, there is moderate to strong evidence of incompatibility, and for equal prior probabilities the posterior probability of compatibility is between 1.3% and 2.5%. If one, despite such evidence for incompatibility, combines the two data sets, we find that the total evidence of neutrinoless double beta decay is negligible. If one ignores the claim, there is weak evidence against the existence of the decay. We also perform approximate frequentist tests of compatibility for fixed ratios of the nuclear matrix elements, as well as of the no signal hypothesis. Generalization to other sets of experiments as well as other mechanisms mediating the decay is possible.

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.

To P or Not to P: Backing Bayesian Statistics.

PubMed

Buchinsky, Farrel J; Chadha, Neil K

2017-12-01

In biomedical research, it is imperative to differentiate chance variation from truth before we generalize what we see in a sample of subjects to the wider population. For decades, we have relied on null hypothesis significance testing, where we calculate P values for our data to decide whether to reject a null hypothesis. This methodology is subject to substantial misinterpretation and errant conclusions. Instead of working backward by calculating the probability of our data if the null hypothesis were true, Bayesian statistics allow us instead to work forward, calculating the probability of our hypothesis given the available data. This methodology gives us a mathematical means of incorporating our "prior probabilities" from previous study data (if any) to produce new "posterior probabilities." Bayesian statistics tell us how confidently we should believe what we believe. It is time to embrace and encourage their use in our otolaryngology research.

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…

The Effects and Side-Effects of Statistics Education: Psychology Students' (Mis-)Conceptions of Probability

ERIC Educational Resources Information Center

Morsanyi, Kinga; Primi, Caterina; Chiesi, Francesca; Handley, Simon

2009-01-01

In three studies we looked at two typical misconceptions of probability: the representativeness heuristic, and the equiprobability bias. The literature on statistics education predicts that some typical errors and biases (e.g., the equiprobability bias) increase with education, whereas others decrease. This is in contrast with reasoning theorists'…

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.…

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…

GPS: Geometry, Probability, and Statistics

ERIC Educational Resources Information Center

Field, Mike

2012-01-01

It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

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

Marleau, Peter; Monterial, Mateusz; Clarke, Shaun

A Bayesian approach is proposed for pulse shape discrimination of photons and neutrons in liquid organic scinitillators. Instead of drawing a decision boundary, each pulse is assigned a photon or neutron confidence probability. In addition, this allows for photon and neutron classification on an event-by-event basis. The sum of those confidence probabilities is used to estimate the number of photon and neutron instances in the data. An iterative scheme, similar to an expectation-maximization algorithm for Gaussian mixtures, is used to infer the ratio of photons-to-neutrons in each measurement. Therefore, the probability space adapts to data with varying photon-to-neutron ratios. Amore » time-correlated measurement of Am–Be and separate measurements of 137Cs, 60Co and 232Th photon sources were used to construct libraries of neutrons and photons. These libraries were then used to produce synthetic data sets with varying ratios of photons-to-neutrons. Probability weighted method that we implemented was found to maintain neutron acceptance rate of up to 90% up to photon-to-neutron ratio of 2000, and performed 9% better than the decision boundary approach. Furthermore, the iterative approach appropriately changed the probability space with an increasing number of photons which kept the neutron population estimate from unrealistically increasing.« less

The Economic Efficiency of Financial Markets

NASA Astrophysics Data System (ADS)

Wang, Yougui

In this paper, we investigate the economic efficiency of markets and specify its applicability to financial markets. The statistical expressions of supply and demand of a market are formulated in terms of willingness prices. By introducing probability of realized exchange, we also formulate the realized market surplus. It can be proved that only when the market is in equilibrium the realized surplus can reach its maximum value. The market efficiency can be measured by the ratio of realized surplus to its maximum value. For a financial market, the market participants are composed of two groups: producers and speculators. The former brings the surplus into the market and the latter provides liquidity to make them realized.

Optimal detection pinhole for lowering speckle noise while maintaining adequate optical sectioning in confocal reflectance microscopes

PubMed Central

Rajadhyaksha, Milind

2012-01-01

Abstract. Coherent speckle influences the resulting image when narrow spectral line-width and single spatial mode illumination are used, though these are the same light-source properties that provide the best radiance-to-cost ratio. However, a suitable size of the detection pinhole can be chosen to maintain adequate optical sectioning while making the probability density of the speckle noise more normal and reducing its effect. The result is a qualitatively better image with improved contrast, which is easier to read. With theoretical statistics and experimental results, we show that the detection pinhole size is a fundamental parameter for designing imaging systems for use in turbid media. PMID:23224184

Statistical Study of Aircraft Icing Probabilities at the 700- and 500- Millibar Levels over Ocean Areas in the Northern Hemisphere

NASA Technical Reports Server (NTRS)

Perkins, Porter J.; Lewis, William; Mulholland, Donald R.

1957-01-01

A statistical study is made of icing data reported from weather reconnaissance aircraft flown by Air Weather Service (USAF). The weather missions studied were flown at fixed flight levels of 500 millibars (18,000 ft) and 700 millibars (10,000 ft) over wide areas of the Pacific, Atlantic, and Arctic Oceans. This report is presented as part of a program conducted by the NACA to obtain extensive icing statistics relevant to aircraft design and operation. The thousands of in-flight observations recorded over a 2- to 4-year period provide reliable statistics on icing encounters for the specific areas, altitudes, and seasons included in the data. The relative frequencies of icing occurrence are presented, together with the estimated icing probabilities and the relation of these probabilities to the frequencies of flight in clouds and cloud temperatures. The results show that aircraft operators can expect icing probabilities to vary widely throughout the year from near zero in the cold Arctic areas in winter up to 7 percent in areas where greater cloudiness and warmer temperatures prevail. The data also reveal a general tendency of colder cloud temperatures to reduce the probability of icing in equally cloudy conditions.

Sandpile-based model for capturing magnitude distributions and spatiotemporal clustering and separation in regional earthquakes

NASA Astrophysics Data System (ADS)

Batac, Rene C.; Paguirigan, Antonino A., Jr.; Tarun, Anjali B.; Longjas, Anthony G.

2017-04-01

We propose a cellular automata model for earthquake occurrences patterned after the sandpile model of self-organized criticality (SOC). By incorporating a single parameter describing the probability to target the most susceptible site, the model successfully reproduces the statistical signatures of seismicity. The energy distributions closely follow power-law probability density functions (PDFs) with a scaling exponent of around -1. 6, consistent with the expectations of the Gutenberg-Richter (GR) law, for a wide range of the targeted triggering probability values. Additionally, for targeted triggering probabilities within the range 0.004-0.007, we observe spatiotemporal distributions that show bimodal behavior, which is not observed previously for the original sandpile. For this critical range of values for the probability, model statistics show remarkable comparison with long-period empirical data from earthquakes from different seismogenic regions. The proposed model has key advantages, the foremost of which is the fact that it simultaneously captures the energy, space, and time statistics of earthquakes by just introducing a single parameter, while introducing minimal parameters in the simple rules of the sandpile. We believe that the critical targeting probability parameterizes the memory that is inherently present in earthquake-generating regions.

Recent Results with CVD Diamond Trackers

NASA Astrophysics Data System (ADS)

Adam, W.; Bauer, C.; Berdermann, E.; Bergonzo, P.; Bogani, F.; Borchi, E.; Brambilla, A.; Bruzzi, M.; Colledani, C.; Conway, J.; Dabrowski, W.; Delpierre, P.; Deneuville, A.; Dulinski, W.; van Eijk, B.; Fallou, A.; Fizzotti, F.; Foulon, F.; Friedl, M.; Gan, K. K.; Gheeraert, E.; Grigoriev, E.; Hallewell, G.; Hall-Wilton, R.; Han, S.; Hartjes, F.; Hrubec, J.; Husson, D.; Kagan, H.; Kania, D.; Kaplon, J.; Karl, C.; Kass, R.; Knöpfle, K. T.; Krammer, M.; Logiudice, A.; Lu, R.; Manfredi, P. F.; Manfredotti, C.; Marshall, R. D.; Meier, D.; Mishina, M.; Oh, A.; Pan, L. S.; Palmieri, V. G.; Pernicka, M.; Peitz, A.; Pirollo, S.; Polesello, P.; Pretzl, K.; Procario, M.; Re, V.; Riester, J. L.; Roe, S.; Roff, D.; Rudge, A.; Runolfsson, O.; Russ, J.; Schnetzer, S.; Sciortino, S.; Speziali, V.; Stelzer, H.; Stone, R.; Suter, B.; Tapper, R. J.; Tesarek, R.; Trawick, M.; Trischuk, W.; Vittone, E.; Walsh, A. M.; Wedenig, R.; Weilhammer, P.; White, C.; Ziock, H.; Zoeller, M.; RD42 Collaboration

1999-08-01

We present recent results on the use of Chemical Vapor Deposition (CVD) diamond microstrip detectors for charged particle tracking. A series of detectors was fabricated using 1 x 1 cm 2 diamonds. Good signal-to-noise ratios were observed using both slow and fast readout electronics. For slow readout electronics, 2 μs shaping time, the most probable signal-to-noise ratio was 50 to 1. For fast readout electronics, 25 ns peaking time, the most probable signal-to-noise ratio was 7 to 1. Using the first 2 x 4 cm 2 diamond from a production CVD reactor with slow readout electronics, the most probable signal-to-noise ratio was 23 to 1. The spatial resolution achieved for the detectors was consistent with the digital resolution expected from the detector pitch.

Survival analysis using inverse probability of treatment weighted methods based on the generalized propensity score.

PubMed

Sugihara, Masahiro

2010-01-01

In survival analysis, treatment effects are commonly evaluated based on survival curves and hazard ratios as causal treatment effects. In observational studies, these estimates may be biased due to confounding factors. The inverse probability of treatment weighted (IPTW) method based on the propensity score is one of the approaches utilized to adjust for confounding factors between binary treatment groups. As a generalization of this methodology, we developed an exact formula for an IPTW log-rank test based on the generalized propensity score for survival data. This makes it possible to compare the group differences of IPTW Kaplan-Meier estimators of survival curves using an IPTW log-rank test for multi-valued treatments. As causal treatment effects, the hazard ratio can be estimated using the IPTW approach. If the treatments correspond to ordered levels of a treatment, the proposed method can be easily extended to the analysis of treatment effect patterns with contrast statistics. In this paper, the proposed method is illustrated with data from the Kyushu Lipid Intervention Study (KLIS), which investigated the primary preventive effects of pravastatin on coronary heart disease (CHD). The results of the proposed method suggested that pravastatin treatment reduces the risk of CHD and that compliance to pravastatin treatment is important for the prevention of CHD. (c) 2009 John Wiley & Sons, Ltd.

Overlapping clusters for distributed computation.

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

Mirrokni, Vahab; Andersen, Reid; Gleich, David F.

2010-11-01

Scalable, distributed algorithms must address communication problems. We investigate overlapping clusters, or vertex partitions that intersect, for graph computations. This setup stores more of the graph than required but then affords the ease of implementation of vertex partitioned algorithms. Our hope is that this technique allows us to reduce communication in a computation on a distributed graph. The motivation above draws on recent work in communication avoiding algorithms. Mohiyuddin et al. (SC09) design a matrix-powers kernel that gives rise to an overlapping partition. Fritzsche et al. (CSC2009) develop an overlapping clustering for a Schwarz method. Both techniques extend an initialmore » partitioning with overlap. Our procedure generates overlap directly. Indeed, Schwarz methods are commonly used to capitalize on overlap. Elsewhere, overlapping communities (Ahn et al, Nature 2009; Mishra et al. WAW2007) are now a popular model of structure in social networks. These have long been studied in statistics (Cole and Wishart, CompJ 1970). We present two types of results: (i) an estimated swapping probability {rho}{infinity}; and (ii) the communication volume of a parallel PageRank solution (link-following {alpha} = 0.85) using an additive Schwarz method. The volume ratio is the amount of extra storage for the overlap (2 means we store the graph twice). Below, as the ratio increases, the swapping probability and PageRank communication volume decreases.« less

Diagnostic Accuracy of Tests for Polyuria in Lithium-Treated Patients.

PubMed

Kinahan, James Conor; NiChorcorain, Aoife; Cunningham, Sean; Freyne, Aideen; Cooney, Colm; Barry, Siobhan; Kelly, Brendan D

2015-08-01

In lithium-treated patients, polyuria increases the risk of dehydration and lithium toxicity. If detected early, it is reversible. Despite its prevalence and associated morbidity in clinical practice, it remains underrecognized and therefore undertreated. The 24-hour urine collection is limited by its convenience and practicality. This study explores the diagnostic accuracy of alternative tests such as questionnaires on subjective polyuria, polydipsia, nocturia (dichotomous and ordinal responses), early morning urine sample osmolality (EMUO), and fluid intake record (FIR). This is a cross-sectional study of 179 lithium-treated patients attending a general adult and an old age psychiatry service. Participants completed the tests after completing an accurate 24-hour urine collection. The diagnostic accuracy of the individual tests was explored using the appropriate statistical techniques. Seventy-nine participants completed all of the tests. Polydipsia severity, EMUO, and FIR significantly differentiated the participants with polyuria (area under the receiver operating characteristic curve of 0.646, 0.760, and 0.846, respectively). Of the tests investigated, the FIR made the largest significant change in the probability that a patient experiences polyuria (<2000 mL/24 hours; interval likelihood ratio, 0.18 and >3500 mL/24 hours; interval likelihood ratio, 14). Symptomatic questioning, EMUO, and an FIR could be used in clinical practice to inform the prescriber of the probability that a lithium-treated patient is experiencing polyuria.

The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation.

PubMed

Chen, Connie; Gribble, Matthew O; Bartroff, Jay; Bay, Steven M; Goldstein, Larry

2017-05-01

The United States's Clean Water Act stipulates in section 303(d) that states must identify impaired water bodies for which total maximum daily loads (TMDLs) of pollution inputs into water bodies are developed. Decision-making procedures about how to list, or delist, water bodies as impaired, or not, per Clean Water Act 303(d) differ across states. In states such as California, whether or not a particular monitoring sample suggests that water quality is impaired can be regarded as a binary outcome variable, and California's current regulatory framework invokes a version of the exact binomial test to consolidate evidence across samples and assess whether the overall water body complies with the Clean Water Act. Here, we contrast the performance of California's exact binomial test with one potential alternative, the Sequential Probability Ratio Test (SPRT). The SPRT uses a sequential testing framework, testing samples as they become available and evaluating evidence as it emerges, rather than measuring all the samples and calculating a test statistic at the end of the data collection process. Through simulations and theoretical derivations, we demonstrate that the SPRT on average requires fewer samples to be measured to have comparable Type I and Type II error rates as the current fixed-sample binomial test. Policymakers might consider efficient alternatives such as SPRT to current procedure. Copyright © 2017 Elsevier Ltd. All rights reserved.

Does the probability of developing ocular trauma-related visual deficiency differ between genders?

PubMed

Blanco-Hernández, Dulce Milagros Razo; Valencia-Aguirre, Jessica Daniela; Lima-Gómez, Virgilio

2011-01-01

Ocular trauma affects males more often than females, but the impact of this condition regarding visual prognosis is unknown. We undertook this study to compare the probability of developing ocular trauma-related visual deficiency between genders, as estimated by the ocular trauma score (OTS). We designed an observational, retrospective, comparative, cross-sectional and open-label study. Female patients aged ≥6 years with ocular trauma were included and matched by age and ocular wall status with male patients at a 1:2 male/female ratio. Initial trauma features and the probability of developing visual deficiency (best corrected visual acuity <20/40) 6 months after the injury, as estimated by the OTS, were compared between genders. The proportion and 95% confidence intervals (95% CI) of visual deficiency 6 months after the injury were estimated. Ocular trauma features and the probability of developing visual deficiency were compared between genders (χ(2) and Fisher's exact test); p value <0.05 was considered significant. Included were 399 eyes (133 from females and 266 from males). Mean age of patients was 25.7 ± 14.6 years. Statistical differences existed in the proportion of zone III in closed globe trauma (p = 0.01) and types A (p = 0.04) and type B (p = 0.02) in open globe trauma. The distribution of the OTS categories was similar for both genders (category 5: p = 0.9); the probability of developing visual deficiency was 32.6% (95% CI = 24.6 to 40.5) in females and 33.2% (95% CI = 27.6 to 38.9) in males (p = 0.9). The probability of developing ocular trauma-related visual deficiency was similar for both genders. The same standard is required.

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.

Statewide analysis of the drainage-area ratio method for 34 streamflow percentile ranges in Texas

USGS Publications Warehouse

Asquith, William H.; Roussel, Meghan C.; Vrabel, Joseph

2006-01-01

The drainage-area ratio method commonly is used to estimate streamflow for sites where no streamflow data are available using data from one or more nearby streamflow-gaging stations. The method is intuitive and straightforward to implement and is in widespread use by analysts and managers of surface-water resources. The method equates the ratio of streamflow at two stream locations to the ratio of the respective drainage areas. In practice, unity often is assumed as the exponent on the drainage-area ratio, and unity also is assumed as a multiplicative bias correction. These two assumptions are evaluated in this investigation through statewide analysis of daily mean streamflow in Texas. The investigation was made by the U.S. Geological Survey in cooperation with the Texas Commission on Environmental Quality. More than 7.8 million values of daily mean streamflow for 712 U.S. Geological Survey streamflow-gaging stations in Texas were analyzed. To account for the influence of streamflow probability on the drainage-area ratio method, 34 percentile ranges were considered. The 34 ranges are the 4 quartiles (0-25, 25-50, 50-75, and 75-100 percent), the 5 intervals of the lower tail of the streamflow distribution (0-1, 1-2, 2-3, 3-4, and 4-5 percent), the 20 quintiles of the 4 quartiles (0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, 35-40, 40-45, 45-50, 50-55, 55-60, 60-65, 65-70, 70-75, 75-80, 80-85, 85-90, 90-95, and 95-100 percent), and the 5 intervals of the upper tail of the streamflow distribution (95-96, 96-97, 97-98, 98-99 and 99-100 percent). For each of the 253,116 (712X711/2) unique pairings of stations and for each of the 34 percentile ranges, the concurrent daily mean streamflow values available for the two stations provided for station-pair application of the drainage-area ratio method. For each station pair, specific statistical summarization (median, mean, and standard deviation) of both the exponent and bias-correction components of the drainage-area ratio method were computed. Statewide statistics (median, mean, and standard deviation) of the station-pair specific statistics subsequently were computed and are tabulated herein. A separate analysis considered conditioning station pairs to those stations within 100 miles of each other and with the absolute value of the logarithm (base-10) of the ratio of the drainage areas greater than or equal to 0.25. Statewide statistics of the conditional station-pair specific statistics were computed and are tabulated. The conditional analysis is preferable because of the anticipation that small separation distances reflect similar hydrologic conditions and the observation of large variation in exponent estimates for similar-sized drainage areas. The conditional analysis determined that the exponent is about 0.89 for streamflow percentiles from 0 to about 50 percent, is about 0.92 for percentiles from about 50 to about 65 percent, and is about 0.93 for percentiles from about 65 to about 85 percent. The exponent decreases rapidly to about 0.70 for percentiles nearing 100 percent. The computation of the bias-correction factor is sensitive to the range analysis interval (range of streamflow percentile); however, evidence suggests that in practice the drainage-area method can be considered unbiased. Finally, for general application, suggested values of the exponent are tabulated for 54 percentiles of daily mean streamflow in Texas; when these values are used, the bias correction is unity.

Statistical inference for tumor growth inhibition T/C ratio.

PubMed

Wu, Jianrong

2010-09-01

The tumor growth inhibition T/C ratio is commonly used to quantify treatment effects in drug screening tumor xenograft experiments. The T/C ratio is converted to an antitumor activity rating using an arbitrary cutoff point and often without any formal statistical inference. Here, we applied a nonparametric bootstrap method and a small sample likelihood ratio statistic to make a statistical inference of the T/C ratio, including both hypothesis testing and a confidence interval estimate. Furthermore, sample size and power are also discussed for statistical design of tumor xenograft experiments. Tumor xenograft data from an actual experiment were analyzed to illustrate the application.

Wildfire cluster detection using space-time scan statistics

NASA Astrophysics Data System (ADS)

Tonini, M.; Tuia, D.; Ratle, F.; Kanevski, M.

2009-04-01

The aim of the present study is to identify spatio-temporal clusters of fires sequences using space-time scan statistics. These statistical methods are specifically designed to detect clusters and assess their significance. Basically, scan statistics work by comparing a set of events occurring inside a scanning window (or a space-time cylinder for spatio-temporal data) with those that lie outside. Windows of increasing size scan the zone across space and time: the likelihood ratio is calculated for each window (comparing the ratio "observed cases over expected" inside and outside): the window with the maximum value is assumed to be the most probable cluster, and so on. Under the null hypothesis of spatial and temporal randomness, these events are distributed according to a known discrete-state random process (Poisson or Bernoulli), which parameters can be estimated. Given this assumption, it is possible to test whether or not the null hypothesis holds in a specific area. In order to deal with fires data, the space-time permutation scan statistic has been applied since it does not require the explicit specification of the population-at risk in each cylinder. The case study is represented by Florida daily fire detection using the Moderate Resolution Imaging Spectroradiometer (MODIS) active fire product during the period 2003-2006. As result, statistically significant clusters have been identified. Performing the analyses over the entire frame period, three out of the five most likely clusters have been identified in the forest areas, on the North of the country; the other two clusters cover a large zone in the South, corresponding to agricultural land and the prairies in the Everglades. Furthermore, the analyses have been performed separately for the four years to analyze if the wildfires recur each year during the same period. It emerges that clusters of forest fires are more frequent in hot seasons (spring and summer), while in the South areas they are widely present along the whole year. The analysis of fires distribution to evaluate if they are statistically more frequent in some area or/and in some period of the year, can be useful to support fire management and to focus on prevention measures.

Daniel Goodman’s empirical approach to Bayesian statistics

USGS Publications Warehouse

Gerrodette, Tim; Ward, Eric; Taylor, Rebecca L.; Schwarz, Lisa K.; Eguchi, Tomoharu; Wade, Paul; Himes Boor, Gina

2016-01-01

Bayesian statistics, in contrast to classical statistics, uses probability to represent uncertainty about the state of knowledge. Bayesian statistics has often been associated with the idea that knowledge is subjective and that a probability distribution represents a personal degree of belief. Dr. Daniel Goodman considered this viewpoint problematic for issues of public policy. He sought to ground his Bayesian approach in data, and advocated the construction of a prior as an empirical histogram of “similar” cases. In this way, the posterior distribution that results from a Bayesian analysis combined comparable previous data with case-specific current data, using Bayes’ formula. Goodman championed such a data-based approach, but he acknowledged that it was difficult in practice. If based on a true representation of our knowledge and uncertainty, Goodman argued that risk assessment and decision-making could be an exact science, despite the uncertainties. In his view, Bayesian statistics is a critical component of this science because a Bayesian analysis produces the probabilities of future outcomes. Indeed, Goodman maintained that the Bayesian machinery, following the rules of conditional probability, offered the best legitimate inference from available data. We give an example of an informative prior in a recent study of Steller sea lion spatial use patterns in Alaska.

Definition and Measurement of Selection Bias: From Constant Ratio to Constant Difference

ERIC Educational Resources Information Center

Cahan, Sorel; Gamliel, Eyal

2006-01-01

Despite its intuitive appeal and popularity, Thorndike's constant ratio (CR) model for unbiased selection is inherently inconsistent in "n"-free selection. Satisfaction of the condition for unbiased selection, when formulated in terms of success/acceptance probabilities, usually precludes satisfaction by the converse probabilities of…

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.

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.

Translational Research for Occupational Therapy: Using SPRE in Hippotherapy for Children with Developmental Disabilities.

PubMed

Weissman-Miller, Deborah; Miller, Rosalie J; Shotwell, Mary P

2017-01-01

Translational research is redefined in this paper using a combination of methods in statistics and data science to enhance the understanding of outcomes and practice in occupational therapy. These new methods are applied, using larger data and smaller single-subject data, to a study in hippotherapy for children with developmental disabilities (DD). The Centers for Disease Control and Prevention estimates DD affects nearly 10 million children, aged 2-19, where diagnoses may be comorbid. Hippotherapy is defined here as a treatment strategy in occupational therapy using equine movement to achieve functional outcomes. Semiparametric ratio estimator (SPRE), a single-subject statistical and small data science model, is used to derive a "change point" indicating where the participant adapts to treatment, from which predictions are made. Data analyzed here is from an institutional review board approved pilot study using the Hippotherapy Evaluation and Assessment Tool measure, where outcomes are given separately for each of four measured domains and the total scores of each participant. Analysis with SPRE, using statistical methods to predict a "change point" and data science graphical interpretations of data, shows the translational comparisons between results from larger mean values and the very different results from smaller values for each HEAT domain in terms of relationships and statistical probabilities.

Generalized t-statistic for two-group classification.

PubMed

Komori, Osamu; Eguchi, Shinto; Copas, John B

2015-06-01

In the classic discriminant model of two multivariate normal distributions with equal variance matrices, the linear discriminant function is optimal both in terms of the log likelihood ratio and in terms of maximizing the standardized difference (the t-statistic) between the means of the two distributions. In a typical case-control study, normality may be sensible for the control sample but heterogeneity and uncertainty in diagnosis may suggest that a more flexible model is needed for the cases. We generalize the t-statistic approach by finding the linear function which maximizes a standardized difference but with data from one of the groups (the cases) filtered by a possibly nonlinear function U. We study conditions for consistency of the method and find the function U which is optimal in the sense of asymptotic efficiency. Optimality may also extend to other measures of discriminatory efficiency such as the area under the receiver operating characteristic curve. The optimal function U depends on a scalar probability density function which can be estimated non-parametrically using a standard numerical algorithm. A lasso-like version for variable selection is implemented by adding L1-regularization to the generalized t-statistic. Two microarray data sets in the study of asthma and various cancers are used as motivating examples. © 2014, The International Biometric Society.

Translational Research for Occupational Therapy: Using SPRE in Hippotherapy for Children with Developmental Disabilities

PubMed Central

Miller, Rosalie J.; Shotwell, Mary P.

2017-01-01

Translational research is redefined in this paper using a combination of methods in statistics and data science to enhance the understanding of outcomes and practice in occupational therapy. These new methods are applied, using larger data and smaller single-subject data, to a study in hippotherapy for children with developmental disabilities (DD). The Centers for Disease Control and Prevention estimates DD affects nearly 10 million children, aged 2–19, where diagnoses may be comorbid. Hippotherapy is defined here as a treatment strategy in occupational therapy using equine movement to achieve functional outcomes. Semiparametric ratio estimator (SPRE), a single-subject statistical and small data science model, is used to derive a “change point” indicating where the participant adapts to treatment, from which predictions are made. Data analyzed here is from an institutional review board approved pilot study using the Hippotherapy Evaluation and Assessment Tool measure, where outcomes are given separately for each of four measured domains and the total scores of each participant. Analysis with SPRE, using statistical methods to predict a “change point” and data science graphical interpretations of data, shows the translational comparisons between results from larger mean values and the very different results from smaller values for each HEAT domain in terms of relationships and statistical probabilities. PMID:29097962

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

NASA Technical Reports Server (NTRS)

Huang, N. E.; Long, S. R.

1980-01-01

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

Probability density cloud as a geometrical tool to describe statistics of scattered light.

PubMed

Yaitskova, Natalia

2017-04-01

First-order statistics of scattered light is described using the representation of the probability density cloud, which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail and are connected to the statistical properties of phase. The moment-generating function for intensity is obtained in a closed form through these parameters. An example of exponentially modified normal distribution is provided to illustrate the functioning of this geometrical approach.

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 study provides the first neurophysiological evidence that the correction of statistical knowledge requires more time than the acquisition of new statistical knowledge. Copyright © 2016 Elsevier Ltd. 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,…

Eliciting and Developing Teachers' Conceptions of Random Processes in a Probability and Statistics Course

ERIC Educational Resources Information Center

Smith, Toni M.; Hjalmarson, Margret A.

2013-01-01

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses…

The Probability of Obtaining Two Statistically Different Test Scores as a Test Index

ERIC Educational Resources Information Center

Muller, Jorg M.

2006-01-01

A new test index is defined as the probability of obtaining two randomly selected test scores (PDTS) as statistically different. After giving a concept definition of the test index, two simulation studies are presented. The first analyzes the influence of the distribution of test scores, test reliability, and sample size on PDTS within classical…

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…

Sets, Probability and Statistics: The Mathematics of Life Insurance.

ERIC Educational Resources Information Center

Clifford, Paul C.; And Others

The practical use of such concepts as sets, probability and statistics are considered by many to be vital and necessary to our everyday life. This student manual is intended to familiarize students with these concepts and to provide practice using real life examples. It also attempts to illustrate how the insurance industry uses such mathematic…

Application of binomial and multinomial probability statistics to the sampling design process of a global grain tracing and recall system

USDA-ARS?s Scientific Manuscript database

Small, coded, pill-sized tracers embedded in grain are proposed as a method for grain traceability. A sampling process for a grain traceability system was designed and investigated by applying probability statistics using a science-based sampling approach to collect an adequate number of tracers fo...

Animating Statistics: A New Kind of Applet for Exploring Probability Distributions

ERIC Educational Resources Information Center

Kahle, David

2014-01-01

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

Pharmacodynamic analysis of ceftriaxone, gatifloxacin,and levofloxacin against Streptococcus pneumoniae with the use of Monte Carlo simulation.

PubMed

Frei, Christopher R; Burgess, David S

2005-09-01

To evaluate the pharmacodynamics of four intravenous antimicrobial regimens-ceftriaxone 1 g, gatifloxacin 400 mg, levofloxacin 500 mg, and levofloxacin 750 mg, each every 24 hours-against recent Streptococcus pneumoniae isolates. Pharmacodynamic analysis using Monte Carlo simulation. The Surveillance Network (TSN) 2002 database. Streptococcus pneumoniae isolates (7866 isolates) were stratified according to penicillin susceptibilities as follows: susceptible (4593), intermediate (1986), and resistant (1287). Risk analysis software was used to simulate 10,000 patients by integrating published pharmacokinetic parameters, their variability, and minimum inhibitory concentration (MIC) distributions from the TSN database. Probability of target attainment was determined for percentage of time above the MIC (%T > MIC) from 0-100% for ceftriaxone and area under the concentration-time curve (AUC):MIC ratio from 0-150 for the fluoroquinolones. For ceftriaxone, probability of target attainment remained 90% or greater against the three isolate groups until a %T > MIC of 70% or greater, and it remained 90% or greater against susceptible and intermediate isolates over the entire interval (%T > MIC 0-100%). For levofloxacin 500 mg, probability of target attainment was 90% at an AUC:MIC < or = 30, but the curve declined sharply with further increases in pharmacodynamic target. Levofloxacin 750 mg achieved a probability of target attainment of 99% at an AUC:MIC ratio < or = 30; the probability remained approximately 90% until a target of 70 or greater, when it declined steeply. Gatifloxacin demonstrated a high probability (99%) of target attainment at an AUC:MIC ratio < or = 30, and it remained above 90% until a target of 70. Ceftriaxone maintained high probability of target attainment over a broad range of pharmacodynamic targets regardless of penicillin susceptibility (%T > MIC 0-60%). Levofloxacin 500 mg maintained high probability of target attainment for AUC:MIC ratios 0-30; whereas, levofloxacin 750 mg and gatifloxacin maintained high probability of target attainment for AUC:MIC ratios 0-60. Rate of decline in the pharmacodynamic curve was most pronounced for the two levofloxacin regimens and more gradual for gatifloxacin and ceftriaxone.

Probability of detection of internal voids in structural ceramics using microfocus radiography

NASA Technical Reports Server (NTRS)

Baaklini, G. Y.; Roth, D. J.

1986-01-01

The reliability of microfocous X-radiography for detecting subsurface voids in structural ceramic test specimens was statistically evaluated. The microfocus system was operated in the projection mode using low X-ray photon energies (20 keV) and a 10 micro m focal spot. The statistics were developed for implanted subsurface voids in green and sintered silicon carbide and silicon nitride test specimens. These statistics were compared with previously-obtained statistics for implanted surface voids in similar specimens. Problems associated with void implantation are discussed. Statistical results are given as probability-of-detection curves at a 95 precent confidence level for voids ranging in size from 20 to 528 micro m in diameter.

Probability of detection of internal voids in structural ceramics using microfocus radiography

NASA Technical Reports Server (NTRS)

Baaklini, G. Y.; Roth, D. J.

1985-01-01

The reliability of microfocus x-radiography for detecting subsurface voids in structural ceramic test specimens was statistically evaluated. The microfocus system was operated in the projection mode using low X-ray photon energies (20 keV) and a 10 micro m focal spot. The statistics were developed for implanted subsurface voids in green and sintered silicon carbide and silicon nitride test specimens. These statistics were compared with previously-obtained statistics for implanted surface voids in similar specimens. Problems associated with void implantation are discussed. Statistical results are given as probability-of-detection curves at a 95 percent confidence level for voids ranging in size from 20 to 528 micro m in diameter.

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…

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

NASA Astrophysics Data System (ADS)

Frahm, Klaus M.; Shepelyansky, Dima L.

2014-04-01

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.

Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma

USGS Publications Warehouse

Esralew, Rachel A.; Smith, S. Jerrod

2010-01-01

Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma. Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states. A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5. Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations. Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma). A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation. The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected. The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region. Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent vari

Confidence intervals for the between-study variance in random-effects meta-analysis using generalised heterogeneity statistics: should we use unequal tails?

PubMed

Jackson, Dan; Bowden, Jack

2016-09-07

Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative. We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained. Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest. We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the '1-4 % split', where greater tail probability is allocated to the upper confidence bound. The 'width-optimal' interval that we present deserves further investigation.

Statistical summaries of selected Iowa streamflow data through September 2013

USGS Publications Warehouse

Eash, David A.; O'Shea, Padraic S.; Weber, Jared R.; Nguyen, Kevin T.; Montgomery, Nicholas L.; Simonson, Adrian J.

2016-01-04

Statistical summaries of streamflow data collected at 184 streamgages in Iowa are presented in this report. All streamgages included for analysis have at least 10 years of continuous record collected before or through September 2013. This report is an update to two previously published reports that presented statistical summaries of selected Iowa streamflow data through September 1988 and September 1996. The statistical summaries include (1) monthly and annual flow durations, (2) annual exceedance probabilities of instantaneous peak discharges (flood frequencies), (3) annual exceedance probabilities of high discharges, and (4) annual nonexceedance probabilities of low discharges and seasonal low discharges. Also presented for each streamgage are graphs of the annual mean discharges, mean annual mean discharges, 50-percent annual flow-duration discharges (median flows), harmonic mean flows, mean daily mean discharges, and flow-duration curves. Two sets of statistical summaries are presented for each streamgage, which include (1) long-term statistics for the entire period of streamflow record and (2) recent-term statistics for or during the 30-year period of record from 1984 to 2013. The recent-term statistics are only calculated for streamgages with streamflow records pre-dating the 1984 water year and with at least 10 years of record during 1984–2013. The streamflow statistics in this report are not adjusted for the effects of water use; although some of this water is used consumptively, most of it is returned to the streams.

K β to K α X-ray intensity ratios and K to L shell vacancy transfer probabilities of Co, Ni, Cu, and Zn

NASA Astrophysics Data System (ADS)

Anand, L. F. M.; Gudennavar, S. B.; Bubbly, S. G.; Kerur, B. R.

2015-12-01

The K to L shell total vacancy transfer probabilities of low Z elements Co, Ni, Cu, and Zn are estimated by measuring the K β to K α intensity ratio adopting the 2π-geometry. The target elements were excited by 32.86 keV barium K-shell X-rays from a weak 137Cs γ-ray source. The emitted K-shell X-rays were detected using a low energy HPGe X-ray detector coupled to a 16 k MCA. The measured intensity ratios and the total vacancy transfer probabilities are compared with theoretical results and others' work, establishing a good agreement.

Probability of Elevated Volatile Organic Compound (VOC) Concentrations in Groundwater in the Eagle River Watershed Valley-Fill Aquifer, Eagle County, North-Central Colorado, 2006-2007

USGS Publications Warehouse

Rupert, Michael G.; Plummer, Niel

2009-01-01

This raster data set delineates the predicted probability of elevated volatile organic compound (VOC) concentrations in groundwater in the Eagle River watershed valley-fill aquifer, Eagle County, North-Central Colorado, 2006-2007. This data set was developed by a cooperative project between the U.S. Geological Survey, Eagle County, the Eagle River Water and Sanitation District, the Town of Eagle, the Town of Gypsum, and the Upper Eagle Regional Water Authority. This project was designed to evaluate potential land-development effects on groundwater and surface-water resources so that informed land-use and water management decisions can be made. This groundwater probability map and its associated probability maps was developed as follows: (1) A point data set of wells with groundwater quality and groundwater age data was overlaid with thematic layers of anthropogenic (related to human activities) and hydrogeologic data by using a geographic information system to assign each well values for depth to groundwater, distance to major streams and canals, distance to gypsum beds, precipitation, soils, and well depth. These data then were downloaded to a statistical software package for analysis by logistic regression. (2) Statistical models predicting the probability of elevated nitrate concentrations, the probability of unmixed young water (using chlorofluorocarbon-11 concentrations and tritium activities), and the probability of elevated volatile organic compound concentrations were developed using logistic regression techniques. (3) The statistical models were entered into a GIS and the probability map was constructed.

Probability of Elevated Nitrate Concentrations in Groundwater in the Eagle River Watershed Valley-Fill Aquifer, Eagle County, North-Central Colorado, 2006-2007

USGS Publications Warehouse

Rupert, Michael G.; Plummer, Niel

2009-01-01

This raster data set delineates the predicted probability of elevated nitrate concentrations in groundwater in the Eagle River watershed valley-fill aquifer, Eagle County, North-Central Colorado, 2006-2007. This data set was developed by a cooperative project between the U.S. Geological Survey, Eagle County, the Eagle River Water and Sanitation District, the Town of Eagle, the Town of Gypsum, and the Upper Eagle Regional Water Authority. This project was designed to evaluate potential land-development effects on groundwater and surface-water resources so that informed land-use and water management decisions can be made. This groundwater probability map and its associated probability maps was developed as follows: (1) A point data set of wells with groundwater quality and groundwater age data was overlaid with thematic layers of anthropogenic (related to human activities) and hydrogeologic data by using a geographic information system to assign each well values for depth to groundwater, distance to major streams and canals, distance to gypsum beds, precipitation, soils, and well depth. These data then were downloaded to a statistical software package for analysis by logistic regression. (2) Statistical models predicting the probability of elevated nitrate concentrations, the probability of unmixed young water (using chlorofluorocarbon-11 concentrations and tritium activities), and the probability of elevated volatile organic compound concentrations were developed using logistic regression techniques. (3) The statistical models were entered into a GIS and the probability map was constructed.

A simple signaling rule for variable life-adjusted display derived from an equivalent risk-adjusted CUSUM chart.

PubMed

Wittenberg, Philipp; Gan, Fah Fatt; Knoth, Sven

2018-04-17

The variable life-adjusted display (VLAD) is the first risk-adjusted graphical procedure proposed in the literature for monitoring the performance of a surgeon. It displays the cumulative sum of expected minus observed deaths. It has since become highly popular because the statistic plotted is easy to understand. But it is also easy to misinterpret a surgeon's performance by utilizing the VLAD, potentially leading to grave consequences. The problem of misinterpretation is essentially caused by the variance of the VLAD's statistic that increases with sample size. In order for the VLAD to be truly useful, a simple signaling rule is desperately needed. Various forms of signaling rules have been developed, but they are usually quite complicated. Without signaling rules, making inferences using the VLAD alone is difficult if not misleading. In this paper, we establish an equivalence between a VLAD with V-mask and a risk-adjusted cumulative sum (RA-CUSUM) chart based on the difference between the estimated probability of death and surgical outcome. Average run length analysis based on simulation shows that this particular RA-CUSUM chart has similar performance as compared to the established RA-CUSUM chart based on the log-likelihood ratio statistic obtained by testing the odds ratio of death. We provide a simple design procedure for determining the V-mask parameters based on a resampling approach. Resampling from a real data set ensures that these parameters can be estimated appropriately. Finally, we illustrate the monitoring of a real surgeon's performance using VLAD with V-mask. Copyright © 2018 John Wiley & Sons, Ltd.

Space-filling, multifractal, localized thermal spikes in Si, Ge and ZnO

NASA Astrophysics Data System (ADS)

Ahmad, Shoaib; Abbas, Muhammad Sabtain; Yousuf, Muhammad; Javeed, Sumera; Zeeshan, Sumaira; Yaqub, Kashif

2018-04-01

The mechanism responsible for the emission of clusters from heavy ion irradiated solids is proposed to be thermal spikes. Collision cascade-based theories describe atomic sputtering but cannot explain the consistently observed experimental evidence for significant cluster emission. Statistical thermodynamic arguments for thermal spikes are employed here for qualitative and quantitative estimation of the thermal spike-induced cluster emission from Si, Ge and ZnO. The evolving cascades and spikes in elemental and molecular semiconducting solids are shown to have fractal characteristics. Power law potential is used to calculate the fractal dimension. With the loss of recoiling particles' energy the successive branching ratios get smaller. The fractal dimension is shown to be dependent upon the exponent of the power law interatomic potential D = 1/2m. Each irradiating ion has the probability of initiating a space-filling, multifractal thermal spike that may sublime a localized region near the surface by emitting clusters in relative ratios that depend upon the energies of formation of respective surface vacancies.

Probabilistic structural analysis methods for improving Space Shuttle engine reliability

NASA Technical Reports Server (NTRS)

Boyce, L.

1989-01-01

Probabilistic structural analysis methods are particularly useful in the design and analysis of critical structural components and systems that operate in very severe and uncertain environments. These methods have recently found application in space propulsion systems to improve the structural reliability of Space Shuttle Main Engine (SSME) components. A computer program, NESSUS, based on a deterministic finite-element program and a method of probabilistic analysis (fast probability integration) provides probabilistic structural analysis for selected SSME components. While computationally efficient, it considers both correlated and nonnormal random variables as well as an implicit functional relationship between independent and dependent variables. The program is used to determine the response of a nickel-based superalloy SSME turbopump blade. Results include blade tip displacement statistics due to the variability in blade thickness, modulus of elasticity, Poisson's ratio or density. Modulus of elasticity significantly contributed to blade tip variability while Poisson's ratio did not. Thus, a rational method for choosing parameters to be modeled as random is provided.

FATTY MUSCLE INFILTRATION IN CUFF TEAR: PRE AND POST OPERATIVE EVALUATION BY MRI.

PubMed

Miyazaki, Alberto Naoki; Santos, Pedro Doneux; da Silva, Luciana Andrade; Sella, Guilherme do Val; Miranda, Eduardo Régis de Alencar Bona; Zampieri, Rodrigo

2015-01-01

To evaluate the fatty infiltration and atrophy of the supraespinatus in the pre- and postoperative of a rotator cuff lesion (RCL), by MRI. Ten patients with full-thickness rotator cuff tears who had undergone surgical arthroscopic rotator cuff repair between September and December 2011 were included. This is a prospective study, with analysis and comparison of fatty infiltration and atrophy of the supraespinatus. The occupation ratio was measured using the magic selection tool in Adobe Photoshop CS3((r)) on T1 oblique sagittal Y-view MRI. Through Photoshop, the proportion occupied by the muscle belly regarding its fossae was calculated. There was a statistically significant increase in the muscle ratio (p=0.013) comparing images pre and postoperative, analyzed by the Wilcoxon T test. The proportion of the supraspinal muscle above the pit increases in the immediate postoperative period, probably due to the traction exerted on the tendon at the time of repair. Level of Evidence II, Cohort Study.

Supernova Driving. II. Compressive Ratio in Molecular-cloud Turbulence

NASA Astrophysics Data System (ADS)

Pan, Liubin; Padoan, Paolo; Haugbølle, Troels; Nordlund, Åke

2016-07-01

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value ≈0.3, lower than the equilibrium value of ≈0.5 found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density probability density function is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.

Environmental and anthropogenic factors affecting the probability of occurrence of Oncomegas wageneri (Cestoda: Trypanorhyncha) in the southern Gulf of Mexico.

PubMed

Vidal-Martínez, Víctor M; Torres-Irineo, Edgar; Romero, David; Gold-Bouchot, Gerardo; Martínez-Meyer, Enrique; Valdés-Lozano, David; Aguirre-Macedo, M Leopoldina

2015-11-26

Understanding the environmental and anthropogenic factors influencing the probability of occurrence of the marine parasitic species is fundamental for determining the circumstances under which they can act as bioindicators of environmental impact. The aim of this study was to determine whether physicochemical variables, polyaromatic hydrocarbons or sewage discharge affect the probability of occurrence of the larval cestode Oncomegas wageneri, which infects the shoal flounder, Syacium gunteri, in the southern Gulf of Mexico. The study area included 162 sampling sites in the southern Gulf of Mexico and covered 288,205 km(2), where the benthic sediments, water and the shoal flounder individuals were collected. We used the boosted generalised additive models (boosted GAM) and the MaxEnt to examine the potential statistical relationships between the environmental variables (nutrients, contaminants and physicochemical variables from the water and sediments) and the probability of the occurrence of this parasite. The models were calibrated using all of the sampling sites (full area) with and without parasite occurrences (n = 162) and a polygon area that included sampling sites with a depth of 1500 m or less (n = 134). Oncomegas wageneri occurred at 29/162 sampling sites. The boosted GAM for the full area and the polygon area accurately predicted the probability of the occurrence of O. wageneri in the study area. By contrast, poor probabilities of occurrence were obtained with the MaxEnt models for the same areas. The variables with the highest frequencies of appearance in the models (proxies for the explained variability) were the polyaromatic hydrocarbons of high molecular weight (PAHH, 95 %), followed by a combination of nutrients, spatial variables and polyaromatic hydrocarbons of low molecular weight (PAHL, 5 %). The contribution of the PAHH to the variability was explained by the fact that these compounds, together with N and P, are carried by rivers that discharge into the ocean, which enhances the growth of hydrocarbonoclastic bacteria and the productivity and number of the intermediate hosts. Our results suggest that sites with PAHL/PAHH ratio values up to 1.89 promote transmission based on the high values of the prevalence of O. wageneri in the study area. In contrast, PAHL/PAHH ratio values ≥ 1.90 can be considered harmful for the transmission stages of O. wageneri and its hosts (copepods, shrimps and shoal flounders). Overall, the results indicate that the PAHHs affect the probability of occurrence of this helminth parasite in the southern Gulf of Mexico.

What Are Probability Surveys used by the National Aquatic Resource Surveys?

EPA Pesticide Factsheets

The National Aquatic Resource Surveys (NARS) use probability-survey designs to assess the condition of the nation’s waters. In probability surveys (also known as sample-surveys or statistical surveys), sampling sites are selected randomly.

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.)

Statistical characterization of high-to-medium frequency mesoscale gravity waves by lidar-measured vertical winds and temperatures in the MLT

NASA Astrophysics Data System (ADS)

Lu, Xian; Chu, Xinzhao; Li, Haoyu; Chen, Cao; Smith, John A.; Vadas, Sharon L.

2017-09-01

We present the first statistical study of gravity waves with periods of 0.3-2.5 h that are persistent and dominant in the vertical winds measured with the University of Colorado STAR Na Doppler lidar in Boulder, CO (40.1°N, 105.2°W). The probability density functions of the wave amplitudes in temperature and vertical wind, ratios of these two amplitudes, phase differences between them, and vertical wavelengths are derived directly from the observations. The intrinsic period and horizontal wavelength of each wave are inferred from its vertical wavelength, amplitude ratio, and a designated eddy viscosity by applying the gravity wave polarization and dispersion relations. The amplitude ratios are positively correlated with the ground-based periods with a coefficient of 0.76. The phase differences between the vertical winds and temperatures (φW -φT) follow a Gaussian distribution with 84.2±26.7°, which has a much larger standard deviation than that predicted for non-dissipative waves ( 3.3°). The deviations of the observed phase differences from their predicted values for non-dissipative waves may indicate wave dissipation. The shorter-vertical-wavelength waves tend to have larger phase difference deviations, implying that the dissipative effects are more significant for shorter waves. The majority of these waves have the vertical wavelengths ranging from 5 to 40 km with a mean and standard deviation of 18.6 and 7.2 km, respectively. For waves with similar periods, multiple peaks in the vertical wavelengths are identified frequently and the ones peaking in the vertical wind are statistically longer than those peaking in the temperature. The horizontal wavelengths range mostly from 50 to 500 km with a mean and median of 180 and 125 km, respectively. Therefore, these waves are mesoscale waves with high-to-medium frequencies. Since they have recently become resolvable in high-resolution general circulation models (GCMs), this statistical study provides an important and timely reference for them.

A likelihood ratio anomaly detector for identifying within-perimeter computer network attacks

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

Grana, Justin; Wolpert, David; Neil, Joshua

The rapid detection of attackers within firewalls of enterprise computer networks is of paramount importance. Anomaly detectors address this problem by quantifying deviations from baseline statistical models of normal network behavior and signaling an intrusion when the observed data deviates significantly from the baseline model. But, many anomaly detectors do not take into account plausible attacker behavior. As a result, anomaly detectors are prone to a large number of false positives due to unusual but benign activity. Our paper first introduces a stochastic model of attacker behavior which is motivated by real world attacker traversal. Then, we develop a likelihoodmore » ratio detector that compares the probability of observed network behavior under normal conditions against the case when an attacker has possibly compromised a subset of hosts within the network. Since the likelihood ratio detector requires integrating over the time each host becomes compromised, we illustrate how to use Monte Carlo methods to compute the requisite integral. We then present Receiver Operating Characteristic (ROC) curves for various network parameterizations that show for any rate of true positives, the rate of false positives for the likelihood ratio detector is no higher than that of a simple anomaly detector and is often lower. Finally, we demonstrate the superiority of the proposed likelihood ratio detector when the network topologies and parameterizations are extracted from real-world networks.« less

A likelihood ratio anomaly detector for identifying within-perimeter computer network attacks

DOE PAGES

Grana, Justin; Wolpert, David; Neil, Joshua; ...

2016-03-11

The rapid detection of attackers within firewalls of enterprise computer networks is of paramount importance. Anomaly detectors address this problem by quantifying deviations from baseline statistical models of normal network behavior and signaling an intrusion when the observed data deviates significantly from the baseline model. But, many anomaly detectors do not take into account plausible attacker behavior. As a result, anomaly detectors are prone to a large number of false positives due to unusual but benign activity. Our paper first introduces a stochastic model of attacker behavior which is motivated by real world attacker traversal. Then, we develop a likelihoodmore » ratio detector that compares the probability of observed network behavior under normal conditions against the case when an attacker has possibly compromised a subset of hosts within the network. Since the likelihood ratio detector requires integrating over the time each host becomes compromised, we illustrate how to use Monte Carlo methods to compute the requisite integral. We then present Receiver Operating Characteristic (ROC) curves for various network parameterizations that show for any rate of true positives, the rate of false positives for the likelihood ratio detector is no higher than that of a simple anomaly detector and is often lower. Finally, we demonstrate the superiority of the proposed likelihood ratio detector when the network topologies and parameterizations are extracted from real-world networks.« less

Application of Bayes' theorem for pulse shape discrimination

NASA Astrophysics Data System (ADS)

Monterial, Mateusz; Marleau, Peter; Clarke, Shaun; Pozzi, Sara

2015-09-01

A Bayesian approach is proposed for pulse shape discrimination of photons and neutrons in liquid organic scinitillators. Instead of drawing a decision boundary, each pulse is assigned a photon or neutron confidence probability. This allows for photon and neutron classification on an event-by-event basis. The sum of those confidence probabilities is used to estimate the number of photon and neutron instances in the data. An iterative scheme, similar to an expectation-maximization algorithm for Gaussian mixtures, is used to infer the ratio of photons-to-neutrons in each measurement. Therefore, the probability space adapts to data with varying photon-to-neutron ratios. A time-correlated measurement of Am-Be and separate measurements of 137Cs, 60Co and 232Th photon sources were used to construct libraries of neutrons and photons. These libraries were then used to produce synthetic data sets with varying ratios of photons-to-neutrons. Probability weighted method that we implemented was found to maintain neutron acceptance rate of up to 90% up to photon-to-neutron ratio of 2000, and performed 9% better than the decision boundary approach. Furthermore, the iterative approach appropriately changed the probability space with an increasing number of photons which kept the neutron population estimate from unrealistically increasing.

Application of Bayes' theorem for pulse shape discrimination

DOE PAGES

Marleau, Peter; Monterial, Mateusz; Clarke, Shaun; ...

2015-06-14

A Bayesian approach is proposed for pulse shape discrimination of photons and neutrons in liquid organic scinitillators. Instead of drawing a decision boundary, each pulse is assigned a photon or neutron confidence probability. In addition, this allows for photon and neutron classification on an event-by-event basis. The sum of those confidence probabilities is used to estimate the number of photon and neutron instances in the data. An iterative scheme, similar to an expectation-maximization algorithm for Gaussian mixtures, is used to infer the ratio of photons-to-neutrons in each measurement. Therefore, the probability space adapts to data with varying photon-to-neutron ratios. Amore » time-correlated measurement of Am–Be and separate measurements of 137Cs, 60Co and 232Th photon sources were used to construct libraries of neutrons and photons. These libraries were then used to produce synthetic data sets with varying ratios of photons-to-neutrons. Probability weighted method that we implemented was found to maintain neutron acceptance rate of up to 90% up to photon-to-neutron ratio of 2000, and performed 9% better than the decision boundary approach. Furthermore, the iterative approach appropriately changed the probability space with an increasing number of photons which kept the neutron population estimate from unrealistically increasing.« less

The reproducibility of research and the misinterpretation of p-values

PubMed Central

2017-01-01

We wish to answer this question: If you observe a ‘significant’ p-value after doing a single unbiased experiment, what is the probability that your result is a false positive? The weak evidence provided by p-values between 0.01 and 0.05 is explored by exact calculations of false positive risks. When you observe p = 0.05, the odds in favour of there being a real effect (given by the likelihood ratio) are about 3 : 1. This is far weaker evidence than the odds of 19 to 1 that might, wrongly, be inferred from the p-value. And if you want to limit the false positive risk to 5%, you would have to assume that you were 87% sure that there was a real effect before the experiment was done. If you observe p = 0.001 in a well-powered experiment, it gives a likelihood ratio of almost 100 : 1 odds on there being a real effect. That would usually be regarded as conclusive. But the false positive risk would still be 8% if the prior probability of a real effect were only 0.1. And, in this case, if you wanted to achieve a false positive risk of 5% you would need to observe p = 0.00045. It is recommended that the terms ‘significant’ and ‘non-significant’ should never be used. Rather, p-values should be supplemented by specifying the prior probability that would be needed to produce a specified (e.g. 5%) false positive risk. It may also be helpful to specify the minimum false positive risk associated with the observed p-value. Despite decades of warnings, many areas of science still insist on labelling a result of p < 0.05 as ‘statistically significant’. This practice must contribute to the lack of reproducibility in some areas of science. This is before you get to the many other well-known problems, like multiple comparisons, lack of randomization and p-hacking. Precise inductive inference is impossible and replication is the only way to be sure. Science is endangered by statistical misunderstanding, and by senior people who impose perverse incentives on scientists. PMID:29308247

Probability and Statistics in Aerospace Engineering

NASA Technical Reports Server (NTRS)

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

1998-01-01

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

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…

A Case Study in Elementary Statistics: The Florida Panther Population

ERIC Educational Resources Information Center

Lazowski, Andrew; Stopper, Geffrey

2013-01-01

We describe a case study that was created to intertwine the fields of biology and mathematics. This project is given in an elementary probability and statistics course for non-math majors. Some goals of this case study include: to expose students to biology in a math course, to apply probability to real-life situations, and to display how far a…

Two-Way Tables: Issues at the Heart of Statistics and Probability for Students and Teachers

ERIC Educational Resources Information Center

Watson, Jane; Callingham, Rosemary

2014-01-01

Some problems exist at the intersection of statistics and probability, creating a dilemma in relation to the best approach to assist student understanding. Such is the case with problems presented in two-way tables representing conditional information. The difficulty can be confounded if the context within which the problem is set is one where…

Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

ERIC Educational Resources Information Center

Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy

2006-01-01

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…

A predictive model to estimate the pretest probability of metastasis in patients with osteosarcoma.

PubMed

Wang, Sisheng; Zheng, Shaoluan; Hu, Kongzu; Sun, Heyan; Zhang, Jinling; Rong, Genxiang; Gao, Jie; Ding, Nan; Gui, Binjie

2017-01-01

Osteosarcomas (OSs) represent a huge challenge to improve the overall survival, especially in metastatic patients. Increasing evidence indicates that both tumor-associated elements but also on host-associated elements are under a remarkable effect on the prognosis of cancer patients, especially systemic inflammatory response. By analyzing a series prognosis of factors, including age, gender, primary tumor size, tumor location, tumor grade, and histological classification, monocyte ratio, and NLR ratio, a clinical predictive model was established by using stepwise logistic regression involved circulating leukocyte to compute the estimated probabilities of metastases for OS patients. The clinical predictive model was described by the following equations: probability of developing metastases = ex/(1 + ex), x = -2.150 +  (1.680 × monocyte ratio) + (1.533 × NLR ratio), where is the base of the natural logarithm, the assignment to each of the 2 variables is 1 if the ratio >1 (otherwise 0). The calculated AUC of the receiver-operating characteristic curve as 0.793 revealed well accuracy of this model (95% CI, 0.740-0.845). The predicted probabilities that we generated with the cross-validation procedure had a similar AUC (0.743; 95% CI, 0.684-0.803). The present model could be used to improve the outcomes of the metastases by developing a predictive model considering circulating leukocyte influence to estimate the pretest probability of developing metastases in patients with OS.

Descriptive data analysis.

PubMed

Thompson, Cheryl Bagley

2009-01-01

This 13th article of the Basics of Research series is first in a short series on statistical analysis. These articles will discuss creating your statistical analysis plan, levels of measurement, descriptive statistics, probability theory, inferential statistics, and general considerations for interpretation of the results of a statistical analysis.

Quantum probabilistic logic programming

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan

2015-05-01

We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.

Introduction to Probability, Part 1 - Basic Concepts. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Blakeslee, David W.; And Others

This book is designed to introduce the reader to some fundamental ideas about probability. The mathematical theory of probability plays an increasingly important role in science, government, industry, business, and economics. An understanding of the basic concepts of probability is essential for the study of statistical methods that are widely…

Statistical inference of seabed sound-speed structure in the Gulf of Oman Basin.

PubMed

Sagers, Jason D; Knobles, David P

2014-06-01

Addressed is the statistical inference of the sound-speed depth profile of a thick soft seabed from broadband sound propagation data recorded in the Gulf of Oman Basin in 1977. The acoustic data are in the form of time series signals recorded on a sparse vertical line array and generated by explosive sources deployed along a 280 km track. The acoustic data offer a unique opportunity to study a deep-water bottom-limited thickly sedimented environment because of the large number of time series measurements, very low seabed attenuation, and auxiliary measurements. A maximum entropy method is employed to obtain a conditional posterior probability distribution (PPD) for the sound-speed ratio and the near-surface sound-speed gradient. The multiple data samples allow for a determination of the average error constraint value required to uniquely specify the PPD for each data sample. Two complicating features of the statistical inference study are addressed: (1) the need to develop an error function that can both utilize the measured multipath arrival structure and mitigate the effects of data errors and (2) the effect of small bathymetric slopes on the structure of the bottom interacting arrivals.

Self-similarity in high Atwood number Rayleigh-Taylor experiments

NASA Astrophysics Data System (ADS)

Mikhaeil, Mark; Suchandra, Prasoon; Pathikonda, Gokul; Ranjan, Devesh

2017-11-01

Self-similarity is a critical concept in turbulent and mixing flows. In the Rayleigh-Taylor instability, theory and simulations have shown that the flow exhibits properties of self-similarity as the mixing Reynolds number exceeds 20000 and the flow enters the turbulent regime. Here, we present results from the first large Atwood number (0.7) Rayleigh-Taylor experimental campaign for mixing Reynolds number beyond 20000 in an effort to characterize the self-similar nature of the instability. Experiments are performed in a statistically steady gas tunnel facility, allowing for the evaluation of turbulence statistics. A visualization diagnostic is used to study the evolution of the mixing width as the instability grows. This allows for computation of the instability growth rate. For the first time in such a facility, stereoscopic particle image velocimetry is used to resolve three-component velocity information in a plane. Velocity means, fluctuations, and correlations are considered as well as their appropriate scaling. Probability density functions of velocity fields, energy spectra, and higher-order statistics are also presented. The energy budget of the flow is described, including the ratio of the kinetic energy to the released potential energy. This work was supported by the DOE-NNSA SSAA Grant DE-NA0002922.

Combined statistical analysis of landslide release and propagation

NASA Astrophysics Data System (ADS)

Mergili, Martin; Rohmaneo, Mohammad; Chu, Hone-Jay

2016-04-01

Statistical methods - often coupled with stochastic concepts - are commonly employed to relate areas affected by landslides with environmental layers, and to estimate spatial landslide probabilities by applying these relationships. However, such methods only concern the release of landslides, disregarding their motion. Conceptual models for mass flow routing are used for estimating landslide travel distances and possible impact areas. Automated approaches combining release and impact probabilities are rare. The present work attempts to fill this gap by a fully automated procedure combining statistical and stochastic elements, building on the open source GRASS GIS software: (1) The landslide inventory is subset into release and deposition zones. (2) We employ a traditional statistical approach to estimate the spatial release probability of landslides. (3) We back-calculate the probability distribution of the angle of reach of the observed landslides, employing the software tool r.randomwalk. One set of random walks is routed downslope from each pixel defined as release area. Each random walk stops when leaving the observed impact area of the landslide. (4) The cumulative probability function (cdf) derived in (3) is used as input to route a set of random walks downslope from each pixel in the study area through the DEM, assigning the probability gained from the cdf to each pixel along the path (impact probability). The impact probability of a pixel is defined as the average impact probability of all sets of random walks impacting a pixel. Further, the average release probabilities of the release pixels of all sets of random walks impacting a given pixel are stored along with the area of the possible release zone. (5) We compute the zonal release probability by increasing the release probability according to the size of the release zone - the larger the zone, the larger the probability that a landslide will originate from at least one pixel within this zone. We quantify this relationship by a set of empirical curves. (6) Finally, we multiply the zonal release probability with the impact probability in order to estimate the combined impact probability for each pixel. We demonstrate the model with a 167 km² study area in Taiwan, using an inventory of landslides triggered by the typhoon Morakot. Analyzing the model results leads us to a set of key conclusions: (i) The average composite impact probability over the entire study area corresponds well to the density of observed landside pixels. Therefore we conclude that the method is valid in general, even though the concept of the zonal release probability bears some conceptual issues that have to be kept in mind. (ii) The parameters used as predictors cannot fully explain the observed distribution of landslides. The size of the release zone influences the composite impact probability to a larger degree than the pixel-based release probability. (iii) The prediction rate increases considerably when excluding the largest, deep-seated, landslides from the analysis. We conclude that such landslides are mainly related to geological features hardly reflected in the predictor layers used.

The impact of differences in EQ-5D and SF-6D utility scores on the acceptability of cost-utility ratios: results across five trial-based cost-utility studies.

PubMed

Joore, Manuela; Brunenberg, Danielle; Nelemans, Patricia; Wouters, Emiel; Kuijpers, Petra; Honig, Adriaan; Willems, Danielle; de Leeuw, Peter; Severens, Johan; Boonen, Annelies

2010-01-01

This article investigates whether differences in utility scores based on the EQ-5D and the SF-6D have impact on the incremental cost-utility ratios in five distinct patient groups. We used five empirical data sets of trial-based cost-utility studies that included patients with different disease conditions and severity (musculoskeletal disease, cardiovascular pulmonary disease, and psychological disorders) to calculate differences in quality-adjusted life-years (QALYs) based on EQ-5D and SF-6D utility scores. We compared incremental QALYs, incremental cost-utility ratios, and the probability that the incremental cost-utility ratio was acceptable within and across the data sets. We observed small differences in incremental QALYs, but large differences in the incremental cost-utility ratios and in the probability that these ratios were acceptable at a given threshold, in the majority of the presented cost-utility analyses. More specifically, in the patient groups with relatively mild health conditions the probability of acceptance of the incremental cost-utility ratio was considerably larger when using the EQ-5D to estimate utility. While in the patient groups with worse health conditions the probability of acceptance of the incremental cost-utility ratio was considerably larger when using the SF-6D to estimate utility. Much of the appeal in using QALYs as measure of effectiveness in economic evaluations is in the comparability across conditions and interventions. The incomparability of the results of cost-utility analyses using different instruments to estimate a single index value for health severely undermines this aspect and reduces the credibility of the use of incremental cost-utility ratios for decision-making.

Effects of Stress Ratio and Microstructure on Fatigue Failure Behavior of Polycrystalline Nickel Superalloy

NASA Astrophysics Data System (ADS)

Zhang, H.; Guan, Z. W.; Wang, Q. Y.; Liu, Y. J.; Li, J. K.

2018-05-01

The effects of microstructure and stress ratio on high cycle fatigue of nickel superalloy Nimonic 80A were investigated. The stress ratios of 0.1, 0.5 and 0.8 were chosen to perform fatigue tests in a frequency of 110 Hz. Cleavage failure was observed, and three competing failure crack initiation modes were discovered by a scanning electron microscope, which were classified as surface without facets, surface with facets and subsurface with facets. With increasing the stress ratio from 0.1 to 0.8, the occurrence probability of surface and subsurface with facets also increased and reached the maximum value at R = 0.5, meanwhile the probability of surface initiation without facets decreased. The effect of microstructure on the fatigue fracture behavior at different stress ratios was also observed and discussed. Based on the Goodman diagram, it was concluded that the fatigue strength of 50% probability of failure at R = 0.1, 0.5 and 0.8 is lower than the modified Goodman line.

Acceptance Probability (P a) Analysis for Process Validation Lifecycle Stages.

PubMed

Alsmeyer, Daniel; Pazhayattil, Ajay; Chen, Shu; Munaretto, Francesco; Hye, Maksuda; Sanghvi, Pradeep

2016-04-01

This paper introduces an innovative statistical approach towards understanding how variation impacts the acceptance criteria of quality attributes. Because of more complex stage-wise acceptance criteria, traditional process capability measures are inadequate for general application in the pharmaceutical industry. The probability of acceptance concept provides a clear measure, derived from specific acceptance criteria for each quality attribute. In line with the 2011 FDA Guidance, this approach systematically evaluates data and scientifically establishes evidence that a process is capable of consistently delivering quality product. The probability of acceptance provides a direct and readily understandable indication of product risk. As with traditional capability indices, the acceptance probability approach assumes that underlying data distributions are normal. The computational solutions for dosage uniformity and dissolution acceptance criteria are readily applicable. For dosage uniformity, the expected AV range may be determined using the s lo and s hi values along with the worst case estimates of the mean. This approach permits a risk-based assessment of future batch performance of the critical quality attributes. The concept is also readily applicable to sterile/non sterile liquid dose products. Quality attributes such as deliverable volume and assay per spray have stage-wise acceptance that can be converted into an acceptance probability. Accepted statistical guidelines indicate processes with C pk > 1.33 as performing well within statistical control and those with C pk < 1.0 as "incapable" (1). A C pk > 1.33 is associated with a centered process that will statistically produce less than 63 defective units per million. This is equivalent to an acceptance probability of >99.99%.

Robust approaches to quantification of margin and uncertainty for sparse data

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

Hund, Lauren; Schroeder, Benjamin B.; Rumsey, Kelin

Characterizing the tails of probability distributions plays a key role in quantification of margins and uncertainties (QMU), where the goal is characterization of low probability, high consequence events based on continuous measures of performance. When data are collected using physical experimentation, probability distributions are typically fit using statistical methods based on the collected data, and these parametric distributional assumptions are often used to extrapolate about the extreme tail behavior of the underlying probability distribution. In this project, we character- ize the risk associated with such tail extrapolation. Specifically, we conducted a scaling study to demonstrate the large magnitude of themore » risk; then, we developed new methods for communicat- ing risk associated with tail extrapolation from unvalidated statistical models; lastly, we proposed a Bayesian data-integration framework to mitigate tail extrapolation risk through integrating ad- ditional information. We conclude that decision-making using QMU is a complex process that cannot be achieved using statistical analyses alone.« less

A study of two statistical methods as applied to shuttle solid rocket booster expenditures

NASA Technical Reports Server (NTRS)

Perlmutter, M.; Huang, Y.; Graves, M.

1974-01-01

The state probability technique and the Monte Carlo technique are applied to finding shuttle solid rocket booster expenditure statistics. For a given attrition rate per launch, the probable number of boosters needed for a given mission of 440 launches is calculated. Several cases are considered, including the elimination of the booster after a maximum of 20 consecutive launches. Also considered is the case where the booster is composed of replaceable components with independent attrition rates. A simple cost analysis is carried out to indicate the number of boosters to build initially, depending on booster costs. Two statistical methods were applied in the analysis: (1) state probability method which consists of defining an appropriate state space for the outcome of the random trials, and (2) model simulation method or the Monte Carlo technique. It was found that the model simulation method was easier to formulate while the state probability method required less computing time and was more accurate.

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

NASA Astrophysics Data System (ADS)

Lian, Shizhong; Chen, Jiangping; Luo, Minghai

2016-06-01

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

Importance Sampling in the Evaluation and Optimization of Buffered Failure Probability

DTIC Science & Technology

2015-07-01

12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12 Vancouver, Canada, July 12-15, 2015...Importance Sampling in the Evaluation and Optimization of Buffered Failure Probability Marwan M. Harajli Graduate Student, Dept. of Civil and Environ...criterion is usually the failure probability . In this paper, we examine the buffered failure probability as an attractive alternative to the failure

Translational Genomics Research Institute: Identification of Pathways Enriched with Condition-Specific Statistical Dependencies Across Four Subtypes of Glioblastoma Multiforme | Office of Cancer Genomics

Cancer.gov

Evaluation of Differential DependencY (EDDY) is a statistical test for the differential dependency relationship of a set of genes between two given conditions. For each condition, possible dependency network structures are enumerated and their likelihoods are computed to represent a probability distribution of dependency networks. The difference between the probability distributions of dependency networks is computed between conditions, and its statistical significance is evaluated with random permutations of condition labels on the samples.  

Translational Genomics Research Institute (TGen): Identification of Pathways Enriched with Condition-Specific Statistical Dependencies Across Four Subtypes of Glioblastoma Multiforme | Office of Cancer Genomics

Cancer.gov

Evaluation of Differential DependencY (EDDY) is a statistical test for the differential dependency relationship of a set of genes between two given conditions. For each condition, possible dependency network structures are enumerated and their likelihoods are computed to represent a probability distribution of dependency networks. The difference between the probability distributions of dependency networks is computed between conditions, and its statistical significance is evaluated with random permutations of condition labels on the samples.  

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

A probabilistic analysis of electrical equipment vulnerability to carbon fibers

NASA Technical Reports Server (NTRS)

Elber, W.

1980-01-01

The statistical problems of airborne carbon fibers falling onto electrical circuits were idealized and analyzed. The probability of making contact between randomly oriented finite length fibers and sets of parallel conductors with various spacings and lengths was developed theoretically. The probability of multiple fibers joining to bridge a single gap between conductors, or forming continuous networks is included. From these theoretical considerations, practical statistical analyses to assess the likelihood of causing electrical malfunctions was produced. The statistics obtained were confirmed by comparison with results of controlled experiments.

Boundary Layer Effect on Behavior of Discrete Models

PubMed Central

Eliáš, Jan

2017-01-01

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson’s ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis. PMID:28772517

An empirical likelihood ratio test robust to individual heterogeneity for differential expression analysis of RNA-seq.

PubMed

Xu, Maoqi; Chen, Liang

2018-01-01

The individual sample heterogeneity is one of the biggest obstacles in biomarker identification for complex diseases such as cancers. Current statistical models to identify differentially expressed genes between disease and control groups often overlook the substantial human sample heterogeneity. Meanwhile, traditional nonparametric tests lose detailed data information and sacrifice the analysis power, although they are distribution free and robust to heterogeneity. Here, we propose an empirical likelihood ratio test with a mean-variance relationship constraint (ELTSeq) for the differential expression analysis of RNA sequencing (RNA-seq). As a distribution-free nonparametric model, ELTSeq handles individual heterogeneity by estimating an empirical probability for each observation without making any assumption about read-count distribution. It also incorporates a constraint for the read-count overdispersion, which is widely observed in RNA-seq data. ELTSeq demonstrates a significant improvement over existing methods such as edgeR, DESeq, t-tests, Wilcoxon tests and the classic empirical likelihood-ratio test when handling heterogeneous groups. It will significantly advance the transcriptomics studies of cancers and other complex disease. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

The association between season of pregnancy and birth-sex among Chinese.

PubMed

Xu, Tan; Lin, Dongdong; Liang, Hui; Chen, Mei; Tong, Weijun; Mu, Yongping; Feng, Cindy Xin; Gao, Yongqing; Zheng, Yumei; Sun, Wenjie

2014-08-11

although numerous studies have reported the association between birth season and sex ratio, few studies have been conducted in subtropical regions in a non-Western setting. The present study assessed the effects of pregnancy season on birth sex ratio in China. We conducted a national population-based retrospective study from 2006-2008 with 3175 children-parents pairs enrolled in the Northeast regions of China. Demographics and data relating to pregnancy and birth were collected and analyzed. A multiple logistical regression model was fitted to estimate the regression coefficient and 95% confidence interval (CI) of refractive error for mother pregnancy season, adjusting for potential confounders. After adjusting for parental age (cut-off point was 30 years), region, nationality, mother education level, and mother miscarriage history, there is a significant statistical different mother pregnancy season on birth-sex. Compared with mothers who were pregnant in spring, those pregnant in summer or winter had a high probability of delivering girls (p < 0.05). The birth-sex ratio varied with months. Our results suggested that mothers pregnant in summer and winter were more likely to deliver girls, compared with those pregnant in spring. Pregnancy season may play an important role in the birth-sex.

Adaptive detection of noise signal according to Neumann-Pearson criterion

NASA Astrophysics Data System (ADS)

Padiryakov, Y. A.

1985-03-01

Optimum detection according to the Neumann-Pearson criterion is considered in the case of a random Gaussian noise signal, stationary during measurement, and a stationary random Gaussian background interference. Detection is based on two samples, their statistics characterized by estimates of their spectral densities, it being a priori known that sample A from the signal channel is either the sum of signal and interference or interference alone and sample B from the reference interference channel is an interference with the same spectral density as that of the interference in sample A for both hypotheses. The probability of correct detection is maximized on the average, first in the 2N-dimensional space of signal spectral density and interference spectral density readings, by fixing the probability of false alarm at each point so as to stabilize it at a constant level against variation of the interference spectral density. Deterministic decision rules are established. The algorithm is then reduced to equivalent detection in the N-dimensional space of the ratio of sample A readings to sample B readings.

Efficient Posterior Probability Mapping Using Savage-Dickey Ratios

PubMed Central

Penny, William D.; Ridgway, Gerard R.

2013-01-01

Statistical Parametric Mapping (SPM) is the dominant paradigm for mass-univariate analysis of neuroimaging data. More recently, a Bayesian approach termed Posterior Probability Mapping (PPM) has been proposed as an alternative. PPM offers two advantages: (i) inferences can be made about effect size thus lending a precise physiological meaning to activated regions, (ii) regions can be declared inactive. This latter facility is most parsimoniously provided by PPMs based on Bayesian model comparisons. To date these comparisons have been implemented by an Independent Model Optimization (IMO) procedure which separately fits null and alternative models. This paper proposes a more computationally efficient procedure based on Savage-Dickey approximations to the Bayes factor, and Taylor-series approximations to the voxel-wise posterior covariance matrices. Simulations show the accuracy of this Savage-Dickey-Taylor (SDT) method to be comparable to that of IMO. Results on fMRI data show excellent agreement between SDT and IMO for second-level models, and reasonable agreement for first-level models. This Savage-Dickey test is a Bayesian analogue of the classical SPM-F and allows users to implement model comparison in a truly interactive manner. PMID:23533640

Ratio-of-Mediator-Probability Weighting for Causal Mediation Analysis in the Presence of Treatment-by-Mediator Interaction

ERIC Educational Resources Information Center

Hong, Guanglei; Deutsch, Jonah; Hill, Heather D.

2015-01-01

Conventional methods for mediation analysis generate biased results when the mediator-outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator…

Ratio-of-Mediator-Probability Weighting for Causal Mediation Analysis in the Presence of Treatment-by-Mediator Interaction

ERIC Educational Resources Information Center

Hong, Guanglei; Deutsch, Jonah; Hill, Heather D.

2015-01-01

Conventional methods for mediation analysis generate biased results when the mediator--outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator…

Sense and Avoid Safety Analysis for Remotely Operated Unmanned Aircraft in the National Airspace System. Version 5

NASA Technical Reports Server (NTRS)

Carreno, Victor

2006-01-01

This document describes a method to demonstrate that a UAS, operating in the NAS, can avoid collisions with an equivalent level of safety compared to a manned aircraft. The method is based on the calculation of a collision probability for a UAS , the calculation of a collision probability for a base line manned aircraft, and the calculation of a risk ratio given by: Risk Ratio = P(collision_UAS)/P(collision_manned). A UAS will achieve an equivalent level of safety for collision risk if the Risk Ratio is less than or equal to one. Calculation of the probability of collision for UAS and manned aircraft is accomplished through event/fault trees.

K{sub β} to K{sub α} X-ray intensity ratios and K to L shell vacancy transfer probabilities of Co, Ni, Cu, and Zn

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

Anand, L. F. M.; Gudennavar, S. B., E-mail: shivappa.b.gudennavar@christuniversity.in; Bubbly, S. G.

The K to L shell total vacancy transfer probabilities of low Z elements Co, Ni, Cu, and Zn are estimated by measuring the K{sub β} to K{sub α} intensity ratio adopting the 2π-geometry. The target elements were excited by 32.86 keV barium K-shell X-rays from a weak {sup 137}Cs γ-ray source. The emitted K-shell X-rays were detected using a low energy HPGe X-ray detector coupled to a 16 k MCA. The measured intensity ratios and the total vacancy transfer probabilities are compared with theoretical results and others’ work, establishing a good agreement.

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…

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, K.C.; Hoyer, K.K.; Humenik, K.E.

1995-10-17

A method and system for monitoring an industrial process and a sensor are disclosed. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test. 17 figs.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, K.C.; Hoyer, K.K.; Humenik, K.E.

1997-05-13

A method and system are disclosed for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test. 17 figs.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, Kenneth C.; Hoyer, Kristin K.; Humenik, Keith E.

1995-01-01

A method and system for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.

System for monitoring an industrial process and determining sensor status

DOEpatents

Gross, Kenneth C.; Hoyer, Kristin K.; Humenik, Keith E.

1997-01-01

A method and system for monitoring an industrial process and a sensor. The method and system include generating a first and second signal characteristic of an industrial process variable. One of the signals can be an artificial signal generated by an auto regressive moving average technique. After obtaining two signals associated with one physical variable, a difference function is obtained by determining the arithmetic difference between the two pairs of signals over time. A frequency domain transformation is made of the difference function to obtain Fourier modes describing a composite function. A residual function is obtained by subtracting the composite function from the difference function and the residual function (free of nonwhite noise) is analyzed by a statistical probability ratio test.

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

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…

Various Effects of Embedded Intrapulse Communications on Pulsed Radar

DTIC Science & Technology

2017-06-01

specific type of interference that may be encountered by radar; however, this introductory information should suffice to illustrate to the reader why...chapter we seek to not merely understand the overall statistical performance of the radar with embedded intrapulse communications but rather to evaluate...Theory Probability of detection, discussed in Chapter 4, assesses the statistical probability of a radar accurately identifying a target given a

Statistical evaluation of vibration analysis techniques

NASA Technical Reports Server (NTRS)

Milner, G. Martin; Miller, Patrice S.

1987-01-01

An evaluation methodology is presented for a selection of candidate vibration analysis techniques applicable to machinery representative of the environmental control and life support system of advanced spacecraft; illustrative results are given. Attention is given to the statistical analysis of small sample experiments, the quantification of detection performance for diverse techniques through the computation of probability of detection versus probability of false alarm, and the quantification of diagnostic performance.

Sample Size Determination for Rasch Model Tests

ERIC Educational Resources Information Center

Draxler, Clemens

2010-01-01

This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations.…

On the significance of δ13C correlations in ancient sediments

NASA Astrophysics Data System (ADS)

Derry, Louis A.

2010-08-01

A graphical analysis of the correlations between δc and ɛTOC was introduced by Rothman et al. (2003) to obtain estimates of the carbon isotopic composition of inputs to the oceans and the organic carbon burial fraction. Applied to Cenozoic data, the method agrees with independent estimates, but with Neoproterozoic data the method yields results that cannot be accommodated with standard models of sedimentary carbon isotope mass balance. We explore the sensitivity of the graphical correlation method and find that the variance ratio between δc and δo is an important control on the correlation of δc and ɛ. If the variance ratio σc/ σo ≥ 1 highly correlated arrays very similar to those obtained from the data are produced from independent random variables. The Neoproterozoic data shows such variance patterns, and the regression parameters for the Neoproterozoic data are statistically indistinguishable from the randomized model at the 95% confidence interval. The projection of the data into δc- ɛ space cannot distinguish between signal and noise, such as post-depositional alteration, under these circumstances. There appears to be no need to invoke unusual carbon cycle dynamics to explain the Neoproterozoic δc- ɛ array. The Cenozoic data have σc/ σo < 1 and the δc vs. ɛ correlation is probably geologically significant, but the analyzed sample size is too small to yield statistically significant results.

A Bayesian pick-the-winner design in a randomized phase II clinical trial.

PubMed

Chen, Dung-Tsa; Huang, Po-Yu; Lin, Hui-Yi; Chiappori, Alberto A; Gabrilovich, Dmitry I; Haura, Eric B; Antonia, Scott J; Gray, Jhanelle E

2017-10-24

Many phase II clinical trials evaluate unique experimental drugs/combinations through multi-arm design to expedite the screening process (early termination of ineffective drugs) and to identify the most effective drug (pick the winner) to warrant a phase III trial. Various statistical approaches have been developed for the pick-the-winner design but have been criticized for lack of objective comparison among the drug agents. We developed a Bayesian pick-the-winner design by integrating a Bayesian posterior probability with Simon two-stage design in a randomized two-arm clinical trial. The Bayesian posterior probability, as the rule to pick the winner, is defined as probability of the response rate in one arm higher than in the other arm. The posterior probability aims to determine the winner when both arms pass the second stage of the Simon two-stage design. When both arms are competitive (i.e., both passing the second stage), the Bayesian posterior probability performs better to correctly identify the winner compared with the Fisher exact test in the simulation study. In comparison to a standard two-arm randomized design, the Bayesian pick-the-winner design has a higher power to determine a clear winner. In application to two studies, the approach is able to perform statistical comparison of two treatment arms and provides a winner probability (Bayesian posterior probability) to statistically justify the winning arm. We developed an integrated design that utilizes Bayesian posterior probability, Simon two-stage design, and randomization into a unique setting. It gives objective comparisons between the arms to determine the winner.

Probability of Unmixed Young Groundwater (defined using chlorofluorocarbon-11 concentrations and tritium activities) in the Eagle River Watershed Valley-Fill Aquifer, Eagle County, North-Central Colorado, 2006-2007

USGS Publications Warehouse

Rupert, Michael G.; Plummer, Niel

2009-01-01

This raster data set delineates the predicted probability of unmixed young groundwater (defined using chlorofluorocarbon-11 concentrations and tritium activities) in groundwater in the Eagle River watershed valley-fill aquifer, Eagle County, North-Central Colorado, 2006-2007. This data set was developed by a cooperative project between the U.S. Geological Survey, Eagle County, the Eagle River Water and Sanitation District, the Town of Eagle, the Town of Gypsum, and the Upper Eagle Regional Water Authority. This project was designed to evaluate potential land-development effects on groundwater and surface-water resources so that informed land-use and water management decisions can be made. This groundwater probability map and its associated probability maps were developed as follows: (1) A point data set of wells with groundwater quality and groundwater age data was overlaid with thematic layers of anthropogenic (related to human activities) and hydrogeologic data by using a geographic information system to assign each well values for depth to groundwater, distance to major streams and canals, distance to gypsum beds, precipitation, soils, and well depth. These data then were downloaded to a statistical software package for analysis by logistic regression. (2) Statistical models predicting the probability of elevated nitrate concentrations, the probability of unmixed young water (using chlorofluorocarbon-11 concentrations and tritium activities), and the probability of elevated volatile organic compound concentrations were developed using logistic regression techniques. (3) The statistical models were entered into a GIS and the probability map was constructed.

Consistency of extreme flood estimation approaches

NASA Astrophysics Data System (ADS)

Felder, Guido; Paquet, Emmanuel; Penot, David; Zischg, Andreas; Weingartner, Rolf

2017-04-01

Estimations of low-probability flood events are frequently used for the planning of infrastructure as well as for determining the dimensions of flood protection measures. There are several well-established methodical procedures to estimate low-probability floods. However, a global assessment of the consistency of these methods is difficult to achieve, the "true value" of an extreme flood being not observable. Anyway, a detailed comparison performed on a given case study brings useful information about the statistical and hydrological processes involved in different methods. In this study, the following three different approaches for estimating low-probability floods are compared: a purely statistical approach (ordinary extreme value statistics), a statistical approach based on stochastic rainfall-runoff simulation (SCHADEX method), and a deterministic approach (physically based PMF estimation). These methods are tested for two different Swiss catchments. The results and some intermediate variables are used for assessing potential strengths and weaknesses of each method, as well as for evaluating the consistency of these methods.

Deep convolutional neural network for mammographic density segmentation

NASA Astrophysics Data System (ADS)

Wei, Jun; Li, Songfeng; Chan, Heang-Ping; Helvie, Mark A.; Roubidoux, Marilyn A.; Lu, Yao; Zhou, Chuan; Hadjiiski, Lubomir; Samala, Ravi K.

2018-02-01

Breast density is one of the most significant factors for cancer risk. In this study, we proposed a supervised deep learning approach for automated estimation of percentage density (PD) on digital mammography (DM). The deep convolutional neural network (DCNN) was trained to estimate a probability map of breast density (PMD). PD was calculated as the ratio of the dense area to the breast area based on the probability of each pixel belonging to dense region or fatty region at a decision threshold of 0.5. The DCNN estimate was compared to a feature-based statistical learning approach, in which gray level, texture and morphological features were extracted from each ROI and the least absolute shrinkage and selection operator (LASSO) was used to select and combine the useful features to generate the PMD. The reference PD of each image was provided by two experienced MQSA radiologists. With IRB approval, we retrospectively collected 347 DMs from patient files at our institution. The 10-fold cross-validation results showed a strong correlation r=0.96 between the DCNN estimation and interactive segmentation by radiologists while that of the feature-based statistical learning approach vs radiologists' segmentation had a correlation r=0.78. The difference between the segmentation by DCNN and by radiologists was significantly smaller than that between the feature-based learning approach and radiologists (p < 0.0001) by two-tailed paired t-test. This study demonstrated that the DCNN approach has the potential to replace radiologists' interactive thresholding in PD estimation on DMs.

A Bayesian Sampler for Optimization of Protein Domain Hierarchies

PubMed Central

2014-01-01

Abstract The process of identifying and modeling functionally divergent subgroups for a specific protein domain class and arranging these subgroups hierarchically has, thus far, largely been done via manual curation. How to accomplish this automatically and optimally is an unsolved statistical and algorithmic problem that is addressed here via Markov chain Monte Carlo sampling. Taking as input a (typically very large) multiple-sequence alignment, the sampler creates and optimizes a hierarchy by adding and deleting leaf nodes, by moving nodes and subtrees up and down the hierarchy, by inserting or deleting internal nodes, and by redefining the sequences and conserved patterns associated with each node. All such operations are based on a probability distribution that models the conserved and divergent patterns defining each subgroup. When we view these patterns as sequence determinants of protein function, each node or subtree in such a hierarchy corresponds to a subgroup of sequences with similar biological properties. The sampler can be applied either de novo or to an existing hierarchy. When applied to 60 protein domains from multiple starting points in this way, it converged on similar solutions with nearly identical log-likelihood ratio scores, suggesting that it typically finds the optimal peak in the posterior probability distribution. Similarities and differences between independently generated, nearly optimal hierarchies for a given domain help distinguish robust from statistically uncertain features. Thus, a future application of the sampler is to provide confidence measures for various features of a domain hierarchy. PMID:24494927

Sensitivity, Specificity, and Posttest Probability of Parotid Fine-Needle Aspiration: A Systematic Review and Meta-analysis.

PubMed

Liu, C Carrie; Jethwa, Ashok R; Khariwala, Samir S; Johnson, Jonas; Shin, Jennifer J

2016-01-01

(1) To analyze the sensitivity and specificity of fine-needle aspiration (FNA) in distinguishing benign from malignant parotid disease. (2) To determine the anticipated posttest probability of malignancy and probability of nondiagnostic and indeterminate cytology with parotid FNA. Independently corroborated computerized searches of PubMed, Embase, and Cochrane Central Register were performed. These were supplemented with manual searches and input from content experts. Inclusion/exclusion criteria specified diagnosis of parotid mass, intervention with both FNA and surgical excision, and enumeration of both cytologic and surgical histopathologic results. The primary outcomes were sensitivity, specificity, and posttest probability of malignancy. Heterogeneity was evaluated with the I(2) statistic. Meta-analysis was performed via a 2-level mixed logistic regression model. Bayesian nomograms were plotted via pooled likelihood ratios. The systematic review yielded 70 criterion-meeting studies, 63 of which contained data that allowed for computation of numerical outcomes (n = 5647 patients; level 2a) and consideration of meta-analysis. Subgroup analyses were performed in studies that were prospective, involved consecutive patients, described the FNA technique utilized, and used ultrasound guidance. The I(2) point estimate was >70% for all analyses, except within prospectively obtained and ultrasound-guided results. Among the prospective subgroup, the pooled analysis demonstrated a sensitivity of 0.882 (95% confidence interval [95% CI], 0.509-0.982) and a specificity of 0.995 (95% CI, 0.960-0.999). The probabilities of nondiagnostic and indeterminate cytology were 0.053 (95% CI, 0.030-0.075) and 0.147 (95% CI, 0.106-0.188), respectively. FNA has moderate sensitivity and high specificity in differentiating malignant from benign parotid lesions. Considerable heterogeneity is present among studies. © American Academy of Otolaryngology-Head and Neck Surgery Foundation 2015.

Sensitivity, Specificity, and Posttest Probability of Parotid Fine-Needle Aspiration: A Systematic Review and Meta-analysis

PubMed Central

Liu, C. Carrie; Jethwa, Ashok R.; Khariwala, Samir S.; Johnson, Jonas; Shin, Jennifer J.

2016-01-01

Objectives (1) To analyze the sensitivity and specificity of fine-needle aspiration (FNA) in distinguishing benign from malignant parotid disease. (2) To determine the anticipated posttest probability of malignancy and probability of non-diagnostic and indeterminate cytology with parotid FNA. Data Sources Independently corroborated computerized searches of PubMed, Embase, and Cochrane Central Register were performed. These were supplemented with manual searches and input from content experts. Review Methods Inclusion/exclusion criteria specified diagnosis of parotid mass, intervention with both FNA and surgical excision, and enumeration of both cytologic and surgical histopathologic results. The primary outcomes were sensitivity, specificity, and posttest probability of malignancy. Heterogeneity was evaluated with the I2 statistic. Meta-analysis was performed via a 2-level mixed logistic regression model. Bayesian nomograms were plotted via pooled likelihood ratios. Results The systematic review yielded 70 criterion-meeting studies, 63 of which contained data that allowed for computation of numerical outcomes (n = 5647 patients; level 2a) and consideration of meta-analysis. Subgroup analyses were performed in studies that were prospective, involved consecutive patients, described the FNA technique utilized, and used ultrasound guidance. The I2 point estimate was >70% for all analyses, except within prospectively obtained and ultrasound-guided results. Among the prospective subgroup, the pooled analysis demonstrated a sensitivity of 0.882 (95% confidence interval [95% CI], 0.509–0.982) and a specificity of 0.995 (95% CI, 0.960–0.999). The probabilities of nondiagnostic and indeterminate cytology were 0.053 (95% CI, 0.030–0.075) and 0.147 (95% CI, 0.106–0.188), respectively. Conclusion FNA has moderate sensitivity and high specificity in differentiating malignant from benign parotid lesions. Considerable heterogeneity is present among studies. PMID:26428476

Probability-based nitrate contamination map of groundwater in Kinmen.

PubMed

Liu, Chen-Wuing; Wang, Yeuh-Bin; Jang, Cheng-Shin

2013-12-01

Groundwater supplies over 50% of drinking water in Kinmen. Approximately 16.8% of groundwater samples in Kinmen exceed the drinking water quality standard (DWQS) of NO3 (-)-N (10 mg/L). The residents drinking high nitrate-polluted groundwater pose a potential risk to health. To formulate effective water quality management plan and assure a safe drinking water in Kinmen, the detailed spatial distribution of nitrate-N in groundwater is a prerequisite. The aim of this study is to develop an efficient scheme for evaluating spatial distribution of nitrate-N in residential well water using logistic regression (LR) model. A probability-based nitrate-N contamination map in Kinmen is constructed. The LR model predicted the binary occurrence probability of groundwater nitrate-N concentrations exceeding DWQS by simple measurement variables as independent variables, including sampling season, soil type, water table depth, pH, EC, DO, and Eh. The analyzed results reveal that three statistically significant explanatory variables, soil type, pH, and EC, are selected for the forward stepwise LR analysis. The total ratio of correct classification reaches 92.7%. The highest probability of nitrate-N contamination map presents in the central zone, indicating that groundwater in the central zone should not be used for drinking purposes. Furthermore, a handy EC-pH-probability curve of nitrate-N exceeding the threshold of DWQS was developed. This curve can be used for preliminary screening of nitrate-N contamination in Kinmen groundwater. This study recommended that the local agency should implement the best management practice strategies to control nonpoint nitrogen sources and carry out a systematic monitoring of groundwater quality in residential wells of the high nitrate-N contamination zones.

Selecting ultra-faint dwarf candidate progenitors in cosmological N-body simulations at high redshifts

NASA Astrophysics Data System (ADS)

Safarzadeh, Mohammadtaher; Ji, Alexander P.; Dooley, Gregory A.; Frebel, Anna; Scannapieco, Evan; Gómez, Facundo A.; O'Shea, Brian W.

2018-06-01

The smallest satellites of the Milky Way ceased forming stars during the epoch of reionization and thus provide archaeological access to galaxy formation at z > 6. Numerical studies of these ultrafaint dwarf galaxies (UFDs) require expensive cosmological simulations with high mass resolution that are carried out down to z = 0. However, if we are able to statistically identify UFD host progenitors at high redshifts with relatively high probabilities, we can avoid this high computational cost. To find such candidates, we analyse the merger trees of Milky Way type haloes from the high-resolution Caterpillar suite of dark matter only simulations. Satellite UFD hosts at z = 0 are identified based on four different abundance matching (AM) techniques. All the haloes at high redshifts are traced forward in time in order to compute the probability of surviving as satellite UFDs today. Our results show that selecting potential UFD progenitors based solely on their mass at z = 12 (8) results in a 10 per cent (20 per cent) chance of obtaining a surviving UFD at z = 0 in three of the AM techniques we adopted. We find that the progenitors of surviving satellite UFDs have lower virial ratios (η), and are preferentially located at large distances from the main MW progenitor, while they show no correlation with concentration parameter. Haloes with favorable locations and virial ratios are ≈3 times more likely to survive as satellite UFD candidates at z = 0.

Childhood growth and development associated with need for full-time special education at school age.

PubMed

Mannerkoski, Minna; Aberg, Laura; Hoikkala, Marianne; Sarna, Seppo; Kaski, Markus; Autti, Taina; Heiskala, Hannu

2009-01-01

To explore how growth measurements and attainment of developmental milestones in early childhood reflect the need for full-time special education (SE). After stratification in this population-based study, 900 pupils in full-time SE groups (age-range 7-16 years, mean 12 years 8 months) at three levels and 301 pupils in mainstream education (age-range 7-16, mean 12 years 9 months) provided data on height and weight from birth to age 7 years and head circumference to age 1 year. Developmental screening was evaluated from age 1 month to 48 months. Statistical methods included a general linear model (growth measurements), binary logistic regression analysis (odds ratios for growth), and multinomial logistic regression analysis (odds ratios for developmental milestones). At 1 year, a 1 standard deviation score (SDS) decrease in height raised the probability of SE placement by 40%, and a 1 SDS decrease in head size by 28%. In developmental screening, during the first months of life the gross motor milestones, especially head support, differentiated the children at levels 0-3. Thereafter, the fine motor milestones and those related to speech and social skills became more important. Children whose growth is mildly impaired, though in the normal range, and who fail to attain certain developmental milestones have an increased probability for SE and thus a need for special attention when toddlers age. Similar to the growth curves, these children seem to have consistent developmental curves (patterns).

Comparison of Expert Adjudicated Coronary Heart Disease and Cardiovascular Disease Mortality With the National Death Index: Results From the REasons for Geographic And Racial Differences in Stroke (REGARDS) Study.

PubMed

Olubowale, Olusola Tope; Safford, Monika M; Brown, Todd M; Durant, Raegan W; Howard, Virginia J; Gamboa, Christopher; Glasser, Stephen P; Rhodes, J David; Levitan, Emily B

2017-05-03

The National Death Index (NDI) is widely used to detect coronary heart disease (CHD) and cardiovascular disease (CVD) deaths, but its reliability has not been examined recently. We compared CHD and CVD deaths detected by NDI with expert adjudication of 4010 deaths that occurred between 2003 and 2013 among participants in the REGARDS (REasons for Geographic And Racial Differences in Stroke) cohort of black and white adults in the United States. NDI derived CHD mortality had sensitivity 53.6%, specificity 90.3%, positive predictive value 54.2%, and negative predictive value 90.1%. NDI-derived CVD mortality had sensitivity 73.4%, specificity 84.5%, positive predictive value 70.6%, and negative predictive value 86.2%. Among NDI-derived CHD and CVD deaths, older age (odds ratios, 1.06 and 1.04 per 1-year increase) was associated with a higher probability of disagreement with the adjudicated cause of death, whereas among REGARDS adjudicated CHD and CVD deaths a history of CHD or CVD was associated with a lower probability of disagreement with the NDI-derived causes of death (odds ratios, 0.59 and 0.67, respectively). The modest accuracy and differential performance of NDI-derived cause of death may impact CHD and CVD mortality statistics. © 2017 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley.

Probability distributions of the electroencephalogram envelope of preterm infants.

PubMed

Saji, Ryoya; Hirasawa, Kyoko; Ito, Masako; Kusuda, Satoshi; Konishi, Yukuo; Taga, Gentaro

2015-06-01

To determine the stationary characteristics of electroencephalogram (EEG) envelopes for prematurely born (preterm) infants and investigate the intrinsic characteristics of early brain development in preterm infants. Twenty neurologically normal sets of EEGs recorded in infants with a post-conceptional age (PCA) range of 26-44 weeks (mean 37.5 ± 5.0 weeks) were analyzed. Hilbert transform was applied to extract the envelope. We determined the suitable probability distribution of the envelope and performed a statistical analysis. It was found that (i) the probability distributions for preterm EEG envelopes were best fitted by lognormal distributions at 38 weeks PCA or less, and by gamma distributions at 44 weeks PCA; (ii) the scale parameter of the lognormal distribution had positive correlations with PCA as well as a strong negative correlation with the percentage of low-voltage activity; (iii) the shape parameter of the lognormal distribution had significant positive correlations with PCA; (iv) the statistics of mode showed significant linear relationships with PCA, and, therefore, it was considered a useful index in PCA prediction. These statistics, including the scale parameter of the lognormal distribution and the skewness and mode derived from a suitable probability distribution, may be good indexes for estimating stationary nature in developing brain activity in preterm infants. The stationary characteristics, such as discontinuity, asymmetry, and unimodality, of preterm EEGs are well indicated by the statistics estimated from the probability distribution of the preterm EEG envelopes. Copyright © 2014 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets.

PubMed

Gladysz, Szymon; Yaitskova, Natalia; Christou, Julian C

2010-11-01

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.

Discrimination of Man-Made Events and Tectonic Earthquakes in Utah Using Data Recorded at Local Distances

NASA Astrophysics Data System (ADS)

Tibi, R.; Young, C. J.; Koper, K. D.; Pankow, K. L.

2017-12-01

Seismic event discrimination methods exploit the differing characteristics—in terms of amplitude and/or frequency content—of the generated seismic phases among the event types to be classified. Most of the commonly used seismic discrimination methods are designed for regional data recorded at distances of about 200 to 2000 km. Relatively little attention has focused on discriminants for local distances (< 200 km), the range at which the smallest events are recorded. Short-period fundamental mode Rayleigh waves (Rg) are commonly observed on seismograms of man-made seismic events, and shallow, naturally occurring tectonic earthquakes recorded at local distances. We leverage the well-known notion that Rg amplitude decreases dramatically with increasing event depth to propose a new depth discriminant based on Rg-to-Sg spectral amplitude ratios. The approach is successfully used to discriminate shallow events from deeper tectonic earthquakes in the Utah region recorded at local distances (< 150 km) by the University of Utah Seismographic Stations (UUSS) regional seismic network. Using Mood's median test, we obtained probabilities of nearly zero that the median Rg-to-Sg spectral amplitude ratios are the same between shallow events on one side (including both shallow tectonic earthquakes and man-made events), and deeper earthquakes on the other side, suggesting that there is a statistically significant difference in the estimated Rg-to-Sg ratios between the two populations. We also observed consistent disparities between the different types of shallow events (e.g., explosions vs. mining-induced events), implying that it may be possible to separate the sub-populations that make up this group. This suggests that using local distance Rg-to-Sg spectral amplitude ratios one can not only discriminate shallow from deeper events, but may also be able to discriminate different populations of shallow events. We also experimented with Pg-to-Sg amplitude ratios in multi-frequency linear discriminant functions to classify man-made events and tectonic earthquakes in Utah. Initial results are very promising, showing probabilities of misclassification of only 2.4-14.3%.

Symptoms of major depression in people with spinal cord injury: implications for screening.

PubMed

Bombardier, Charles H; Richards, J Scott; Krause, James S; Tulsky, David; Tate, Denise G

2004-11-01

To provide psychometric data on a self-report measure of major depressive disorder (MDD) and to determine whether somatic symptoms are nonspecific or count toward the diagnosis. Survey. Data from the National Spinal Cord Injury Statistical Center representing 16 Model Spinal Cord Injury Systems. Eight hundred forty-nine people with spinal cord injury who completed a standardized follow-up evaluation 1 year after injury. Not applicable. The Patient Health Questionnaire-9 (PHQ-9), a measure of MDD as defined by the Diagnostic and Statistical Manual of Mental Disorders, 4th Edition . We computed descriptive statistics on rates of depressive symptoms and probable MDD, evaluated internal consistency and construct validity, and analyzed the accuracy of individual items as predictors of MDD. Exactly 11.4% of participants met criteria for probable MDD. Probable MDD was associated with poorer subjective health, lower satisfaction with life, and more difficulty in daily role functioning. Probable MDD was not related to most demographic or injury-related variables. Both somatic and psychologic symptoms predicted probable MDD. The PHQ-9 has promise as a tool with which to identify probable MDD in people with SCI. Somatic symptoms should be counted toward the diagnosis and should alert health care providers to the likelihood of MDD. More efficient screening is only one of the quality improvement efforts needed to enhance management of MDD.

Occupation times and ergodicity breaking in biased continuous time random walks

NASA Astrophysics Data System (ADS)

Bel, Golan; Barkai, Eli

2005-12-01

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

Explorations in Statistics: The Analysis of Ratios and Normalized Data

ERIC Educational Resources Information Center

Curran-Everett, Douglas

2013-01-01

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This ninth installment of "Explorations in Statistics" explores the analysis of ratios and normalized--or standardized--data. As researchers, we compute a ratio--a numerator divided by a denominator--to compute a…

Active contours on statistical manifolds and texture segmentation

Treesearch

Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman

2005-01-01

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto a set of probability density functions. In this novel framework, color or texture features are measured at each image point and their statistical...

Active contours on statistical manifolds and texture segmentaiton

Treesearch

Sang-Mook Lee; A. Lynn Abbott; Neil A. Clark; Philip A. Araman

2005-01-01

A new approach to active contours on statistical manifolds is presented. The statistical manifolds are 2- dimensional Riemannian manifolds that are statistically defined by maps that transform a parameter domain onto-a set of probability density functions. In this novel framework, color or texture features are measured at each Image point and their statistical...

Familiar units prevail over statistical cues in word segmentation.

PubMed

Poulin-Charronnat, Bénédicte; Perruchet, Pierre; Tillmann, Barbara; Peereman, Ronald

2017-09-01

In language acquisition research, the prevailing position is that listeners exploit statistical cues, in particular transitional probabilities between syllables, to discover words of a language. However, other cues are also involved in word discovery. Assessing the weight learners give to these different cues leads to a better understanding of the processes underlying speech segmentation. The present study evaluated whether adult learners preferentially used known units or statistical cues for segmenting continuous speech. Before the exposure phase, participants were familiarized with part-words of a three-word artificial language. This design allowed the dissociation of the influence of statistical cues and familiar units, with statistical cues favoring word segmentation and familiar units favoring (nonoptimal) part-word segmentation. In Experiment 1, performance in a two-alternative forced choice (2AFC) task between words and part-words revealed part-word segmentation (even though part-words were less cohesive in terms of transitional probabilities and less frequent than words). By contrast, an unfamiliarized group exhibited word segmentation, as usually observed in standard conditions. Experiment 2 used a syllable-detection task to remove the likely contamination of performance by memory and strategy effects in the 2AFC task. Overall, the results suggest that familiar units overrode statistical cues, ultimately questioning the need for computation mechanisms of transitional probabilities (TPs) in natural language speech segmentation.

Diagnosis of students' ability in a statistical course based on Rasch probabilistic outcome

NASA Astrophysics Data System (ADS)

Mahmud, Zamalia; Ramli, Wan Syahira Wan; Sapri, Shamsiah; Ahmad, Sanizah

2017-06-01

Measuring students' ability and performance are important in assessing how well students have learned and mastered the statistical courses. Any improvement in learning will depend on the student's approaches to learning, which are relevant to some factors of learning, namely assessment methods carrying out tasks consisting of quizzes, tests, assignment and final examination. This study has attempted an alternative approach to measure students' ability in an undergraduate statistical course based on the Rasch probabilistic model. Firstly, this study aims to explore the learning outcome patterns of students in a statistics course (Applied Probability and Statistics) based on an Entrance-Exit survey. This is followed by investigating students' perceived learning ability based on four Course Learning Outcomes (CLOs) and students' actual learning ability based on their final examination scores. Rasch analysis revealed that students perceived themselves as lacking the ability to understand about 95% of the statistics concepts at the beginning of the class but eventually they had a good understanding at the end of the 14 weeks class. In terms of students' performance in their final examination, their ability in understanding the topics varies at different probability values given the ability of the students and difficulty of the questions. Majority found the probability and counting rules topic to be the most difficult to learn.

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.

SOCR: Statistics Online Computational Resource

PubMed Central

Dinov, Ivo D.

2011-01-01

The need for hands-on computer laboratory experience in undergraduate and graduate statistics education has been firmly established in the past decade. As a result a number of attempts have been undertaken to develop novel approaches for problem-driven statistical thinking, data analysis and result interpretation. In this paper we describe an integrated educational web-based framework for: interactive distribution modeling, virtual online probability experimentation, statistical data analysis, visualization and integration. Following years of experience in statistical teaching at all college levels using established licensed statistical software packages, like STATA, S-PLUS, R, SPSS, SAS, Systat, etc., we have attempted to engineer a new statistics education environment, the Statistics Online Computational Resource (SOCR). This resource performs many of the standard types of statistical analysis, much like other classical tools. In addition, it is designed in a plug-in object-oriented architecture and is completely platform independent, web-based, interactive, extensible and secure. Over the past 4 years we have tested, fine-tuned and reanalyzed the SOCR framework in many of our undergraduate and graduate probability and statistics courses and have evidence that SOCR resources build student’s intuition and enhance their learning. PMID:21451741

Quantile-based bias correction and uncertainty quantification of extreme event attribution statements

DOE PAGES

Jeon, Soyoung; Paciorek, Christopher J.; Wehner, Michael F.

2016-02-16

Extreme event attribution characterizes how anthropogenic climate change may have influenced the probability and magnitude of selected individual extreme weather and climate events. Attribution statements often involve quantification of the fraction of attributable risk (FAR) or the risk ratio (RR) and associated confidence intervals. Many such analyses use climate model output to characterize extreme event behavior with and without anthropogenic influence. However, such climate models may have biases in their representation of extreme events. To account for discrepancies in the probabilities of extreme events between observational datasets and model datasets, we demonstrate an appropriate rescaling of the model output basedmore » on the quantiles of the datasets to estimate an adjusted risk ratio. Our methodology accounts for various components of uncertainty in estimation of the risk ratio. In particular, we present an approach to construct a one-sided confidence interval on the lower bound of the risk ratio when the estimated risk ratio is infinity. We demonstrate the methodology using the summer 2011 central US heatwave and output from the Community Earth System Model. In this example, we find that the lower bound of the risk ratio is relatively insensitive to the magnitude and probability of the actual event.« less

Physical and cognitive doping in university students using the unrelated question model (UQM): Assessing the influence of the probability of receiving the sensitive question on prevalence estimation.

PubMed

Dietz, Pavel; Quermann, Anne; van Poppel, Mireille Nicoline Maria; Striegel, Heiko; Schröter, Hannes; Ulrich, Rolf; Simon, Perikles

2018-01-01

In order to increase the value of randomized response techniques (RRTs) as tools for studying sensitive issues, the present study investigated whether the prevalence estimate for a sensitive item [Formula: see text] assessed with the unrelated questionnaire method (UQM) is influenced by changing the probability of receiving the sensitive question p. A short paper-and-pencil questionnaire was distributed to 1.243 university students assessing the 12-month prevalence of physical and cognitive doping using two versions of the UQM with different probabilities for receiving the sensitive question (p ≈ 1/3 and p ≈ 2/3). Likelihood ratio tests were used to assess whether the prevalence estimates for physical and cognitive doping differed significantly between p ≈ 1/3 and p ≈ 2/3. The order of questions (physical doping and cognitive doping) as well as the probability of receiving the sensitive question (p ≈ 1/3 or p ≈ 2/3) were counterbalanced across participants. Statistical power analyses were performed to determine sample size. The prevalence estimate for physical doping with p ≈ 1/3 was 22.5% (95% CI: 10.8-34.1), and 12.8% (95% CI: 7.6-18.0) with p ≈ 2/3. For cognitive doping with p ≈ 1/3, the estimated prevalence was 22.5% (95% CI: 11.0-34.1), whereas it was 18.0% (95% CI: 12.5-23.5) with p ≈ 2/3. Likelihood-ratio tests revealed that prevalence estimates for both physical and cognitive doping, respectively, did not differ significantly under p ≈ 1/3 and p ≈ 2/3 (physical doping: χ2 = 2.25, df = 1, p = 0.13; cognitive doping: χ2 = 0.49, df = 1, p = 0.48). Bayes factors computed with the Savage-Dickey method favored the null ("the prevalence estimates are identical under p ≈ 1/3 and p ≈ 2/3") over the alternative ("the prevalence estimates differ under p ≈ 1/3 and p ≈ 2/3") hypothesis for both physical doping (BF = 2.3) and cognitive doping (BF = 5.3). The present results suggest that prevalence estimates for physical and cognitive doping assessed by the UQM are largely unaffected by the probability for receiving the sensitive question p.

Application of at-site peak-streamflow frequency analyses for very low annual exceedance probabilities

USGS Publications Warehouse

Asquith, William H.; Kiang, Julie E.; Cohn, Timothy A.

2017-07-17

The U.S. Geological Survey (USGS), in cooperation with the U.S. Nuclear Regulatory Commission, has investigated statistical methods for probabilistic flood hazard assessment to provide guidance on very low annual exceedance probability (AEP) estimation of peak-streamflow frequency and the quantification of corresponding uncertainties using streamgage-specific data. The term “very low AEP” implies exceptionally rare events defined as those having AEPs less than about 0.001 (or 1 × 10–3 in scientific notation or for brevity 10–3). Such low AEPs are of great interest to those involved with peak-streamflow frequency analyses for critical infrastructure, such as nuclear power plants. Flood frequency analyses at streamgages are most commonly based on annual instantaneous peak streamflow data and a probability distribution fit to these data. The fitted distribution provides a means to extrapolate to very low AEPs. Within the United States, the Pearson type III probability distribution, when fit to the base-10 logarithms of streamflow, is widely used, but other distribution choices exist. The USGS-PeakFQ software, implementing the Pearson type III within the Federal agency guidelines of Bulletin 17B (method of moments) and updates to the expected moments algorithm (EMA), was specially adapted for an “Extended Output” user option to provide estimates at selected AEPs from 10–3 to 10–6. Parameter estimation methods, in addition to product moments and EMA, include L-moments, maximum likelihood, and maximum product of spacings (maximum spacing estimation). This study comprehensively investigates multiple distributions and parameter estimation methods for two USGS streamgages (01400500 Raritan River at Manville, New Jersey, and 01638500 Potomac River at Point of Rocks, Maryland). The results of this study specifically involve the four methods for parameter estimation and up to nine probability distributions, including the generalized extreme value, generalized log-normal, generalized Pareto, and Weibull. Uncertainties in streamflow estimates for corresponding AEP are depicted and quantified as two primary forms: quantile (aleatoric [random sampling] uncertainty) and distribution-choice (epistemic [model] uncertainty). Sampling uncertainties of a given distribution are relatively straightforward to compute from analytical or Monte Carlo-based approaches. Distribution-choice uncertainty stems from choices of potentially applicable probability distributions for which divergence among the choices increases as AEP decreases. Conventional goodness-of-fit statistics, such as Cramér-von Mises, and L-moment ratio diagrams are demonstrated in order to hone distribution choice. The results generally show that distribution choice uncertainty is larger than sampling uncertainty for very low AEP values.

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.

Statistics of the work done on a quantum critical system by quenching a control parameter.

PubMed

Silva, Alessandro

2008-09-19

We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian. We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity emerging usually in the context of dephasing. Using this connection we characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field. We show that for local quenches starting at criticality the probability distribution of the work displays an interesting edge singularity.

Probability of Detection (POD) as a statistical model for the validation of qualitative methods.

PubMed

Wehling, Paul; LaBudde, Robert A; Brunelle, Sharon L; Nelson, Maria T

2011-01-01

A statistical model is presented for use in validation of qualitative methods. This model, termed Probability of Detection (POD), harmonizes the statistical concepts and parameters between quantitative and qualitative method validation. POD characterizes method response with respect to concentration as a continuous variable. The POD model provides a tool for graphical representation of response curves for qualitative methods. In addition, the model allows comparisons between candidate and reference methods, and provides calculations of repeatability, reproducibility, and laboratory effects from collaborative study data. Single laboratory study and collaborative study examples are given.

Simulating statistics of lightning-induced and man made fires

NASA Astrophysics Data System (ADS)

Krenn, R.; Hergarten, S.

2009-04-01

The frequency-area distributions of forest fires show power-law behavior with scaling exponents α in a quite narrow range, relating wildfire research to the theoretical framework of self-organized criticality. Examples of self-organized critical behavior can be found in computer simulations of simple cellular automata. The established self-organized critical Drossel-Schwabl forest fire model (DS-FFM) is one of the most widespread models in this context. Despite its qualitative agreement with event-size statistics from nature, its applicability is still questioned. Apart from general concerns that the DS-FFM apparently oversimplifies the complex nature of forest dynamics, it significantly overestimates the frequency of large fires. We present a straightforward modification of the model rules that increases the scaling exponent α by approximately 1•3 and brings the simulated event-size statistics close to those observed in nature. In addition, combined simulations of both the original and the modified model predict a dependence of the overall distribution on the ratio of lightning induced and man made fires as well as a difference between their respective event-size statistics. The increase of the scaling exponent with decreasing lightning probability as well as the splitting of the partial distributions are confirmed by the analysis of the Canadian Large Fire Database. As a consequence, lightning induced and man made forest fires cannot be treated separately in wildfire modeling, hazard assessment and forest management.

Lagrangian statistics in weakly forced two-dimensional turbulence.

PubMed

Rivera, Michael K; Ecke, Robert E

2016-01-01

Measurements of Lagrangian single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. Lagrangian correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of Lagrangian velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary Eulerian velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.

Relative Contributions of Agricultural Drift, Para-Occupational ...

EPA Pesticide Factsheets

Background: Increased pesticide concentrations in house dust in agricultural areas have been attributed to several exposure pathways, including agricultural drift, para-occupational, and residential use. Objective: To guide future exposure assessment efforts, we quantified relative contributions of these pathways using meta-regression models of published data on dust pesticide concentrations. Methods: From studies in North American agricultural areas published from 1995-2015, we abstracted dust pesticide concentrations reported as summary statistics (e.g., geometric means (GM)). We analyzed these data using mixed-effects meta-regression models that weighted each summary statistic by its inverse variance. Dependent variables were either the log-transformed GM (drift) or the log-transformed ratio of GMs from two groups (para-occupational, residential use). Results: For the drift pathway, predicted GMs decreased sharply and nonlinearly, with GMs 64% lower in homes 250 m versus 23 m from fields (inter-quartile range of published data) based on 52 statistics from 7 studies. For the para-occupational pathway, GMs were 2.3 times higher (95% confidence interval [CI]: 1.5-3.3; 15 statistics, 5 studies) in homes of farmers who applied pesticides more versus less recently or frequently. For the residential use pathway, GMs were 1.3 (95%CI: 1.1-1.4) and 1.5 (95%CI: 1.2-1.9) times higher in treated versus untreated homes, when the probability that a pesticide was used for

Generalizing Terwilliger's likelihood approach: a new score statistic to test for genetic association.

PubMed

el Galta, Rachid; Uitte de Willige, Shirley; de Visser, Marieke C H; Helmer, Quinta; Hsu, Li; Houwing-Duistermaat, Jeanine J

2007-09-24

In this paper, we propose a one degree of freedom test for association between a candidate gene and a binary trait. This method is a generalization of Terwilliger's likelihood ratio statistic and is especially powerful for the situation of one associated haplotype. As an alternative to the likelihood ratio statistic, we derive a score statistic, which has a tractable expression. For haplotype analysis, we assume that phase is known. By means of a simulation study, we compare the performance of the score statistic to Pearson's chi-square statistic and the likelihood ratio statistic proposed by Terwilliger. We illustrate the method on three candidate genes studied in the Leiden Thrombophilia Study. We conclude that the statistic follows a chi square distribution under the null hypothesis and that the score statistic is more powerful than Terwilliger's likelihood ratio statistic when the associated haplotype has frequency between 0.1 and 0.4 and has a small impact on the studied disorder. With regard to Pearson's chi-square statistic, the score statistic has more power when the associated haplotype has frequency above 0.2 and the number of variants is above five.

Flux-ratio anomalies from discs and other baryonic structures in the Illustris simulation

NASA Astrophysics Data System (ADS)

Hsueh, Jen-Wei; Despali, Giulia; Vegetti, Simona; Xu, Dandan; Fassnacht, Christopher D.; Metcalf, R. Benton

2018-04-01

The flux ratios in the multiple images of gravitationally lensed quasars can provide evidence for dark matter substructure in the halo of the lensing galaxy if the flux ratios differ from those predicted by a smooth model of the lensing galaxy mass distribution. However, it is also possible that baryonic structures in the lensing galaxy, such as edge-on discs, can produce flux-ratio anomalies. In this work, we present the first statistical analysis of flux-ratio anomalies due to baryons from a numerical simulation perspective. We select galaxies with various morphological types in the Illustris simulation and ray trace through the simulated haloes, which include baryons in the main lensing galaxies but exclude any substructures, in order to explore the pure baryonic effects. Our ray-tracing results show that the baryonic components can be a major contribution to the flux-ratio anomalies in lensed quasars and that edge-on disc lenses induce the strongest anomalies. We find that the baryonic components increase the probability of finding high flux-ratio anomalies in the early-type lenses by about 8 per cent and by about 10-20 per cent in the disc lenses. The baryonic effects also induce astrometric anomalies in 13 per cent of the mock lenses. Our results indicate that the morphology of the lens galaxy becomes important in the analysis of flux-ratio anomalies when considering the effect of baryons, and that the presence of baryons may also partially explain the discrepancy between the observed (high) anomaly frequency and what is expected due to the presence of subhaloes as predicted by the cold dark matter simulations.

Is dietary diversity a proxy measurement of nutrient adequacy in Iranian elderly women?

PubMed

Tavakoli, Sogand; Dorosty-Motlagh, Ahmad Reza; Hoshiar-Rad, Anahita; Eshraghian, Mohamad Reza; Sotoudeh, Gity; Azadbakht, Leila; Karimi, Mehrdad; Jalali-Farahani, Sara

2016-10-01

To investigate whether consumption of more diverse diets would increase the probability of nutrients adequacy among elderly women in Tehran, Iran. This cross-sectional study was conducted on 292 women aged ≥60 years who were randomly selected from 10 public health centers among 31 centers in south area of Tehran. Because of some limitations we randomly chose these 10 centers. The sample sizes provided 80% statistical power to meet the aim of study for test the relationship between Nutrient Adequacy Ratio (NAR), Mean Adequacy Ratio (MAR) as a dependent variable and total Dietary Diversity Score (DDS) as an independent variable. Dietary intakes were assessed by two 24-h recall questionnaires. The mean probability of adequacy across 12 nutrients and energy were calculated using the Dietary Reference Index (DRI). Dietary diversity Score was defined according to diet quality index revised (Haines et al. method). To investigate the relationship between MAR and DDS some demographic and socioeconomic variables were examined. Mean ± SD of total dietary diversity was 4.22 ± 1.28 (range 1.07-6.93). The Fruit and vegetable groups had the highest (1.27 ± 0.65, range 0-2.0) and the lowest (0.56 ± 0.36, range 0-1.71) diversity score, respectively. We observed that total DDS has significant positive correlation with MAR (r = 0.65, P < 0.001). Total DDS was significantly associated with NAR of all 12 studied nutrients (P < 0.01); probability adequacy of vitamin B2 revealed the strongest (r = 0.63, P < 0.01) and vitamin B12 revealed the weakest (r = 0.28, P < 0.01) relationship with total DDS. When maximizing sensitivity and specificity, the best cut-off point for achieving MAR≥1 was 4.5 for DDS. The results of our study showed that DDS is an appropriate indicator of the probability of nutrient adequacy in Tehranian elderly women. Copyright © 2016 Elsevier Ltd. All rights reserved.

Determination of physical height from crown dimensions of deciduous tooth: A dental morphometric study.

PubMed

Ramanna, C; Kamath, Venkatesh V; Sharada, C; Srikanth, N

2016-01-01

Dental morphometrics is a subject of great significance in forensic odontology in identification of an individual. Use of teeth to represent a physical profile is valuable for identification of an individual. The present study aims to assess the clinical crown length (CL) of erupted deciduous teeth and height of the child. A correlation of these parameters was attempted to arrive at a mathematical equation which would formulate a ratio of tooth CL to individual height that would support in estimating the probable height of the child. About 60 children (30 males and 30 females) of age ranged from 3-6 years were included in this study. Clinical vertical CLs of the deciduous dentition (tooth numbers 51, 52, 53, 54, and 55) were calculated using digital Vernier calipers (Aerospace Ltd., Bengaluru, Karnataka, India) on the cast models. Child height was measured using a standard measuring tape. Ratios of deciduous CL to height of the child were recorded. Linear stepwise forward regression analysis was applied to predict the probability of CL of a tooth most likely to support in prediction of physical height of the child. Tabulated results showed a probable correlation between tooth CL and height of the child. Tooth CLs of deciduous upper right second molar (55) among the males, lateral incisor (52) among females, and canine (53) using the combined male and female data were statistically significant, and they approximately predicted the child height with minimal variations. Mathematically derived equations based on linear stepwise forward regression analysis using sixty children data are height prediction (derived from combined data of male and female children) = 400.558 + 90.264 (53 CL), male child height prediction (derived from data of male children) = 660.290 + 72.970 (55 CL), and female child height prediction (derived from data of female children) = -187.942 + 194.818 (52 CL). In conclusion, clinical vertical CL is an important parameter in prediction of individual height and possible identification of the individual. An extension of the similar technique to all the deciduous dentition using a larger group of children would probably give us the best options available among vertical CLs for prediction of the child height.

A statistical model for investigating binding probabilities of DNA nucleotide sequences using microarrays.

PubMed

Lee, Mei-Ling Ting; Bulyk, Martha L; Whitmore, G A; Church, George M

2002-12-01

There is considerable scientific interest in knowing the probability that a site-specific transcription factor will bind to a given DNA sequence. Microarray methods provide an effective means for assessing the binding affinities of a large number of DNA sequences as demonstrated by Bulyk et al. (2001, Proceedings of the National Academy of Sciences, USA 98, 7158-7163) in their study of the DNA-binding specificities of Zif268 zinc fingers using microarray technology. In a follow-up investigation, Bulyk, Johnson, and Church (2002, Nucleic Acid Research 30, 1255-1261) studied the interdependence of nucleotides on the binding affinities of transcription proteins. Our article is motivated by this pair of studies. We present a general statistical methodology for analyzing microarray intensity measurements reflecting DNA-protein interactions. The log probability of a protein binding to a DNA sequence on an array is modeled using a linear ANOVA model. This model is convenient because it employs familiar statistical concepts and procedures and also because it is effective for investigating the probability structure of the binding mechanism.

Active Learning? Not with My Syllabus!

ERIC Educational Resources Information Center

Ernst, Michael D.

2012-01-01

We describe an approach to teaching probability that minimizes the amount of class time spent on the topic while also providing a meaningful (dice-rolling) activity to get students engaged. The activity, which has a surprising outcome, illustrates the basic ideas of informal probability and how probability is used in statistical inference.…

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

PubMed

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

2016-12-15

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

Streamflow characteristics at streamgages in northern Afghanistan and selected locations

USGS Publications Warehouse

Olson, Scott A.; Williams-Sether, Tara

2010-01-01

Statistical summaries of streamflow data for 79 historical streamgages in Northern Afghanistan and other selected historical streamgages are presented in this report. The summaries for each streamgage include (1) station description, (2) graph of the annual mean discharge for the period of record, (3) statistics of monthly and annual mean discharges, (4) monthly and annual flow duration, (5) probability of occurrence of annual high discharges, (6) probability of occurrence of annual low discharges, (7) probability of occurrence of seasonal low discharges, (8) annual peak discharges for the period of record, and (9) monthly and annual mean discharges for the period of record.

A comprehensive statistical investigation of schlieren image velocimetry (SIV) using high-velocity helium jet

NASA Astrophysics Data System (ADS)

Biswas, Sayan; Qiao, Li

2017-03-01

A detailed statistical assessment of seedless velocity measurement using Schlieren Image Velocimetry (SIV) was explored using open source Robust Phase Correlation (RPC) algorithm. A well-known flow field, an axisymmetric turbulent helium jet, was analyzed near and intermediate region (0≤ x/d≤ 20) for two different Reynolds numbers, Re d = 11,000 and Re d = 22,000 using schlieren with horizontal knife-edge, schlieren with vertical knife-edge and shadowgraph technique, and the resulted velocity fields from SIV techniques were compared to traditional Particle Image Velocimetry (PIV) measurements. A novel, inexpensive, easy to setup two-camera SIV technique had been demonstrated to measure high-velocity turbulent jet, with jet exit velocities 304 m/s (Mach = 0.3) and 611 m/s (Mach = 0.6), respectively. Several image restoration and enhancement techniques were tested to improve signal to noise ratio (SNR) in schlieren and shadowgraph images. Processing and post-processing parameters for SIV techniques were examined in detail. A quantitative comparison between self-seeded SIV techniques and traditional PIV had been made using correlation statistics. While the resulted flow field from schlieren with horizontal knife-edge and shadowgraph showed excellent agreement with PIV measurements, schlieren with vertical knife-edge performed poorly. The performance of spatial cross-correlations at different jet locations using SIV techniques and PIV was evaluated. Turbulence quantities like turbulence intensity, mean velocity fields, Reynolds shear stress influenced spatial correlations and correlation plane SNR heavily. Several performance metrics such as primary peak ratio (PPR), peak to correlation energy (PCE), the probability distribution of signal and noise were used to compare capability and potential of different SIV techniques.

Sequential Probability Ratio Test for Collision Avoidance Maneuver Decisions

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Markley, F. Landis

2010-01-01

When facing a conjunction between space objects, decision makers must chose whether to maneuver for collision avoidance or not. We apply a well-known decision procedure, the sequential probability ratio test, to this problem. We propose two approaches to the problem solution, one based on a frequentist method, and the other on a Bayesian method. The frequentist method does not require any prior knowledge concerning the conjunction, while the Bayesian method assumes knowledge of prior probability densities. Our results show that both methods achieve desired missed detection rates, but the frequentist method's false alarm performance is inferior to the Bayesian method's

Statistics, Handle with Care: Detecting Multiple Model Components with the Likelihood Ratio Test

NASA Astrophysics Data System (ADS)

Protassov, Rostislav; van Dyk, David A.; Connors, Alanna; Kashyap, Vinay L.; Siemiginowska, Aneta

2002-05-01

The likelihood ratio test (LRT) and the related F-test, popularized in astrophysics by Eadie and coworkers in 1971, Bevington in 1969, Lampton, Margon, & Bowyer, in 1976, Cash in 1979, and Avni in 1978, do not (even asymptotically) adhere to their nominal χ2 and F-distributions in many statistical tests common in astrophysics, thereby casting many marginal line or source detections and nondetections into doubt. Although the above authors illustrate the many legitimate uses of these statistics, in some important cases it can be impossible to compute the correct false positive rate. For example, it has become common practice to use the LRT or the F-test to detect a line in a spectral model or a source above background despite the lack of certain required regularity conditions. (These applications were not originally suggested by Cash or by Bevington.) In these and other settings that involve testing a hypothesis that is on the boundary of the parameter space, contrary to common practice, the nominal χ2 distribution for the LRT or the F-distribution for the F-test should not be used. In this paper, we characterize an important class of problems in which the LRT and the F-test fail and illustrate this nonstandard behavior. We briefly sketch several possible acceptable alternatives, focusing on Bayesian posterior predictive probability values. We present this method in some detail since it is a simple, robust, and intuitive approach. This alternative method is illustrated using the gamma-ray burst of 1997 May 8 (GRB 970508) to investigate the presence of an Fe K emission line during the initial phase of the observation. There are many legitimate uses of the LRT and the F-test in astrophysics, and even when these tests are inappropriate, there remain several statistical alternatives (e.g., judicious use of error bars and Bayes factors). Nevertheless, there are numerous cases of the inappropriate use of the LRT and similar tests in the literature, bringing substantive scientific results into question.

Cardiorespiratory dynamics measured from continuous ECG monitoring improves detection of deterioration in acute care patients: A retrospective cohort study

PubMed Central

Clark, Matthew T.; Calland, James Forrest; Enfield, Kyle B.; Voss, John D.; Lake, Douglas E.; Moorman, J. Randall

2017-01-01

Background Charted vital signs and laboratory results represent intermittent samples of a patient’s dynamic physiologic state and have been used to calculate early warning scores to identify patients at risk of clinical deterioration. We hypothesized that the addition of cardiorespiratory dynamics measured from continuous electrocardiography (ECG) monitoring to intermittently sampled data improves the predictive validity of models trained to detect clinical deterioration prior to intensive care unit (ICU) transfer or unanticipated death. Methods and findings We analyzed 63 patient-years of ECG data from 8,105 acute care patient admissions at a tertiary care academic medical center. We developed models to predict deterioration resulting in ICU transfer or unanticipated death within the next 24 hours using either vital signs, laboratory results, or cardiorespiratory dynamics from continuous ECG monitoring and also evaluated models using all available data sources. We calculated the predictive validity (C-statistic), the net reclassification improvement, and the probability of achieving the difference in likelihood ratio χ2 for the additional degrees of freedom. The primary outcome occurred 755 times in 586 admissions (7%). We analyzed 395 clinical deteriorations with continuous ECG data in the 24 hours prior to an event. Using only continuous ECG measures resulted in a C-statistic of 0.65, similar to models using only laboratory results and vital signs (0.63 and 0.69 respectively). Addition of continuous ECG measures to models using conventional measurements improved the C-statistic by 0.01 and 0.07; a model integrating all data sources had a C-statistic of 0.73 with categorical net reclassification improvement of 0.09 for a change of 1 decile in risk. The difference in likelihood ratio χ2 between integrated models with and without cardiorespiratory dynamics was 2158 (p value: <0.001). Conclusions Cardiorespiratory dynamics from continuous ECG monitoring detect clinical deterioration in acute care patients and improve performance of conventional models that use only laboratory results and vital signs. PMID:28771487

Cardiorespiratory dynamics measured from continuous ECG monitoring improves detection of deterioration in acute care patients: A retrospective cohort study.

PubMed

Moss, Travis J; Clark, Matthew T; Calland, James Forrest; Enfield, Kyle B; Voss, John D; Lake, Douglas E; Moorman, J Randall

2017-01-01

Charted vital signs and laboratory results represent intermittent samples of a patient's dynamic physiologic state and have been used to calculate early warning scores to identify patients at risk of clinical deterioration. We hypothesized that the addition of cardiorespiratory dynamics measured from continuous electrocardiography (ECG) monitoring to intermittently sampled data improves the predictive validity of models trained to detect clinical deterioration prior to intensive care unit (ICU) transfer or unanticipated death. We analyzed 63 patient-years of ECG data from 8,105 acute care patient admissions at a tertiary care academic medical center. We developed models to predict deterioration resulting in ICU transfer or unanticipated death within the next 24 hours using either vital signs, laboratory results, or cardiorespiratory dynamics from continuous ECG monitoring and also evaluated models using all available data sources. We calculated the predictive validity (C-statistic), the net reclassification improvement, and the probability of achieving the difference in likelihood ratio χ2 for the additional degrees of freedom. The primary outcome occurred 755 times in 586 admissions (7%). We analyzed 395 clinical deteriorations with continuous ECG data in the 24 hours prior to an event. Using only continuous ECG measures resulted in a C-statistic of 0.65, similar to models using only laboratory results and vital signs (0.63 and 0.69 respectively). Addition of continuous ECG measures to models using conventional measurements improved the C-statistic by 0.01 and 0.07; a model integrating all data sources had a C-statistic of 0.73 with categorical net reclassification improvement of 0.09 for a change of 1 decile in risk. The difference in likelihood ratio χ2 between integrated models with and without cardiorespiratory dynamics was 2158 (p value: <0.001). Cardiorespiratory dynamics from continuous ECG monitoring detect clinical deterioration in acute care patients and improve performance of conventional models that use only laboratory results and vital signs.

Uncertainty quantification and risk analyses of CO2 leakage in heterogeneous geological formations

NASA Astrophysics Data System (ADS)

Hou, Z.; Murray, C. J.; Rockhold, M. L.

2012-12-01

A stochastic sensitivity analysis framework is adopted to evaluate the impact of spatial heterogeneity in permeability on CO2 leakage risk. The leakage is defined as the total mass of CO2 moving into the overburden through the caprock-overburden interface, in both gaseous and liquid (dissolved) phases. The entropy-based framework has the ability to quantify the uncertainty associated with the input parameters in the form of prior pdfs (probability density functions). Effective sampling of the prior pdfs enables us to fully explore the parameter space and systematically evaluate the individual and combined effects of the parameters of interest on CO2 leakage risk. The parameters that are considered in the study include: mean, variance, and horizontal to vertical spatial anisotropy ratio for caprock permeability, and those same parameters for reservoir permeability. Given the sampled spatial variogram parameters, multiple realizations of permeability fields were generated using GSLIB subroutines. For each permeability field, a numerical simulator, STOMP, (in the water-salt-CO2-energy operational mode) is used to simulate the CO2 migration within the reservoir and caprock up to 50 years after injection. Due to intensive computational demand, we run both a scalable version simulator eSTOMP and serial STOMP on various supercomputers. We then perform statistical analyses and summarize the relationships between the parameters of interest (mean/variance/anisotropy ratio of caprock and reservoir permeability) and CO2 leakage ratio. We also present the effects of those parameters on CO2 plume radius and reservoir injectivity. The statistical analysis provides a reduced order model that can be used to estimate the impact of heterogeneity on caprock leakage.

Encoding of low-quality DNA profiles as genotype probability matrices for improved profile comparisons, relatedness evaluation and database searches.

PubMed

Ryan, K; Williams, D Gareth; Balding, David J

2016-11-01

Many DNA profiles recovered from crime scene samples are of a quality that does not allow them to be searched against, nor entered into, databases. We propose a method for the comparison of profiles arising from two DNA samples, one or both of which can have multiple donors and be affected by low DNA template or degraded DNA. We compute likelihood ratios to evaluate the hypothesis that the two samples have a common DNA donor, and hypotheses specifying the relatedness of two donors. Our method uses a probability distribution for the genotype of the donor of interest in each sample. This distribution can be obtained from a statistical model, or we can exploit the ability of trained human experts to assess genotype probabilities, thus extracting much information that would be discarded by standard interpretation rules. Our method is compatible with established methods in simple settings, but is more widely applicable and can make better use of information than many current methods for the analysis of mixed-source, low-template DNA profiles. It can accommodate uncertainty arising from relatedness instead of or in addition to uncertainty arising from noisy genotyping. We describe a computer program GPMDNA, available under an open source licence, to calculate LRs using the method presented in this paper. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Crash Lethality Model

DTIC Science & Technology

2012-06-06

Statistical Data ........................................................................................... 45 31 Parametric Model for Rotor Wing Debris...Area .............................................................. 46 32 Skid Distance Statistical Data...results. The curve that related the BC value to the probability of skull fracture resulted in a tight confidence interval and a two tailed statistical p

Time-dependent fracture probability of bilayer, lithium-disilicate-based, glass-ceramic, molar crowns as a function of core/veneer thickness ratio and load orientation.

PubMed

Anusavice, Kenneth J; Jadaan, Osama M; Esquivel-Upshaw, Josephine F

2013-11-01

Recent reports on bilayer ceramic crown prostheses suggest that fractures of the veneering ceramic represent the most common reason for prosthesis failure. The aims of this study were to test the hypotheses that: (1) an increase in core ceramic/veneer ceramic thickness ratio for a crown thickness of 1.6mm reduces the time-dependent fracture probability (Pf) of bilayer crowns with a lithium-disilicate-based glass-ceramic core, and (2) oblique loading, within the central fossa, increases Pf for 1.6-mm-thick crowns compared with vertical loading. Time-dependent fracture probabilities were calculated for 1.6-mm-thick, veneered lithium-disilicate-based glass-ceramic molar crowns as a function of core/veneer thickness ratio and load orientation in the central fossa area. Time-dependent fracture probability analyses were computed by CARES/Life software and finite element analysis, using dynamic fatigue strength data for monolithic discs of a lithium-disilicate glass-ceramic core (Empress 2), and ceramic veneer (Empress 2 Veneer Ceramic). Predicted fracture probabilities (Pf) for centrally loaded 1.6-mm-thick bilayer crowns over periods of 1, 5, and 10 years are 1.2%, 2.7%, and 3.5%, respectively, for a core/veneer thickness ratio of 1.0 (0.8mm/0.8mm), and 2.5%, 5.1%, and 7.0%, respectively, for a core/veneer thickness ratio of 0.33 (0.4mm/1.2mm). CARES/Life results support the proposed crown design and load orientation hypotheses. The application of dynamic fatigue data, finite element stress analysis, and CARES/Life analysis represent an optimal approach to optimize fixed dental prosthesis designs produced from dental ceramics and to predict time-dependent fracture probabilities of ceramic-based fixed dental prostheses that can minimize the risk for clinical failures. Copyright © 2013 Academy of Dental Materials. All rights reserved.

Time-dependent fracture probability of bilayer, lithium-disilicate-based glass-ceramic molar crowns as a function of core/veneer thickness ratio and load orientation

PubMed Central

Anusavice, Kenneth J.; Jadaan, Osama M.; Esquivel–Upshaw, Josephine

2013-01-01

Recent reports on bilayer ceramic crown prostheses suggest that fractures of the veneering ceramic represent the most common reason for prosthesis failure. Objective The aims of this study were to test the hypotheses that: (1) an increase in core ceramic/veneer ceramic thickness ratio for a crown thickness of 1.6 mm reduces the time-dependent fracture probability (Pf) of bilayer crowns with a lithium-disilicate-based glass-ceramic core, and (2) oblique loading, within the central fossa, increases Pf for 1.6-mm-thick crowns compared with vertical loading. Materials and methods Time-dependent fracture probabilities were calculated for 1.6-mm-thick, veneered lithium-disilicate-based glass-ceramic molar crowns as a function of core/veneer thickness ratio and load orientation in the central fossa area. Time-dependent fracture probability analyses were computed by CARES/Life software and finite element analysis, using dynamic fatigue strength data for monolithic discs of a lithium-disilicate glass-ceramic core (Empress 2), and ceramic veneer (Empress 2 Veneer Ceramic). Results Predicted fracture probabilities (Pf) for centrally-loaded 1,6-mm-thick bilayer crowns over periods of 1, 5, and 10 years are 1.2%, 2.7%, and 3.5%, respectively, for a core/veneer thickness ratio of 1.0 (0.8 mm/0.8 mm), and 2.5%, 5.1%, and 7.0%, respectively, for a core/veneer thickness ratio of 0.33 (0.4 mm/1.2 mm). Conclusion CARES/Life results support the proposed crown design and load orientation hypotheses. Significance The application of dynamic fatigue data, finite element stress analysis, and CARES/Life analysis represent an optimal approach to optimize fixed dental prosthesis designs produced from dental ceramics and to predict time-dependent fracture probabilities of ceramic-based fixed dental prostheses that can minimize the risk for clinical failures. PMID:24060349

Robustness of Multiple Objective Decision Analysis Preference Functions

DTIC Science & Technology

2002-06-01

p p′ : The probability of some event. ,i ip q : The probability of event . i Π : An aggregation of proportional data used in calculating a test ...statistical tests of the significance of the term and also is conducted in a multivariate framework rather than the ROSA univariate approach. A...residual error is ˆ−e = y y (45) The coefficient provides a ready indicator of the contribution for the associated variable and statistical tests

Adaptive and Optimal Control of Stochastic Dynamical Systems

DTIC Science & Technology

2015-09-14

Advances in Statistics, Probability and Actuarial Sciences , Vol. 1, World Scientific, 2012, 451- 463. [4] T. E. Duncan and B. Pasik-Duncan, A...S. N. Cohen, T. K. Siu and H. Yang) Advances in Statistics, Probability and Actuarial Sciences , Vol. 1, World Scientific, 2012, 451-463. 4. T. E...games with gen- eral noise processes, Models and Methods in Economics and Management Science : Essays in Honor of Charles S. Tapiero, (eds. F. El

Camera-Model Identification Using Markovian Transition Probability Matrix

NASA Astrophysics Data System (ADS)

Xu, Guanshuo; Gao, Shang; Shi, Yun Qing; Hu, Ruimin; Su, Wei

Detecting the (brands and) models of digital cameras from given digital images has become a popular research topic in the field of digital forensics. As most of images are JPEG compressed before they are output from cameras, we propose to use an effective image statistical model to characterize the difference JPEG 2-D arrays of Y and Cb components from the JPEG images taken by various camera models. Specifically, the transition probability matrices derived from four different directional Markov processes applied to the image difference JPEG 2-D arrays are used to identify statistical difference caused by image formation pipelines inside different camera models. All elements of the transition probability matrices, after a thresholding technique, are directly used as features for classification purpose. Multi-class support vector machines (SVM) are used as the classification tool. The effectiveness of our proposed statistical model is demonstrated by large-scale experimental results.

Observation of non-classical correlations in sequential measurements of photon polarization

NASA Astrophysics Data System (ADS)

Suzuki, Yutaro; Iinuma, Masataka; Hofmann, Holger F.

2016-10-01

A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.

Statistical uncertainty in the Medicare shared savings program.

PubMed

DeLia, Derek; Hoover, Donald; Cantor, Joel C

2012-01-01

Analyze statistical risks facing CMS and Accountable Care Organizations (ACOs) under the Medicare Shared Savings Program (MSSP). We calculate the probability that shared savings formulas lead to inappropriate payment, payment denial, and/or financial penalties, assuming that ACOs generate real savings in Medicare spending ranging from 0-10%. We also calculate expected payments from CMS to ACOs under these scenarios. The probability of an incorrect outcome is heavily dependent on ACO enrollment size. For example, in the MSSP two-sided model, an ACO with 5,000 enrollees that keeps spending constant faces a 0.24 probability of being inappropriately rewarded for savings and a 0.26 probability of paying an undeserved penalty for increased spending. For an ACO with 50,000 enrollees, both of these probabilities of incorrect outcomes are equal to 0.02. The probability of inappropriate payment denial declines as real ACO savings increase. Still, for ACOs with 5,000 patients, the probability of denial is at least 0.15 even when true savings are 5-7%. Depending on ACO size and the real ACO savings rate, expected ACO payments vary from $115,000 to $35.3 million. Our analysis indicates there may be greater statistical uncertainty in the MSSP than previously recognized. CMS and ACOs will have to consider this uncertainty in their financial, administrative, and care management planning. We also suggest analytic strategies that can be used to refine ACO payment formulas in the longer term to ensure that the MSSP (and other ACO initiatives that will be influenced by it) work as efficiently as possible.

Statistical Uncertainty in the Medicare Shared Savings Program

PubMed Central

DeLia, Derek; Hoover, Donald; Cantor, Joel C.

2012-01-01

Objective Analyze statistical risks facing CMS and Accountable Care Organizations (ACOs) under the Medicare Shared Savings Program (MSSP). Methods We calculate the probability that shared savings formulas lead to inappropriate payment, payment denial, and/or financial penalties, assuming that ACOs generate real savings in Medicare spending ranging from 0–10%. We also calculate expected payments from CMS to ACOs under these scenarios. Results The probability of an incorrect outcome is heavily dependent on ACO enrollment size. For example, in the MSSP two-sided model, an ACO with 5,000 enrollees that keeps spending constant faces a 0.24 probability of being inappropriately rewarded for savings and a 0.26 probability of paying an undeserved penalty for increased spending. For an ACO with 50,000 enrollees, both of these probabilities of incorrect outcomes are equal to 0.02. The probability of inappropriate payment denial declines as real ACO savings increase. Still, for ACOs with 5,000 patients, the probability of denial is at least 0.15 even when true savings are 5–7%. Depending on ACO size and the real ACO savings rate, expected ACO payments vary from $115,000 to $35.3 million. Discussion Our analysis indicates there may be greater statistical uncertainty in the MSSP than previously recognized. CMS and ACOs will have to consider this uncertainty in their financial, administrative, and care management planning. We also suggest analytic strategies that can be used to refine ACO payment formulas in the longer term to ensure that the MSSP (and other ACO initiatives that will be influenced by it) work as efficiently as possible. PMID:24800155

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.

Estimating adult sex ratios in nature.

PubMed

Ancona, Sergio; Dénes, Francisco V; Krüger, Oliver; Székely, Tamás; Beissinger, Steven R

2017-09-19

Adult sex ratio (ASR, the proportion of males in the adult population) is a central concept in population and evolutionary biology, and is also emerging as a major factor influencing mate choice, pair bonding and parental cooperation in both human and non-human societies. However, estimating ASR is fraught with difficulties stemming from the effects of spatial and temporal variation in the numbers of males and females, and detection/capture probabilities that differ between the sexes. Here, we critically evaluate methods for estimating ASR in wild animal populations, reviewing how recent statistical advances can be applied to handle some of these challenges. We review methods that directly account for detection differences between the sexes using counts of unmarked individuals (observed, trapped or killed) and counts of marked individuals using mark-recapture models. We review a third class of methods that do not directly sample the number of males and females, but instead estimate the sex ratio indirectly using relationships that emerge from demographic measures, such as survival, age structure, reproduction and assumed dynamics. We recommend that detection-based methods be used for estimating ASR in most situations, and point out that studies are needed that compare different ASR estimation methods and control for sex differences in dispersal.This article is part of the themed issue 'Adult sex ratios and reproductive decisions: a critical re-examination of sex differences in human and animal societies'. © 2017 The Author(s).

SUPERNOVA DRIVING. II. COMPRESSIVE RATIO IN MOLECULAR-CLOUD TURBULENCE

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

Pan, Liubin; Padoan, Paolo; Haugbølle, Troels

2016-07-01

The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of themore » compressive ratio, with a mean value ≈0.3, lower than the equilibrium value of ≈0.5 found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density probability density function is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.« less

Bacteriological profile of neonatal sepsis in a secondary care hospital in rural Tamil Nadu, Southern India.

PubMed

Pavan Kumar, Doniparthi Venkata; Mohan, Jesinth; Rakesh, P S; Prasad, Jasmine; Joseph, Lenikumar

2017-01-01

Neonatal sepsis is a leading cause of neonatal mortality and morbidity in the world. The objective of the current study was to detect the common causative microorganisms of neonatal sepsis and their antimicrobial resistance patterns in a rural secondary hospital in Tamil Nadu, India. Neonates (0-28 days) admitted to this newborn care unit from October 2013 to September 2015, with a diagnosis of probable sepsis were studied. All the enrolled babies had blood cultures taken and were followed up till final outcome, which was discharge or death, irrespective of culture result. Univariate analysis was performed for factors associated with culture positivity, generating odds ratios, and confidence intervals. Among the 107 babies with a diagnosis of probable sepsis, 28 (26.2%) had shown bacteria in culture. The majority (94.4%) were of early-onset sepsis. The predominant organisms were Staphylococcus aureus (10/28) and Klebsiella (6/28). 100% of Gram-negative bacilli and 90% of Staphylococcus were resistant to Ampicillin. Gentamicin resistance among Gram-negative bacilli and Staphylococcus was 52.9% and 20%, respectively, while third-generation cephalosporin resistance was 31.2% and 20%, respectively. Among the neonates diagnosed as probable sepsis, idiopathic prematurity ( P = 0.007) was found to have a statistically significant association with culture-positive sepsis. The culture positivity rate among the neonates with probable sepsis in the current study was 26%. An alarmingly high degree of antibiotic resistance observed calls for robust infection control practices and an urgent evaluation and development of individual and national antibiotic policies for neonatal sepsis.

The FERRUM Project: Experimental Transition Probabilities of [Fe II] and Astrophysical Applications

NASA Technical Reports Server (NTRS)

Hartman, H.; Derkatch, A.; Donnelly, M. P.; Gull, T.; Hibbert, A.; Johannsson, S.; Lundberg, H.; Mannervik, S.; Norlin, L. -O.; Rostohar, D.

2002-01-01

We report on experimental transition probabilities for thirteen forbidden [Fe II] lines originating from three different metastable Fe II levels. Radiative lifetimes have been measured of two metastable states by applying a laser probing technique on a stored ion beam. Branching ratios for the radiative decay channels, i.e. M1 and E2 transitions, are derived from observed intensity ratios of forbidden lines in astrophysical spectra and compared with theoretical data. The lifetimes and branching ratios are combined to derive absolute transition probabilities, A-values. We present the first experimental lifetime values for the two Fe II levels a(sup 4)G(sub 9/2) and b(sup 2)H(sub 11/2) and A-values for 13 forbidden transitions from a(sup 6)S(sub 5/2), a(sup 4)G(sub 9/2) and b(sup 4)D(sub 7/2) in the optical region. A discrepancy between the measured and calculated values of the lifetime for the b(sup 2)H(sub 11/2) level is discussed in terms of level mixing. We have used the code CIV3 to calculate transition probabilities of the a(sup 6)D-a(sup 6)S transitions. We have also studied observational branching ratios for lines from 5 other metastable Fe II levels and compared them to calculated values. A consistency in the deviation between calibrated observational intensity ratios and theoretical branching ratios for lines in a wider wavelength region supports the use of [Fe II] lines for determination of reddening.

Randomized central limit theorems: A unified theory.

PubMed

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles' aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles' extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic-scaling all ensemble components by a common deterministic scale. However, there are "random environment" settings in which the underlying scaling schemes are stochastic-scaling the ensemble components by different random scales. Examples of such settings include Holtsmark's law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)-in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes-and present "randomized counterparts" to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

Randomized central limit theorems: A unified theory

NASA Astrophysics Data System (ADS)

Eliazar, Iddo; Klafter, Joseph

2010-08-01

The central limit theorems (CLTs) characterize the macroscopic statistical behavior of large ensembles of independent and identically distributed random variables. The CLTs assert that the universal probability laws governing ensembles’ aggregate statistics are either Gaussian or Lévy, and that the universal probability laws governing ensembles’ extreme statistics are Fréchet, Weibull, or Gumbel. The scaling schemes underlying the CLTs are deterministic—scaling all ensemble components by a common deterministic scale. However, there are “random environment” settings in which the underlying scaling schemes are stochastic—scaling the ensemble components by different random scales. Examples of such settings include Holtsmark’s law for gravitational fields and the Stretched Exponential law for relaxation times. In this paper we establish a unified theory of randomized central limit theorems (RCLTs)—in which the deterministic CLT scaling schemes are replaced with stochastic scaling schemes—and present “randomized counterparts” to the classic CLTs. The RCLT scaling schemes are shown to be governed by Poisson processes with power-law statistics, and the RCLTs are shown to universally yield the Lévy, Fréchet, and Weibull probability laws.

GASP cloud- and particle-encounter statistics and their application to LPC aircraft studies. Volume 1: Analysis and conclusions

NASA Technical Reports Server (NTRS)

Jasperson, W. H.; Nastrom, G. D.; Davis, R. E.; Holdeman, J. D.

1984-01-01

Summary studies are presented for the entire cloud observation archieve from the NASA Global Atmospheric Sampling Program (GASP). Studies are also presented for GASP particle concentration data gathered concurrently with the cloud observations. Cloud encounters are shown on about 15 percent of the data samples overall, but the probability of cloud encounter is shown to vary significantly with altitude, latitude, and distance from the tropopause. Several meteorological circulation features are apparent in the latitudinal distribution of cloud cover, and the cloud encounter statistics are shown to be consistent with the classical mid-latitude cyclone model. Observations of clouds spaced more closely than 90 minutes are shown to be statistically dependent. The statistics for cloud and particle encounter are utilized to estimate the frequency of cloud encounter on long range airline routes, and to assess the probability and extent of laminar flow loss due to cloud or particle encounter by aircraft utilizing laminar flow control (LFC). It is shown that the probability of extended cloud encounter is too low, of itself, to make LFC impractical.

Comparison of probability statistics for automated ship detection in SAR imagery

NASA Astrophysics Data System (ADS)

Henschel, Michael D.; Rey, Maria T.; Campbell, J. W. M.; Petrovic, D.

1998-12-01

This paper discuses the initial results of a recent operational trial of the Ocean Monitoring Workstation's (OMW) ship detection algorithm which is essentially a Constant False Alarm Rate filter applied to Synthetic Aperture Radar data. The choice of probability distribution and methodologies for calculating scene specific statistics are discussed in some detail. An empirical basis for the choice of probability distribution used is discussed. We compare the results using a l-look, k-distribution function with various parameter choices and methods of estimation. As a special case of sea clutter statistics the application of a (chi) 2-distribution is also discussed. Comparisons are made with reference to RADARSAT data collected during the Maritime Command Operation Training exercise conducted in Atlantic Canadian Waters in June 1998. Reference is also made to previously collected statistics. The OMW is a commercial software suite that provides modules for automated vessel detection, oil spill monitoring, and environmental monitoring. This work has been undertaken to fine tune the OMW algorithm's, with special emphasis on the false alarm rate of each algorithm.

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

NASA Astrophysics Data System (ADS)

Kosov, Daniel S.

2017-09-01

Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using the master equation approach, we compute the joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times τ1 and τ2 means that the density matrix of the molecule is not fully renewed after time τ1 and the probability of observing waiting time τ2 for the second electron transfer depends on the previous electron waiting time τ1. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in the Franck-Condon blockade regime, extremely rare tunneling events become positively correlated.

Characterizing the radial content of orbital-angular-momentum photonic states impaired by weak-to-strong atmospheric turbulence.

PubMed

Chen, Chunyi; Yang, Huamin

2016-08-22

The changes in the radial content of orbital-angular-momentum (OAM) photonic states described by Laguerre-Gaussian (LG) modes with a radial index of zero, suffering from turbulence-induced distortions, are explored by numerical simulations. For a single-photon field with a given LG mode propagating through weak-to-strong atmospheric turbulence, both the average LG and OAM mode densities are dependent only on two nondimensional parameters, i.e., the Fresnel ratio and coherence-width-to-beam-radius (CWBR) ratio. It is found that atmospheric turbulence causes the radially-adjacent-mode mixing, besides the azimuthally-adjacent-mode mixing, in the propagated photonic states; the former is relatively slighter than the latter. With the same Fresnel ratio, the probabilities that a photon can be found in the zero-index radial mode of intended OAM states in terms of the relative turbulence strength behave very similarly; a smaller Fresnel ratio leads to a slower decrease in the probabilities as the relative turbulence strength increases. A photon can be found in various radial modes with approximately equal probability when the relative turbulence strength turns great enough. The use of a single-mode fiber in OAM measurements can result in photon loss and hence alter the observed transition probability between various OAM states. The bit error probability in OAM-based free-space optical communication systems that transmit photonic modes belonging to the same orthogonal LG basis may depend on what digit is sent.

Optical pulse characteristics of sonoluminescence at low acoustic drive levels.

PubMed

Arakeri, V H; Giri, A

2001-06-01

From a nonaqueous alkali-metal salt solution, it is possible to observe sonoluminescence (SL) at low acoustic drive levels with the ratio of the acoustic pressure amplitude to the ambient pressure being about 1. In this case, the emission has a narrowband spectral content and consists of a few flashes of light from a levitated gas bubble going through an unstable motion. A systematic statistical study of the optical pulse characteristics of this form of SL is reported here. The results support our earlier findings [Phys. Rev. E 58, R2713 (1998)], but in addition we have clearly established a variation in the optical pulse duration with certain physical parameters such as the gas thermal conductivity. Quantitatively, the SL optical pulse width is observed to vary from 10 ns to 165 ns with the most probable value being 82 ns, for experiments with krypton-saturated sodium salt ethylene glycol solution. With argon, the variation is similar to that of krypton but the most probable value is reduced to 62 ns. The range is significantly smaller with helium, being from 22 ns to 65 ns with the most probable value also being reduced to 42 ns. The observed large variation, for example with krypton, under otherwise fixed controllable experimental parameters indicates that it is an inherent property of the observed SL process, which is transient in nature. It is this feature that necessitated our statistical study. Numerical simulations of the SL process using the bubble dynamics approach of Kamath, Prosperetti, and Egolfopoulos [J. Acoust. Soc. Am. 94, 248 (1993)] suggest that a key uncontrolled parameter, namely the initial bubble radius, may be responsible for the observations. In spite of the fact that certain parameters in the numerical computations have to be fixed from a best fit to one set of experimental data, the observed overall experimental trends of optical pulse characteristics are predicted reasonably well.

Optical pulse characteristics of sonoluminescence at low acoustic drive levels

NASA Astrophysics Data System (ADS)

Arakeri, Vijay H.; Giri, Asis

2001-06-01

From a nonaqueous alkali-metal salt solution, it is possible to observe sonoluminescence (SL) at low acoustic drive levels with the ratio of the acoustic pressure amplitude to the ambient pressure being about 1. In this case, the emission has a narrowband spectral content and consists of a few flashes of light from a levitated gas bubble going through an unstable motion. A systematic statistical study of the optical pulse characteristics of this form of SL is reported here. The results support our earlier findings [Phys. Rev. E 58, R2713 (1998)], but in addition we have clearly established a variation in the optical pulse duration with certain physical parameters such as the gas thermal conductivity. Quantitatively, the SL optical pulse width is observed to vary from 10 ns to 165 ns with the most probable value being 82 ns, for experiments with krypton-saturated sodium salt ethylene glycol solution. With argon, the variation is similar to that of krypton but the most probable value is reduced to 62 ns. The range is significantly smaller with helium, being from 22 ns to 65 ns with the most probable value also being reduced to 42 ns. The observed large variation, for example with krypton, under otherwise fixed controllable experimental parameters indicates that it is an inherent property of the observed SL process, which is transient in nature. It is this feature that necessitated our statistical study. Numerical simulations of the SL process using the bubble dynamics approach of Kamath, Prosperetti, and Egolfopoulos [J. Acoust. Soc. Am. 94, 248 (1993)] suggest that a key uncontrolled parameter, namely the initial bubble radius, may be responsible for the observations. In spite of the fact that certain parameters in the numerical computations have to be fixed from a best fit to one set of experimental data, the observed overall experimental trends of optical pulse characteristics are predicted reasonably well.

Dealing with non-unique and non-monotonic response in particle sizing instruments

NASA Astrophysics Data System (ADS)

Rosenberg, Phil

2017-04-01

A number of instruments used as de-facto standards for measuring particle size distributions are actually incapable of uniquely determining the size of an individual particle. This is due to non-unique or non-monotonic response functions. Optical particle counters have non monotonic response due to oscillations in the Mie response curves, especially for large aerosol and small cloud droplets. Scanning mobility particle sizers respond identically to two particles where the ratio of particle size to particle charge is approximately the same. Images of two differently sized cloud or precipitation particles taken by an optical array probe can have similar dimensions or shadowed area depending upon where they are in the imaging plane. A number of methods exist to deal with these issues, including assuming that positive and negative errors cancel, smoothing response curves, integrating regions in measurement space before conversion to size space and matrix inversion. Matrix inversion (also called kernel inversion) has the advantage that it determines the size distribution which best matches the observations, given specific information about the instrument (a matrix which specifies the probability that a particle of a given size will be measured in a given instrument size bin). In this way it maximises use of the information in the measurements. However this technique can be confused by poor counting statistics which can cause erroneous results and negative concentrations. Also an effective method for propagating uncertainties is yet to be published or routinely implemented. Her we present a new alternative which overcomes these issues. We use Bayesian methods to determine the probability that a given size distribution is correct given a set of instrument data and then we use Markov Chain Monte Carlo methods to sample this many dimensional probability distribution function to determine the expectation and (co)variances - hence providing a best guess and an uncertainty for the size distribution which includes contributions from the non-unique response curve, counting statistics and can propagate calibration uncertainties.

Fixed forced detection for fast SPECT Monte-Carlo simulation

NASA Astrophysics Data System (ADS)

Cajgfinger, T.; Rit, S.; Létang, J. M.; Halty, A.; Sarrut, D.

2018-03-01

Monte-Carlo simulations of SPECT images are notoriously slow to converge due to the large ratio between the number of photons emitted and detected in the collimator. This work proposes a method to accelerate the simulations based on fixed forced detection (FFD) combined with an analytical response of the detector. FFD is based on a Monte-Carlo simulation but forces the detection of a photon in each detector pixel weighted by the probability of emission (or scattering) and transmission to this pixel. The method was evaluated with numerical phantoms and on patient images. We obtained differences with analog Monte Carlo lower than the statistical uncertainty. The overall computing time gain can reach up to five orders of magnitude. Source code and examples are available in the Gate V8.0 release.

Ku-band radar threshold analysis

NASA Technical Reports Server (NTRS)

Weber, C. L.; Polydoros, A.

1979-01-01

The statistics of the CFAR threshold for the Ku-band radar was determined. Exact analytical results were developed for both the mean and standard deviations in the designated search mode. The mean value is compared to the results of a previously reported simulation. The analytical results are more optimistic than the simulation results, for which no explanation is offered. The normalized standard deviation is shown to be very sensitive to signal-to-noise ratio and very insensitive to the noise correlation present in the range gates of the designated search mode. The substantial variation in the CFAR threshold is dominant at large values of SNR where the normalized standard deviation is greater than 0.3. Whether or not this significantly affects the resulting probability of detection is a matter which deserves additional attention.

A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions.

PubMed

Shankar, P Mohana

2003-03-01

A compound probability density function (pdf) is presented to describe the envelope of the backscattered echo from tissue. This pdf allows local and global variation in scattering cross sections in tissue. The ultrasonic backscattering cross sections are assumed to be gamma distributed. The gamma distribution also is used to model the randomness in the average cross sections. This gamma-gamma model results in the compound scattering pdf for the envelope. The relationship of this compound pdf to the Rayleigh, K, and Nakagami distributions is explored through an analysis of the signal-to-noise ratio of the envelopes and random number simulations. The three parameter compound pdf appears to be flexible enough to represent envelope statistics giving rise to Rayleigh, K, and Nakagami distributions.

Fixed forced detection for fast SPECT Monte-Carlo simulation.

PubMed

Cajgfinger, T; Rit, S; Létang, J M; Halty, A; Sarrut, D

2018-03-02

Monte-Carlo simulations of SPECT images are notoriously slow to converge due to the large ratio between the number of photons emitted and detected in the collimator. This work proposes a method to accelerate the simulations based on fixed forced detection (FFD) combined with an analytical response of the detector. FFD is based on a Monte-Carlo simulation but forces the detection of a photon in each detector pixel weighted by the probability of emission (or scattering) and transmission to this pixel. The method was evaluated with numerical phantoms and on patient images. We obtained differences with analog Monte Carlo lower than the statistical uncertainty. The overall computing time gain can reach up to five orders of magnitude. Source code and examples are available in the Gate V8.0 release.

Assessing the Chances of Success: Naive Statistics versus Kind Experience

ERIC Educational Resources Information Center

Hogarth, Robin M.; Mukherjee, Kanchan; Soyer, Emre

2013-01-01

Additive integration of information is ubiquitous in judgment and has been shown to be effective even when multiplicative rules of probability theory are prescribed. We explore the generality of these findings in the context of estimating probabilities of success in contests. We first define a normative model of these probabilities that takes…

Investigating the Relationship between Conceptual and Procedural Errors in the Domain of Probability Problem-Solving.

ERIC Educational Resources Information Center

O'Connell, Ann Aileen

The relationships among types of errors observed during probability problem solving were studied. Subjects were 50 graduate students in an introductory probability and statistics course. Errors were classified as text comprehension, conceptual, procedural, and arithmetic. Canonical correlation analysis was conducted on the frequencies of specific…

Duality of circulation decay statistics and survival probability

DOT National Transportation Integrated Search

2010-09-01

Survival probability and circulation decay history have both been used for setting wake turbulence separation standards. Conceptually a strong correlation should exist between these two characterizations of the vortex behavior, however, the literatur...

Using transportation accident databases to investigate ignition and explosion probabilities of flammable spills.

PubMed

Ronza, A; Vílchez, J A; Casal, J

2007-07-19

Risk assessment of hazardous material spill scenarios, and quantitative risk assessment in particular, make use of event trees to account for the possible outcomes of hazardous releases. Using event trees entails the definition of probabilities of occurrence for events such as spill ignition and blast formation. This study comprises an extensive analysis of ignition and explosion probability data proposed in previous work. Subsequently, the results of the survey of two vast US federal spill databases (HMIRS, by the Department of Transportation, and MINMOD, by the US Coast Guard) are reported and commented on. Some tens of thousands of records of hydrocarbon spills were analysed. The general pattern of statistical ignition and explosion probabilities as a function of the amount and the substance spilled is discussed. Equations are proposed based on statistical data that predict the ignition probability of hydrocarbon spills as a function of the amount and the substance spilled. Explosion probabilities are put forth as well. Two sets of probability data are proposed: it is suggested that figures deduced from HMIRS be used in land transportation risk assessment, and MINMOD results with maritime scenarios assessment. Results are discussed and compared with previous technical literature.

Two statistical mechanics aspects of complex networks

NASA Astrophysics Data System (ADS)

Thurner, Stefan; Biely, Christoly

2006-12-01

By adopting an ensemble interpretation of non-growing rewiring networks, network theory can be reduced to a counting problem of possible network states and an identification of their associated probabilities. We present two scenarios of how different rewirement schemes can be used to control the state probabilities of the system. In particular, we review how by generalizing the linking rules of random graphs, in combination with superstatistics and quantum mechanical concepts, one can establish an exact relation between the degree distribution of any given network and the nodes’ linking probability distributions. In a second approach, we control state probabilities by a network Hamiltonian, whose characteristics are motivated by biological and socio-economical statistical systems. We demonstrate that a thermodynamics of networks becomes a fully consistent concept, allowing to study e.g. ‘phase transitions’ and computing entropies through thermodynamic relations.

Scenarios for Evolving Seismic Crises: Possible Communication Strategies

NASA Astrophysics Data System (ADS)

Steacy, S.

2015-12-01

Recent advances in operational earthquake forecasting mean that we are very close to being able to confidently compute changes in earthquake probability as seismic crises develop. For instance, we now have statistical models such as ETAS and STEP which demonstrate considerable skill in forecasting earthquake rates and recent advances in Coulomb based models are also showing much promise. Communicating changes in earthquake probability is likely be very difficult, however, as the absolute probability of a damaging event is likely to remain quite small despite a significant increase in the relative value. Here, we use a hybrid Coulomb/statistical model to compute probability changes for a series of earthquake scenarios in New Zealand. We discuss the strengths and limitations of the forecasts and suggest a number of possible mechanisms that might be used to communicate results in an actual developing seismic crisis.

On the inequivalence of the CH and CHSH inequalities due to finite statistics

NASA Astrophysics Data System (ADS)

Renou, M. O.; Rosset, D.; Martin, A.; Gisin, N.

2017-06-01

Different variants of a Bell inequality, such as CHSH and CH, are known to be equivalent when evaluated on nonsignaling outcome probability distributions. However, in experimental setups, the outcome probability distributions are estimated using a finite number of samples. Therefore the nonsignaling conditions are only approximately satisfied and the robustness of the violation depends on the chosen inequality variant. We explain that phenomenon using the decomposition of the space of outcome probability distributions under the action of the symmetry group of the scenario, and propose a method to optimize the statistical robustness of a Bell inequality. In the process, we describe the finite group composed of relabeling of parties, measurement settings and outcomes, and identify correspondences between the irreducible representations of this group and properties of outcome probability distributions such as normalization, signaling or having uniform marginals.

Quantifying prognosis with risk predictions.

PubMed

Pace, Nathan L; Eberhart, Leopold H J; Kranke, Peter R

2012-01-01

Prognosis is a forecast, based on present observations in a patient, of their probable outcome from disease, surgery and so on. Research methods for the development of risk probabilities may not be familiar to some anaesthesiologists. We briefly describe methods for identifying risk factors and risk scores. A probability prediction rule assigns a risk probability to a patient for the occurrence of a specific event. Probability reflects the continuum between absolute certainty (Pi = 1) and certified impossibility (Pi = 0). Biomarkers and clinical covariates that modify risk are known as risk factors. The Pi as modified by risk factors can be estimated by identifying the risk factors and their weighting; these are usually obtained by stepwise logistic regression. The accuracy of probabilistic predictors can be separated into the concepts of 'overall performance', 'discrimination' and 'calibration'. Overall performance is the mathematical distance between predictions and outcomes. Discrimination is the ability of the predictor to rank order observations with different outcomes. Calibration is the correctness of prediction probabilities on an absolute scale. Statistical methods include the Brier score, coefficient of determination (Nagelkerke R2), C-statistic and regression calibration. External validation is the comparison of the actual outcomes to the predicted outcomes in a new and independent patient sample. External validation uses the statistical methods of overall performance, discrimination and calibration and is uniformly recommended before acceptance of the prediction model. Evidence from randomised controlled clinical trials should be obtained to show the effectiveness of risk scores for altering patient management and patient outcomes.

Interference in the classical probabilistic model and its representation in complex Hilbert space

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei Yu.

2005-10-01

The notion of a context (complex of physical conditions, that is to say: specification of the measurement setup) is basic in this paper.We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present already in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and only then probability”. We construct the representation of the general contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function (in particular, Schrödinger's dynamics) can be considered as Hilbert space projections of a realistic dynamics in a “prespace”. The basic condition for representing of the prespace-dynamics is the law of statistical conservation of energy-conservation of probabilities. In general the Hilbert space projection of the “prespace” dynamics can be nonlinear and even irreversible (but it is always unitary). Methods developed in this paper can be applied not only to quantum mechanics, but also to classical statistical mechanics. The main quantum-like structures (e.g., interference of probabilities) might be found in some models of classical statistical mechanics. Quantum-like probabilistic behavior can be demonstrated by biological systems. In particular, it was recently found in some psychological experiments.

A Performance Comparison on the Probability Plot Correlation Coefficient Test using Several Plotting Positions for GEV Distribution.

NASA Astrophysics Data System (ADS)

Ahn, Hyunjun; Jung, Younghun; Om, Ju-Seong; Heo, Jun-Haeng

2014-05-01

It is very important to select the probability distribution in Statistical hydrology. Goodness of fit test is a statistical method that selects an appropriate probability model for a given data. The probability plot correlation coefficient (PPCC) test as one of the goodness of fit tests was originally developed for normal distribution. Since then, this test has been widely applied to other probability models. The PPCC test is known as one of the best goodness of fit test because it shows higher rejection powers among them. In this study, we focus on the PPCC tests for the GEV distribution which is widely used in the world. For the GEV model, several plotting position formulas are suggested. However, the PPCC statistics are derived only for the plotting position formulas (Goel and De, In-na and Nguyen, and Kim et al.) in which the skewness coefficient (or shape parameter) are included. And then the regression equations are derived as a function of the shape parameter and sample size for a given significance level. In addition, the rejection powers of these formulas are compared using Monte-Carlo simulation. Keywords: Goodness-of-fit test, Probability plot correlation coefficient test, Plotting position, Monte-Carlo Simulation ACKNOWLEDGEMENTS This research was supported by a grant 'Establishing Active Disaster Management System of Flood Control Structures by using 3D BIM Technique' [NEMA-12-NH-57] from the Natural Hazard Mitigation Research Group, National Emergency Management Agency of Korea.

The large-scale correlations of multicell densities and profiles: implications for cosmic variance estimates

NASA Astrophysics Data System (ADS)

Codis, Sandrine; Bernardeau, Francis; Pichon, Christophe

2016-08-01

In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of their two-point correlation function to the two-point correlation of the underlying dark matter distribution. They describe how cell densities are spatially correlated. They are computed here via the so-called large deviation principle in the quasi-linear regime. Their large-separation limit is presented and successfully compared to simulations for density and density slopes: this regime is shown to be rapidly reached allowing to get sub-percent precision for a wide range of densities and variances. The corresponding asymptotic limit provides an estimate of the cosmic variance of standard concentric cell statistics applied to finite surveys. More generally, no assumption on the separation is required for some specific moments of the two-point statistics, for instance when predicting the generating function of cumulants containing any powers of concentric densities in one location and one power of density at some arbitrary distance from the rest. This exact `one external leg' cumulant generating function is used in particular to probe the rate of convergence of the large-separation approximation.

Measuring the Number of M Dwarfs per M Dwarf Using Kepler Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Shan, Yutong; Johnson, John A.; Morton, Timothy D.

2015-11-01

We measure the binarity of detached M dwarfs in the Kepler field with orbital periods in the range of 1-90 days. Kepler’s photometric precision and nearly continuous monitoring of stellar targets over time baselines ranging from 3 months to 4 years make its detection efficiency for eclipsing binaries nearly complete over this period range and for all radius ratios. Our investigation employs a statistical framework akin to that used for inferring planetary occurrence rates from planetary transits. The obvious simplification is that eclipsing binaries have a vastly improved detection efficiency that is limited chiefly by their geometric probabilities to eclipse. For the M-dwarf sample observed by the Kepler Mission, the fractional incidence of eclipsing binaries implies that there are {0.11}-0.04+0.02 close stellar companions per apparently single M dwarf. Our measured binarity is higher than previous inferences of the occurrence rate of close binaries via radial velocity techniques, at roughly the 2σ level. This study represents the first use of eclipsing binary detections from a high quality transiting planet mission to infer binary statistics. Application of this statistical framework to the eclipsing binaries discovered by future transit surveys will establish better constraints on short-period M+M binary rate, as well as binarity measurements for stars of other spectral types.

Statistical description of non-Gaussian samples in the F2 layer of the ionosphere during heliogeophysical disturbances

NASA Astrophysics Data System (ADS)

Sergeenko, N. P.

2017-11-01

An adequate statistical method should be developed in order to predict probabilistically the range of ionospheric parameters. This problem is solved in this paper. The time series of the critical frequency of the layer F2- foF2( t) were subjected to statistical processing. For the obtained samples {δ foF2}, statistical distributions and invariants up to the fourth order are calculated. The analysis shows that the distributions differ from the Gaussian law during the disturbances. At levels of sufficiently small probability distributions, there are arbitrarily large deviations from the model of the normal process. Therefore, it is attempted to describe statistical samples {δ foF2} based on the Poisson model. For the studied samples, the exponential characteristic function is selected under the assumption that time series are a superposition of some deterministic and random processes. Using the Fourier transform, the characteristic function is transformed into a nonholomorphic excessive-asymmetric probability-density function. The statistical distributions of the samples {δ foF2} calculated for the disturbed periods are compared with the obtained model distribution function. According to the Kolmogorov's criterion, the probabilities of the coincidence of a posteriori distributions with the theoretical ones are P 0.7-0.9. The conducted analysis makes it possible to draw a conclusion about the applicability of a model based on the Poisson random process for the statistical description and probabilistic variation estimates during heliogeophysical disturbances of the variations {δ foF2}.

The beta distribution: A statistical model for world cloud cover

NASA Technical Reports Server (NTRS)

Falls, L. W.

1973-01-01

Much work has been performed in developing empirical global cloud cover models. This investigation was made to determine an underlying theoretical statistical distribution to represent worldwide cloud cover. The beta distribution with probability density function is given to represent the variability of this random variable. It is shown that the beta distribution possesses the versatile statistical characteristics necessary to assume the wide variety of shapes exhibited by cloud cover. A total of 160 representative empirical cloud cover distributions were investigated and the conclusion was reached that this study provides sufficient statical evidence to accept the beta probability distribution as the underlying model for world cloud cover.

On the Study of Statistical Intuitions.

DTIC Science & Technology

1981-05-15

teller; 3. Linda is a bank teller who is PAGE 10 active in the feminist movement. In a large sample of statistically naive undergraduates, 86% judged...Linda is both a bank teller and an active feminist must be smaller than the probability that she is a bank teller. (ii) B is more probable than A...because Linda resembles a bank teller who is active in the feminist movement more than she resembles a bank teller. Argument (i) favoring the conjunction

The impacts of recent smoking control policies on individual smoking choice: the case of Japan

PubMed Central

2013-01-01

Abstract This article comprehensively examines the impact of recent smoking control policies in Japan, increases in cigarette taxes and the enforcement of the Health Promotion Law, on individual smoking choice by using multi-year and nationwide individual survey data to overcome the analytical problems of previous Japanese studies. In the econometric analyses, I specify a simple binary choice model based on a random utility model to examine the effects of smoking control policies on individual smoking choice by employing the instrumental variable probit model to control for the endogeneity of cigarette prices. The empirical results show that an increase in cigarette prices statistically significantly reduces the smoking probability of males by 1.0 percent and that of females by 1.4 to 2.0 percent. The enforcement of the Health Promotion Law has a statistically significant effect on reducing the smoking probability of males by 15.2 percent and of females by 11.9 percent. Furthermore, an increase in cigarette prices has a statistically significant negative effect on the smoking probability of office workers, non-workers, male manual workers, and female unemployed people, and the enforcement of the Health Promotion Law has a statistically significant effect on decreasing the smoking probabilities of office workers, female manual workers, and male non-workers. JEL classification C25, C26, I18 PMID:23497490

Methods for estimating drought streamflow probabilities for Virginia streams

USGS Publications Warehouse

Austin, Samuel H.

2014-01-01

Maximum likelihood logistic regression model equations used to estimate drought flow probabilities for Virginia streams are presented for 259 hydrologic basins in Virginia. Winter streamflows were used to estimate the likelihood of streamflows during the subsequent drought-prone summer months. The maximum likelihood logistic regression models identify probable streamflows from 5 to 8 months in advance. More than 5 million streamflow daily values collected over the period of record (January 1, 1900 through May 16, 2012) were compiled and analyzed over a minimum 10-year (maximum 112-year) period of record. The analysis yielded the 46,704 equations with statistically significant fit statistics and parameter ranges published in two tables in this report. These model equations produce summer month (July, August, and September) drought flow threshold probabilities as a function of streamflows during the previous winter months (November, December, January, and February). Example calculations are provided, demonstrating how to use the equations to estimate probable streamflows as much as 8 months in advance.

Understanding common statistical methods, Part I: descriptive methods, probability, and continuous data.

PubMed

Skinner, Carl G; Patel, Manish M; Thomas, Jerry D; Miller, Michael A

2011-01-01

Statistical methods are pervasive in medical research and general medical literature. Understanding general statistical concepts will enhance our ability to critically appraise the current literature and ultimately improve the delivery of patient care. This article intends to provide an overview of the common statistical methods relevant to medicine.

Employment Status of Depressed Individuals in an 11-Year Follow-up: Results From the Finnish Health 2011 Survey.

PubMed

Markkula, Niina; Kivekäs, Teija; Suvisaari, Jaana; Virtanen, Marianna; Ahola, Kirsi

2017-07-01

The aim of this study was to describe the employment and mental health status of persons with depressive disorders after an 11-year follow-up, and identify individual and work-related factors that predict adverse outcomes. Two nationally representative health surveys, Health 2000 and its follow-up, Health 2011 were used, and persons with depressive disorders at baseline (n = 275) were re-interviewed after 11 years. Information on employment status was available for all 263 participants in 2011. About 15.7% had been granted disability pension by 2011, while 55.5% were employed and 18.2% on old-age pension. High job control was the only statistically significant predictor of lower probability of disability pension (adjusted odds ratio 0.42, 95% confidence interval [95% CI] 0.23 to 0.77). Being unmarried (adjusted odds ratio 2.99, 95% CI 1.19 to 7.52) was associated with persistent depressive disorder. Job control emerged as an important predictor of long-term employment outcomes among depressed individuals.

Digit ratio (2D:4D) and male facial attractiveness: new data and a meta-analysis.

PubMed

Hönekopp, Johannes

2013-10-01

Digit ratio (2D:4D) appears to correlate negatively with prenatal testosterone (T) effects in humans. As T probably increases facial masculinity, which in turn might be positively related to male facial attractiveness, a number of studies have looked into the relationship between 2D:4D and male facial attractiveness, showing equivocal results. Here, I present the largest and third largest samples so far, which investigate the relationship between 2D:4D and male facial attractiveness in adolescents (n = 115) and young men (n = 80). I then present random-effects meta-analyses of the available data (seven to eight samples, overall n = 362 to 469). These showed small (r ≈ -.09), statistically non-significant relationships between 2D:4D measures and male facial attractiveness. Thus, 2D:4D studies offer no convincing evidence at present that prenatal T has a positive effect on male facial attractiveness. However, a consideration of confidence intervals shows that, at present, a theoretically meaningful relationship between 2D:4D and male facial attractiveness cannot be ruled out either.

Age estimation by pulp-to-tooth area ratio using cone-beam computed tomography: A preliminary analysis.

PubMed

Rai, Arpita; Acharya, Ashith B; Naikmasur, Venkatesh G

2016-01-01

Age estimation of living or deceased individuals is an important aspect of forensic sciences. Conventionally, pulp-to-tooth area ratio (PTR) measured from periapical radiographs have been utilized as a nondestructive method of age estimation. Cone-beam computed tomography (CBCT) is a new method to acquire three-dimensional images of the teeth in living individuals. The present study investigated age estimation based on PTR of the maxillary canines measured in three planes obtained from CBCT image data. Sixty subjects aged 20-85 years were included in the study. For each tooth, mid-sagittal, mid-coronal, and three axial sections-cementoenamel junction (CEJ), one-fourth root level from CEJ, and mid-root-were assessed. PTR was calculated using AutoCAD software after outlining the pulp and tooth. All statistical analyses were performed using an SPSS 17.0 software program. Linear regression analysis showed that only PTR in axial plane at CEJ had significant age correlation ( r = 0.32; P < 0.05). This is probably because of clearer demarcation of pulp and tooth outline at this level.

Open area 2 × 2 MIMO channel model for 2 GHz low-elevation links with diversity and capacity applications

NASA Astrophysics Data System (ADS)

Zelený, J.; Pérez-Fontán, F.; Pechac, P.; Mariño-Espiñeira, P.

2017-05-01

In civil surveillance applications, unmanned aerial vehicles (UAV) are being increasingly used in floods, fires, and law enforcement scenarios. In order to transfer large amounts of information from UAV-mounted cameras, relays, or sensors, large bandwidths are needed in comparison to those required for remotely commanding the UAV. This demands the use of higher-frequency bands, in all probability in the vicinity of 2 or 5 GHz. Novel hardware developments need propagation channel models for the ample range of operational scenarios envisaged, including multiple-input, multiple-output (MIMO) deployments. These configurations may enable a more robust transmission by increasing either the carrier-to-noise ratio statistics or the achievable capacity. In this paper, a 2 × 2 MIMO propagation channel model for an open-field environment capable of synthesizing a narrowband time series at 2 GHz is described. Maximal ratio combining diversity and capacity improvements are also evaluated through synthetic series and compared with measurement results. A simple flat, open scenario was evaluated based on which other, more complex environments can be modeled.

A New Statistic for Evaluating Item Response Theory Models for Ordinal Data. CRESST Report 839

ERIC Educational Resources Information Center

Cai, Li; Monroe, Scott

2014-01-01

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

Using GAISE and NCTM Standards as Frameworks for Teaching Probability and Statistics to Pre-Service Elementary and Middle School Mathematics Teachers

ERIC Educational Resources Information Center

Metz, Mary Louise

2010-01-01

Statistics education has become an increasingly important component of the mathematics education of today's citizens. In part to address the call for a more statistically literate citizenship, The "Guidelines for Assessment and Instruction in Statistics Education (GAISE)" were developed in 2005 by the American Statistical Association. These…

Playing at Statistical Mechanics

ERIC Educational Resources Information Center

Clark, Paul M.; And Others

1974-01-01

Discussed are the applications of counting techniques of a sorting game to distributions and concepts in statistical mechanics. Included are the following distributions: Fermi-Dirac, Bose-Einstein, and most probable. (RH)

Statistics Online Computational Resource for Education

ERIC Educational Resources Information Center

Dinov, Ivo D.; Christou, Nicolas

2009-01-01

The Statistics Online Computational Resource (http://www.SOCR.ucla.edu) provides one of the largest collections of free Internet-based resources for probability and statistics education. SOCR develops, validates and disseminates two core types of materials--instructional resources and computational libraries. (Contains 2 figures.)

Meta-analysis for aggregated survival data with competing risks: a parametric approach using cumulative incidence functions.

PubMed

Bonofiglio, Federico; Beyersmann, Jan; Schumacher, Martin; Koller, Michael; Schwarzer, Guido

2016-09-01

Meta-analysis of a survival endpoint is typically based on the pooling of hazard ratios (HRs). If competing risks occur, the HRs may lose translation into changes of survival probability. The cumulative incidence functions (CIFs), the expected proportion of cause-specific events over time, re-connect the cause-specific hazards (CSHs) to the probability of each event type. We use CIF ratios to measure treatment effect on each event type. To retrieve information on aggregated, typically poorly reported, competing risks data, we assume constant CSHs. Next, we develop methods to pool CIF ratios across studies. The procedure computes pooled HRs alongside and checks the influence of follow-up time on the analysis. We apply the method to a medical example, showing that follow-up duration is relevant both for pooled cause-specific HRs and CIF ratios. Moreover, if all-cause hazard and follow-up time are large enough, CIF ratios may reveal additional information about the effect of treatment on the cumulative probability of each event type. Finally, to improve the usefulness of such analysis, better reporting of competing risks data is needed. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Précis of statistical significance: rationale, validity, and utility.

PubMed

Chow, S L

1998-04-01

The null-hypothesis significance-test procedure (NHSTP) is defended in the context of the theory-corroboration experiment, as well as the following contrasts: (a) substantive hypotheses versus statistical hypotheses, (b) theory corroboration versus statistical hypothesis testing, (c) theoretical inference versus statistical decision, (d) experiments versus nonexperimental studies, and (e) theory corroboration versus treatment assessment. The null hypothesis can be true because it is the hypothesis that errors are randomly distributed in data. Moreover, the null hypothesis is never used as a categorical proposition. Statistical significance means only that chance influences can be excluded as an explanation of data; it does not identify the nonchance factor responsible. The experimental conclusion is drawn with the inductive principle underlying the experimental design. A chain of deductive arguments gives rise to the theoretical conclusion via the experimental conclusion. The anomalous relationship between statistical significance and the effect size often used to criticize NHSTP is more apparent than real. The absolute size of the effect is not an index of evidential support for the substantive hypothesis. Nor is the effect size, by itself, informative as to the practical importance of the research result. Being a conditional probability, statistical power cannot be the a priori probability of statistical significance. The validity of statistical power is debatable because statistical significance is determined with a single sampling distribution of the test statistic based on H0, whereas it takes two distributions to represent statistical power or effect size. Sample size should not be determined in the mechanical manner envisaged in power analysis. It is inappropriate to criticize NHSTP for nonstatistical reasons. At the same time, neither effect size, nor confidence interval estimate, nor posterior probability can be used to exclude chance as an explanation of data. Neither can any of them fulfill the nonstatistical functions expected of them by critics.

Angiotensin Receptor Blockers and Risk of Prostate Cancer among United States Veterans

PubMed Central

Rao, Gowtham A; Mann, Joshua R.; Bottai, Matteo; Uemura, Hiroji; Burch, James B; Bennett, Charles Lee; Haddock, Kathlyn Sue; Hébert, James R

2013-01-01

Objectives To address concerns regarding increased risk of prostate cancer (PrCA) among Angiotensin Receptor Blocker users, we used national retrospective data from the Department of Veterans Affairs (VA) through the Veterans Affairs Informatics and Computing Infrastructure (VINCI). Methods We identified a total of 543,824 unique Veterans who were classified into either ARB treated or not-treated in 1:15 ratio. The two groups were balanced using inverse probability of treatment weights. A double-robust cox-proportional hazards model was used to estimate the hazard ratio for PrCA incidence. To evaluate for a potential Gleason score stage migration we conducted weighted Cochrane-Armitage test. Results Post weighting, the rates of PrCA in treated and not-treated groups were 506 (1.5%) and 8,269 (1.6%), respectively; representing a hazard ratio of (0.91, p-value 0.049). There was no significant difference in Gleason scores between the two groups. Conclusions We found a small, but statistically significant, reduction in the incidence of clinically detected PrCA among patients assigned to receive ARB with no countervailing effect on degree of differentiation (as indicated by Gleason score). Findings from this study support FDA’s recent conclusion that ARB use does not increase risk of incident PrCA. PMID:23686462

Investigation of the quasi-simultaneous arrival (QSA) effect on a CAMECA IMS 7f-GEO.

PubMed

Jones, Clive; Fike, David A; Peres, Paula

2017-04-15

IMS 7f-GEO isotope ratio applications increasingly involve analyses (e.g., S - or O - isotopes, coupled with primary ion currents <30 pA) for which quasi-simultaneous arrival (QSA) could compromise precision and accuracy of data. QSA and associated correction have been widely investigated for the CAMECA NanoSIMS instruments, but not for the IMS series. Sulfur and oxygen isotopic ratio experiments were performed using an electron multiplier (EM) detector, employing Cs + primary ion currents of 1, 2, 5 and 11.5 pA (nominal) and a variety of secondary ion transmissions to vary QSA probability. An experiment to distinguish between QSA undercounting and purported aperture-related mass fractionation was performed using an EM for 16 O - and 18 O - plus an additional 16 O - measurement using a Faraday cup (FC) detector. An experiment to investigate the accuracy of the QSA correction was performed by comparing S isotopic ratios obtained using an EM with those obtained on the same sample using dual FCs. The QSA effect was observed on the IMS-7f-GEO, and QSA coefficients (β) of ~0.66 were determined, in agreement with reported NanoSIMS measurements, but different from the value (0.5) predicted using Poisson statistics. Aperture-related fractionation was not sufficient to explain the difference but uncertainties in primary ion flux measurement could play a role. When QSA corrected, the isotope ratio data obtained using the EM agreed with the dual FC data, within statistical error. QSA undercounting could compromise isotope ratio analyses requiring ~1 × 10 5 counts per second for the major isotope and primary currents <20 pA. The error could be >8‰ for a 1 pA primary current. However, correction can be accurately applied. For instrumental mass fractionation (IMF)-corrected data, the magnitude of the error resulting from not correcting for QSA is dependent on the difference in secondary ion count rate between the unknown and standard analyses. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

The intrinsic three-dimensional shape of galactic bars

NASA Astrophysics Data System (ADS)

Méndez-Abreu, J.; Costantin, L.; Aguerri, J. A. L.; de Lorenzo-Cáceres, A.; Corsini, E. M.

2018-06-01

We present the first statistical study on the intrinsic three-dimensional (3D) shape of a sample of 83 galactic bars extracted from the CALIFA survey. We use the galaXYZ code to derive the bar intrinsic shape with a statistical approach. The method uses only the geometric information (ellipticities and position angles) of bars and discs obtained from a multi-component photometric decomposition of the galaxy surface-brightness distributions. We find that bars are predominantly prolate-triaxial ellipsoids (68%), with a small fraction of oblate-triaxial ellipsoids (32%). The typical flattening (intrinsic C/A semiaxis ratio) of the bars in our sample is 0.34, which matches well the typical intrinsic flattening of stellar discs at these galaxy masses. We demonstrate that, for prolate-triaxial bars, the intrinsic shape of bars depends on the galaxy Hubble type and stellar mass (bars in massive S0 galaxies are thicker and more circular than those in less massive spirals). The bar intrinsic shape correlates with bulge, disc, and bar parameters. In particular with the bulge-to-total (B/T) luminosity ratio, disc g - r color, and central surface brightness of the bar, confirming the tight link between bars and their host galaxies. Combining the probability distributions of the intrinsic shape of bulges and bars in our sample we show that 52% (16%) of bulges are thicker (flatter) than the surrounding bar at 1σ level. We suggest that these percentages might be representative of the fraction of classical and disc-like bulges in our sample, respectively.

Cost-effectiveness of targeted screening for abdominal aortic aneurysm. Monte Carlo-based estimates.

PubMed

Pentikäinen, T J; Sipilä, T; Rissanen, P; Soisalon-Soininen, S; Salo, J

2000-01-01

This article reports a cost-effectiveness analysis of targeted screening for abdominal aortic aneurysm (AAA). A major emphasis was on the estimation of distributions of costs and effectiveness. We performed a Monte Carlo simulation using C programming language in a PC environment. Data on survival and costs, and a majority of screening probabilities, were from our own empirical studies. Natural history data were based on the literature. Each screened male gained 0.07 life-years at an incremental cost of FIM 3,300. The expected values differed from zero very significantly. For females, expected gains were 0.02 life-years at an incremental cost of FIM 1,100, which was not statistically significant. Cost-effectiveness ratios and their 95% confidence intervals were FIM 48,000 (27,000-121,000) and 54,000 (22,000-infinity) for males and females, respectively. Sensitivity analysis revealed that the results for males were stable. Individual variation in life-year gains was high. Males seemed to benefit from targeted AAA screening, and the results were stable. As far as the cost-effectiveness ratio is considered acceptable, screening for males seemed to be justified. However, our assumptions about growth and rupture behavior of AAAs might be improved with further clinical and epidemiological studies. As a point estimate, females benefited in a similar manner, but the results were not statistically significant. The evidence of this study did not justify screening of females.

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

Developing and Testing a Model to Predict Outcomes of Organizational Change

PubMed Central

Gustafson, David H; Sainfort, François; Eichler, Mary; Adams, Laura; Bisognano, Maureen; Steudel, Harold

2003-01-01

Objective To test the effectiveness of a Bayesian model employing subjective probability estimates for predicting success and failure of health care improvement projects. Data Sources Experts' subjective assessment data for model development and independent retrospective data on 221 healthcare improvement projects in the United States, Canada, and the Netherlands collected between 1996 and 2000 for validation. Methods A panel of theoretical and practical experts and literature in organizational change were used to identify factors predicting the outcome of improvement efforts. A Bayesian model was developed to estimate probability of successful change using subjective estimates of likelihood ratios and prior odds elicited from the panel of experts. A subsequent retrospective empirical analysis of change efforts in 198 health care organizations was performed to validate the model. Logistic regression and ROC analysis were used to evaluate the model's performance using three alternative definitions of success. Data Collection For the model development, experts' subjective assessments were elicited using an integrative group process. For the validation study, a staff person intimately involved in each improvement project responded to a written survey asking questions about model factors and project outcomes. Results Logistic regression chi-square statistics and areas under the ROC curve demonstrated a high level of model performance in predicting success. Chi-square statistics were significant at the 0.001 level and areas under the ROC curve were greater than 0.84. Conclusions A subjective Bayesian model was effective in predicting the outcome of actual improvement projects. Additional prospective evaluations as well as testing the impact of this model as an intervention are warranted. PMID:12785571

Polymorphism at the 3'-UTR of the thymidylate synthase gene: A potential predictor for outcomes in Caucasian patients with esophageal adenocarcinoma treated with preoperative chemoradiation

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

Liao Zhongxing; Liu Hongji; Swisher, Stephen G.

2006-03-01

Purpose: To test the hypothesis that TS3'UTR polymorphisms predict outcomes in 146 Caucasian patients with esophageal adenocarcinoma treated with preoperative 5-fluorouracil-based chemoradiation. Methods and Materials: DNA was extracted from hematoxylin-and-eosin stained histologic slides of normal esophageal or gastric mucosa sections from paraffin blocks of esophagectomy specimens. Genotypes of the TS3'UTR polymorphism were determined by polymerase chain reaction for a 6-bp insertion. The genotype groups (0bp/0bp, 6bp/0bp, and 6bp/6bp) were compared for clinical features and overall survival, recurrence-free-survival, locoregional control (LRC), and distant metastasis control. Multivariable Cox regression analyses were performed to find independent predictors for the stated outcomes. Results: Theremore » was a trend of association between 6bp/6bp genotype and a decreased risk of local regional recurrence (hazards ratio = 0.211, 95% confidence interval = 0.041-1.095, p = 0.06) compared with other genotypes. There was a trend that patients with 6bp/6bp genotype had a higher 3-year probability of LRC compared with patients with the other two genotypes combined (p = 0.07); however, the difference was not statistically significant. Conclusions: The null hypotheses were not rejected in this study, probably owing to small sample size or the single gene examined. Prospective studies with adequate statistical power analyzing a family of genes involved in the 5-fluorouracil metabolism are needed to assess genetic determinants of treatment-related outcomes in esophageal adenocarcinoma.« less

Suggestions for Teaching Mathematics Using Laboratory Approaches. 6. Probability. Experimental Edition.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Elementary Curriculum Development.

This guide is the sixth in a series of publications to assist teachers in using a laboratory approach to mathematics. Twenty activities on probability and statistics for the elementary grades are described in terms of purpose, materials needed, and procedures to be used. Objectives of these activities include basic probability concepts; gathering,…

Multi-scale Characterization and Modeling of Surface Slope Probability Distribution for ~20-km Diameter Lunar Craters

NASA Astrophysics Data System (ADS)

Mahanti, P.; Robinson, M. S.; Boyd, A. K.

2013-12-01

Craters ~20-km diameter and above significantly shaped the lunar landscape. The statistical nature of the slope distribution on their walls and floors dominate the overall slope distribution statistics for the lunar surface. Slope statistics are inherently useful for characterizing the current topography of the surface, determining accurate photometric and surface scattering properties, and in defining lunar surface trafficability [1-4]. Earlier experimental studies on the statistical nature of lunar surface slopes were restricted either by resolution limits (Apollo era photogrammetric studies) or by model error considerations (photoclinometric and radar scattering studies) where the true nature of slope probability distribution was not discernible at baselines smaller than a kilometer[2,3,5]. Accordingly, historical modeling of lunar surface slopes probability distributions for applications such as in scattering theory development or rover traversability assessment is more general in nature (use of simple statistical models such as the Gaussian distribution[1,2,5,6]). With the advent of high resolution, high precision topographic models of the Moon[7,8], slopes in lunar craters can now be obtained at baselines as low as 6-meters allowing unprecedented multi-scale (multiple baselines) modeling possibilities for slope probability distributions. Topographic analysis (Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Camera (NAC) 2-m digital elevation models (DEM)) of ~20-km diameter Copernican lunar craters revealed generally steep slopes on interior walls (30° to 36°, locally exceeding 40°) over 15-meter baselines[9]. In this work, we extend the analysis from a probability distribution modeling point-of-view with NAC DEMs to characterize the slope statistics for the floors and walls for the same ~20-km Copernican lunar craters. The difference in slope standard deviations between the Gaussian approximation and the actual distribution (2-meter sampling) was computed over multiple scales. This slope analysis showed that local slope distributions are non-Gaussian for both crater walls and floors. Over larger baselines (~100 meters), crater wall slope probability distributions do approximate Gaussian distributions better, but have long distribution tails. Crater floor probability distributions however, were always asymmetric (for the baseline scales analyzed) and less affected by baseline scale variations. Accordingly, our results suggest that use of long tailed probability distributions (like Cauchy) and a baseline-dependant multi-scale model can be more effective in describing the slope statistics for lunar topography. Refrences: [1]Moore, H.(1971), JGR,75(11) [2]Marcus, A. H.(1969),JGR,74 (22).[3]R.J. Pike (1970),U.S. Geological Survey Working Paper [4]N. C. Costes, J. E. Farmer and E. B. George (1972),NASA Technical Report TR R-401 [5]M. N. Parker and G. L. Tyler(1973), Radio Science, 8(3),177-184 [6]Alekseev, V. A.et al (1968), Soviet Astronomy, Vol. 11, p.860 [7]Burns et al. (2012) Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XXXIX-B4, 483-488.[8]Smith et al. (2010) GRL 37, L18204, DOI: 10.1029/2010GL043751. [9]Wagner R., Robinson, M., Speyerer E., Mahanti, P., LPSC 2013, #2924.

CANCER CONTROL AND POPULATION SCIENCES FAST STATS

EPA Science Inventory

Fast Stats links to tables, charts, and graphs of cancer statistics for all major cancer sites by age, sex, race, and geographic area. The statistics include incidence, mortality, prevalence, and the probability of developing or dying from cancer. A large set of statistics is ava...

Use of Fermi-Dirac statistics for defects in solids

NASA Astrophysics Data System (ADS)

Johnson, R. A.

1981-12-01

The Fermi-Dirac distribution function is an approximation describing a special case of Boltzmann statistics. A general occupation probability formula is derived and a criterion given for the use of Fermi-Dirac statistics. Application to classical problems of defects in solids is discussed.

Frame synchronization methods based on channel symbol measurements

NASA Technical Reports Server (NTRS)

Dolinar, S.; Cheung, K.-M.

1989-01-01

The current DSN frame synchronization procedure is based on monitoring the decoded bit stream for the appearance of a sync marker sequence that is transmitted once every data frame. The possibility of obtaining frame synchronization by processing the raw received channel symbols rather than the decoded bits is explored. Performance results are derived for three channel symbol sync methods, and these are compared with results for decoded bit sync methods reported elsewhere. It is shown that each class of methods has advantages or disadvantages under different assumptions on the frame length, the global acquisition strategy, and the desired measure of acquisition timeliness. It is shown that the sync statistics based on decoded bits are superior to the statistics based on channel symbols, if the desired operating region utilizes a probability of miss many orders of magnitude higher than the probability of false alarm. This operating point is applicable for very large frame lengths and minimal frame-to-frame verification strategy. On the other hand, the statistics based on channel symbols are superior if the desired operating point has a miss probability only a few orders of magnitude greater than the false alarm probability. This happens for small frames or when frame-to-frame verifications are required.

The Heuristic Value of p in Inductive Statistical Inference

PubMed Central

Krueger, Joachim I.; Heck, Patrick R.

2017-01-01

Many statistical methods yield the probability of the observed data – or data more extreme – under the assumption that a particular hypothesis is true. This probability is commonly known as ‘the’ p-value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p-value has been subjected to much speculation, analysis, and criticism. We explore how well the p-value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p-value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p-value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say. PMID:28649206

The Heuristic Value of p in Inductive Statistical Inference.

PubMed

Krueger, Joachim I; Heck, Patrick R

2017-01-01

Many statistical methods yield the probability of the observed data - or data more extreme - under the assumption that a particular hypothesis is true. This probability is commonly known as 'the' p -value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p -value has been subjected to much speculation, analysis, and criticism. We explore how well the p -value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p -value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p -value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say.

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

Sampaio, R.; Suomela, S.; Ala-Nissila, T.; Anders, J.; Philbin, T. G.

2018-01-01

At nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.

Misinterpretation of statistical distance in security of quantum key distribution shown by simulation

NASA Astrophysics Data System (ADS)

Iwakoshi, Takehisa; Hirota, Osamu

2014-10-01

This study will test an interpretation in quantum key distribution (QKD) that trace distance between the distributed quantum state and the ideal mixed state is a maximum failure probability of the protocol. Around 2004, this interpretation was proposed and standardized to satisfy both of the key uniformity in the context of universal composability and operational meaning of the failure probability of the key extraction. However, this proposal has not been verified concretely yet for many years while H. P. Yuen and O. Hirota have thrown doubt on this interpretation since 2009. To ascertain this interpretation, a physical random number generator was employed to evaluate key uniformity in QKD. In this way, we calculated statistical distance which correspond to trace distance in quantum theory after a quantum measurement is done, then we compared it with the failure probability whether universal composability was obtained. As a result, the degree of statistical distance of the probability distribution of the physical random numbers and the ideal uniformity was very large. It is also explained why trace distance is not suitable to guarantee the security in QKD from the view point of quantum binary decision theory.

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

NASA Technical Reports Server (NTRS)

Pierson, Willard J., Jr.

1989-01-01

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

A method of classification for multisource data in remote sensing based on interval-valued probabilities

NASA Technical Reports Server (NTRS)

Kim, Hakil; Swain, Philip H.

1990-01-01

An axiomatic approach to intervalued (IV) probabilities is presented, where the IV probability is defined by a pair of set-theoretic functions which satisfy some pre-specified axioms. On the basis of this approach representation of statistical evidence and combination of multiple bodies of evidence are emphasized. Although IV probabilities provide an innovative means for the representation and combination of evidential information, they make the decision process rather complicated. It entails more intelligent strategies for making decisions. The development of decision rules over IV probabilities is discussed from the viewpoint of statistical pattern recognition. The proposed method, so called evidential reasoning method, is applied to the ground-cover classification of a multisource data set consisting of Multispectral Scanner (MSS) data, Synthetic Aperture Radar (SAR) data, and digital terrain data such as elevation, slope, and aspect. By treating the data sources separately, the method is able to capture both parametric and nonparametric information and to combine them. Then the method is applied to two separate cases of classifying multiband data obtained by a single sensor. In each case a set of multiple sources is obtained by dividing the dimensionally huge data into smaller and more manageable pieces based on the global statistical correlation information. By a divide-and-combine process, the method is able to utilize more features than the conventional maximum likelihood method.

Atom counting in HAADF STEM using a statistical model-based approach: methodology, possibilities, and inherent limitations.

PubMed

De Backer, A; Martinez, G T; Rosenauer, A; Van Aert, S

2013-11-01

In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration. © 2013 Elsevier B.V. All rights reserved.

An evaluation of the NASA/GSFC Barnes field spectral reflectometer model 14-758, using signal/noise as a measure of utility

NASA Astrophysics Data System (ADS)

Bell, R.; Labovitz, M. L.

1982-07-01

A Barnes field spectral reflectometer which collected information in 373 channels covering the region from 0.4 to 2.5 micrometers was assessed for signal utility. A band was judged unsatisfactory if the probability was 0.1 or greater than its signal to noise ratio was less than eight to one. For each of the bands the probability of a noisy observation was estimated under a binomial assumption from a set of field crop spectra covering an entire growing season. A 95% confidence interval was calculated about each estimate and bands whose lower confidence limits were greater than 0.1 were judged unacceptable. As a result, 283 channels were deemed statistically satisfactory. Excluded channels correspond to portions of the electromagnetic spectrum (EMS) where high atmospheric absorption and filter wheel overlap occur. In addition, the analyses uncovered intervals of unsatisfactory detection capability within the blue, red and far infrared regions of vegetation spectra. From the results of the analysis it was recommended that 90 channels monitored by the instrument under consideration be eliminated from future studies. These channels are tabulated and discussed.

An evaluation of the NASA/GSFC Barnes field spectral reflecometer model 14-758, using signal/noise as a measure of utility

NASA Technical Reports Server (NTRS)

Bell, R.; Labovitz, M. L.

1982-01-01

A Barnes field spectral reflectometer which collected information in 373 channels covering the region from 0.4 to 2.5 micrometers was assessed for signal utility. A band was judged unsatisfactory if the probability was 0.1 or greater than its signal to noise ratio was less than eight to one. For each of the bands the probability of a noisy observation was estimated under a binomial assumption from a set of field crop spectra covering an entire growing season. A 95% confidence interval was calculated about each estimate and bands whose lower confidence limits were greater than 0.1 were judged unacceptable. As a result, 283 channels were deemed statistically satisfactory. Excluded channels correspond to portions of the electromagnetic spectrum (EMS) where high atmospheric absorption and filter wheel overlap occur. In addition, the analyses uncovered intervals of unsatisfactory detection capability within the blue, red and far infrared regions of vegetation spectra. From the results of the analysis it was recommended that 90 channels monitored by the instrument under consideration be eliminated from future studies. These channels are tabulated and discussed.

Statistically based material properties: A military handbook-17 perspective

NASA Technical Reports Server (NTRS)

Neal, Donald M.; Vangel, Mark G.

1990-01-01

The statistical procedures and their importance in obtaining composite material property values in designing structures for aircraft and military combat systems are described. The property value is such that the strength exceeds this value with a prescribed probability with 95 percent confidence in the assertion. The survival probabilities are the 99th percentile and 90th percentile for the A and B basis values respectively. The basis values for strain to failure measurements are defined in a similar manner. The B value is the primary concern.