Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap
Flachaire, Emmanuel
2005-01-01
International audience In regression models, appropriate bootstrap methods for inference robust to heteroskedasticity of unknown form are the wild bootstrap and the pairs bootstrap. The finite sample performance of a heteroskedastic-robust test is investigated with Monte Carlo experiments. The simulation results suggest that one specific version of the wild bootstrap outperforms the other versions of the wild bootstrap and of the pairs bootstrap. It is the only one for which the bootstrap ...
Bootstrapping Macroeconometric Models
2001-01-01
This paper outlines a bootstrapping approach to the estimation and analysis of macroeconometric models. It integrates for dynamic, nonlinear, simultaneous equation models the bootstrapping approach to evaluating estimators initiated by Efron (1979) and the stochastic simulation approach to evaluating models' properties initiated by Adelman and Adelman (1959). It also estimates for a particular model the gain in coverage accuracy from using bootstrap confidence intervals over asymptotic confid...
Bootstrap and Wild Bootstrap for High Dimensional Linear Models
Mammen, Enno
1993-01-01
In this paper two bootstrap procedures are considered for the estimation of the distribution of linear contrasts and of F-test statistics in high dimensional linear models. An asymptotic approach will be chosen where the dimension p of the model may increase for sample size $n\\rightarrow\\infty$. The range of validity will be compared for the normal approximation and for the bootstrap procedures. Furthermore, it will be argued that the rates of convergence are different for the bootstrap proce...
Unsupervised model compression for multilayer bootstrap networks
ZHANG, XIAO-LEI
2015-01-01
Recently, multilayer bootstrap network (MBN) has demonstrated promising performance in unsupervised dimensionality reduction. It can learn compact representations in standard data sets, i.e. MNIST and RCV1. However, as a bootstrap method, the prediction complexity of MBN is high. In this paper, we propose an unsupervised model compression framework for this general problem of unsupervised bootstrap methods. The framework compresses a large unsupervised bootstrap model into a small model by ta...
Statistical bootstrap model and annihilations
Möhring, H J
1974-01-01
The statistical bootstrap model (SBM) describes the decay of single, high mass, hadronic states (fireballs, clusters) into stable particles. Coupling constants B, one for each isospin multiplet of stable particles, are the only free parameter of the model. They are related to the maximum temperature parameter T/sub 0/. The various versions of the SMB can be classified into two groups: full statistical bootstrap models and linear ones. The main results of the model are the following: i) All momentum spectra are isotropic; especially the exclusive ones are described by invariant phase space. The inclusive and semi-inclusive single-particle distributions are asymptotically of pure exponential shape; the slope is governed by T /sub 0/ only. ii) The model parameter B for pions has been obtained by fitting the multiplicity distribution in pp and pn at rest, and corresponds to T/sub 0/=0.167 GeV in the full SBM with exotics. The average pi /sup -/ multiplicity for the linear and the full SBM (both with exotics) is c...
Limitations of bootstrap current models
We assess the accuracy and limitations of two analytic models of the tokamak bootstrap current: (1) the well-known Sauter model (1999 Phys. Plasmas 6 2834, 2002 Phys. Plasmas 9 5140) and (2) a recent modification of the Sauter model by Koh et al (2012 Phys. Plasmas 19 072505). For this study, we use simulations from the first-principles kinetic code NEO as the baseline to which the models are compared. Tests are performed using both theoretical parameter scans as well as core-to-edge scans of real DIII-D and NSTX plasma profiles. The effects of extreme aspect ratio, large impurity fraction, energetic particles, and high collisionality are studied. In particular, the error in neglecting cross-species collisional coupling—an approximation inherent to both analytic models—is quantified. Furthermore, the implications of the corrections from kinetic NEO simulations on MHD equilibrium reconstructions is studied via integrated modeling with kinetic EFIT. (paper)
A new approach to bootstrap inference in functional coefficient models
Herwartz, Helmut; Xu, Fang
2007-01-01
We introduce a new, factor based bootstrap approach which is robust under heteroskedastic error terms for inference in functional coefficient models. Modeling the functional coefficient parametrically, the bootstrap approximation of an F statistic is shown to hold asymptotically. In simulation studies with both parametric and nonparametric functional coefficients, factor based bootstrap inference outperforms the wild bootstrap and pairs bootstrap approach according to its size features. Apply...
Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models
Goncalves, Silvia; White, Halbert
2002-01-01
The bootstrap is an increasingly popular method for performing statistical inference. This paper provides the theoretical foundation for using the bootstrap as a valid tool of inference for quasi-maximum likelihood estimators (QMLE). We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply our results to two block bootstrap methods, the moving blocks bootstrap of Künsch (1989) and Liu a...
Bootstrapped models for intrinsic random functions
Campbell, K.
1988-08-01
Use of intrinsic random function stochastic models as a basis for estimation in geostatistical work requires the identification of the generalized covariance function of the underlying process. The fact that this function has to be estimated from data introduces an additional source of error into predictions based on the model. This paper develops the sample reuse procedure called the bootstrap in the context of intrinsic random functions to obtain realistic estimates of these errors. Simulation results support the conclusion that bootstrap distributions of functionals of the process, as well as their kriging variance, provide a reasonable picture of variability introduced by imperfect estimation of the generalized covariance function.
Non-Parametric Data Dependent Bootstrap for Conditional Moment Model
Bruce E. Hansen
2000-01-01
A new non-parametric bootstrap is introduced for dependent data. The bootstrap is based on a weighted empirical-likelihood estimate of the one-step-ahead conditional distribution, imposing the conditional moment restrictions implied by the model. This is the first dependent-data bootstrap procedure which imposes conditional moment restrictions on a bootstrap distribution. The method can be applied to form confidence intervals and p-values from hypothesis tests in Generalized Method of Moments...
Bootstrapped models for intrinsic random functions
Campbell, K.
1987-01-01
The use of intrinsic random function stochastic models as a basis for estimation in geostatistical work requires the identification of the generalized covariance function of the underlying process, and the fact that this function has to be estimated from the data introduces an additional source of error into predictions based on the model. This paper develops the sample reuse procedure called the ''bootstrap'' in the context of intrinsic random functions to obtain realistic estimates of these errors. Simulation results support the conclusion that bootstrap distributions of functionals of the process, as well as of their ''kriging variance,'' provide a reasonable picture of the variability introduced by imperfect estimation of the generalized covariance function.
Model Based Bootstrap Methods for Interval Censored Data
Sen, Bodhisattva; Xu, Gongjun
2013-01-01
We investigate the performance of model based bootstrap methods for constructing point-wise confidence intervals around the survival function with interval censored data. We show that bootstrapping from the nonparametric maximum likelihood estimator of the survival function is inconsistent for both the current status and case 2 interval censoring models. A model based smoothed bootstrap procedure is proposed and shown to be consistent. In addition, simulation studies are conducted to illustra...
Bootstrap determination of the cointegration rank in heteroskedastic VAR models
Cavaliere, Guiseppe; Rahbæk, Anders; Taylor, A.M. Robert
2014-01-01
In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio (PLR) co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of...... the underlying vector autoregressive (VAR) model which obtain under the reduced rank null hypothesis. They propose methods based on an independent and individual distributed (i.i.d.) bootstrap resampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co......-integrated VAR model with i.i.d. innovations. In this paper we investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap resampling scheme, when time-varying behavior is present in either the conditional or unconditional variance of the innovations. We...
The wild bootstrap for multilevel models
Modugno, Lucia; Giannerini, Simone
2015-01-01
In this paper we study the performance of the most popular bootstrap schemes for multilevel data. Also, we propose a modified version of the wild bootstrap procedure for hierarchical data structures. The wild bootstrap does not require homoscedasticity or assumptions on the distribution of the error processes. Hence, it is a valuable tool for robust inference in a multilevel framework. We assess the finite size performances of the schemes through a Monte Carlo study. The results show that for...
A model study in hadron statistical bootstrap
Hagedorn, Rolf
1973-01-01
In the framework of the statistical bootstrap the decay of a fireball is considered as an exact inverse of its statistical composition. This assumption leads to a bootstrap formulated in terms of integral equations for all kinds of distributions of the fireball's decay products. Solutions of the equations are obtained in terms of power series and of K-transforms and determine in the general case their asymptotic behaviour for large fireball mass. Relations to a thermodynamical description are established and illustrated by effective temperatures. The approach to the asymptotic limits is easy to investigate in a simplified linear bootstrap where the K-transforms can be more explicitly calculated. (30 refs).
Bootstrap inference longitudinal semiparametric regression model
Pane, Rahmawati; Otok, Bambang Widjanarko; Zain, Ismaini; Budiantara, I. Nyoman
2016-02-01
Semiparametric regression contains two components, i.e. parametric and nonparametric component. Semiparametric regression model is represented by yt i=μ (x˜'ti,zt i)+εt i where μ (x˜'ti,zt i)=x˜'tiβ ˜+g (zt i) and yti is response variable. It is assumed to have a linear relationship with the predictor variables x˜'ti=(x1 i 1,x2 i 2,…,xT i r) . Random error εti, i = 1, …, n, t = 1, …, T is normally distributed with zero mean and variance σ2 and g(zti) is a nonparametric component. The results of this study showed that the PLS approach on longitudinal semiparametric regression models obtain estimators β˜^t=[X'H(λ)X]-1X'H(λ )y ˜ and g˜^λ(z )=M (λ )y ˜ . The result also show that bootstrap was valid on longitudinal semiparametric regression model with g^λ(b )(z ) as nonparametric component estimator.
Bootstrap tests in linear models with many regressors
Patrick Richard
2014-01-01
This paper is concerned with bootstrap hypothesis testing in high dimensional linear regression models. Using a theoretical framework recently introduced by Anatolyev (2012), we show that bootstrap F, LR and LM tests are asymptotically valid even when the numbers of estimated parameters and tested restrictions are not asymptotically negligible fractions of the sample size. These results are derived for models with iid error terms, but Monte Carlo evidence suggests that they extend to the wild...
No unitary bootstrap for the fractal Ising model
Golden, John
2015-01-01
We consider the conformal bootstrap for spacetime dimension $1
Bootstrapping Critical Ising Model on Three Dimensional Real Projective Space
Nakayama, Yu
2016-04-01
Given conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three dimensional real projective space. We check the rapid convergence of our bootstrap program in two dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three dimensional real projective space is less than 1%. Our method opens up a novel way to solve conformal field theories on nontrivial geometries.
Automatic bootstrapping of a morphable face model using multiple components
Haar, F.B. ter; Veltkamp, R.C.
2009-01-01
We present a new bootstrapping algorithm to automatically enhance a 3D morphable face model with new face data. Our algorithm is based on a morphable model fitting method that uses a set of predefined face components. This fitting method produces accurate model fits to 3D face data with noise and ho
A Bootstrap Cointegration Rank Test for Panels of VAR Models
Callot, Laurent
functions of the individual Cointegrated VARs (CVAR) models. A bootstrap based procedure is used to compute empirical distributions of the trace test statistics for these individual models. From these empirical distributions two panel trace test statistics are constructed. The satisfying small sample...
More on analytic bootstrap for O(N) models
Dey, Parijat; Sen, Kallol
2016-01-01
This note is an extension of a recent work on the analytical bootstrapping of $O(N)$ models. An additonal feature of the $O(N)$ model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor $(T_{\\mu\
Urbanski, P.; Kowalska, E.
1997-12-31
The principle of the bootstrap methodology applied for the assessment of parameters and prediction ability of the linear regression models was presented. Application of this method was shown on the example of calibration of the radioisotope sulphuric acid concentration gauge. The bootstrap method allows to determine not only the numerical values of the regression coefficients, but also enables to investigate their distributions. (author). 11 refs, 12 figs, 3 tabs.
A Bootstrap Cointegration Rank Test for Panels of VAR Models
Callot, Laurent
2010-01-01
This paper proposes a sequential procedure to determine the common cointegration rank of panels of cointegrated VARs. It shows how a panel of cointegrated VARs can be transformed in a set of independent individual models. The likelihood function of the transformed panel is the sum of the likelihood functions of the individual Cointegrated VARs (CVAR) models. A bootstrap based procedure is used to compute empirical distributions of the trace test statistics for these individual models. From th...
BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES
林路; 张润楚
2004-01-01
This paper introduces a method of bootstrap wavelet estimation in a nonparametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estimators are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes.
MacKinnon, James G.
2007-01-01
This paper surveys bootstrap and Monte Carlo methods for testing hypotheses in econometrics. Several different ways of computing bootstrap P values are discussed, including the double bootstrap and the fast double bootstrap. It is emphasized that there are many different procedures for generating bootstrap samples for regression models and other types of model. As an illustration, a simulation experiment examines the performance of several methods of bootstrapping the supF test for structural...
Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models
Cavaliere, Giuseppe; Rahbek, Anders; Taylor, A. M. Robert
In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of...... the underlying VAR model which obtain under the reduced rank null hypothesis. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations. In this paper we...... investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically...
Bootstrap Determination of the Co-integration Rank in Heteroskedastic VAR Models
Cavaliere, Giuseppe; Rahbek, Anders; Taylor, A.M.Robert
In a recent paper Cavaliere et al. (2012) develop bootstrap implementations of the (pseudo-) likelihood ratio [PLR] co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of...... the underlying VAR model which obtain under the reduced rank null hypothesis. They propose methods based on an i.i.d. bootstrap re-sampling scheme and establish the validity of their proposed bootstrap procedures in the context of a co-integrated VAR model with i.i.d. innovations. In this paper we...... investigate the properties of their bootstrap procedures, together with analogous procedures based on a wild bootstrap re-sampling scheme, when time-varying behaviour is present in either the conditional or unconditional variance of the innovations. We show that the bootstrap PLR tests are asymptotically...
Full Hirshman-Sigmar model for bootstrap current estimate in the ETE small aspect ratio Tokamak
An estimate of the bootstrap current through the full Hirshman-Sigmar model, which is the most accurate available for thermal plasmas up to now, will be carried out the ETE tokamak. These results will be compared to previous calculations performed with the single-ion collisionless Hirshman model in order to check possible limitations imposed by this model on the bootstrap current estimate. The dependences of the bootstrap current profile upon the plasma parameters will also be briefly illustrated. (author)
Cluster expansion in the truncated bootstrap model and linear graphs theory
Using the formalism of linear graphs theory, we obtain the cluster expansion for the grand potential of interacting hadronic systems in the framework of the truncated bootstrap model. We show that the coefficients of the expansion are constructed from two classes of Cayley-tree graphs contributing with opposite sign, related to the two-phase nature of the truncated bootstrap model. (orig.)
The critical behavior of hadronic matter: Comparison of lattice and bootstrap model calculations
Turko, L.
2015-01-01
Statistical bootstrap model and the related concept of the limiting temperature begun the discussion about phase transitions in the hadronic matter. This was also the origin of the quark-gluon plazma concept. We discuss here to which extend lattice studies of QCD critical behavior at non-zero chemical potential are compatible with the statistical bootstrap model calculations.
Bootstrapping and Bartlett corrections in the cointegrated VAR model
P.H. Omtzigt; S. Fachin
2003-01-01
The small sample properties of tests on long-run coefficients in cointegrated systems are still a matter of concern to applied econometricians. We compare the performance of the Bartlett correction, the bootstrap and the fast double bootstrap for tests on ccointegration parameters in the maximum lik
Bootstrapping and Bartlett corrections in the cointegrated VAR model
Omtzigt, P.H.; Fachin, S.
2002-01-01
The small sample properties of tests on long-run coefficients in cointegrated systems are still a matter of concern to applied econometricians. We compare the performance of the Bartlett correction, the bootstrap and the fast double bootstrap for tests on ccointegration parameters in the maximum likelihood framework. We show by means of a theoretical result and simulations that all three procedures should be based on the unrestricted estimate of the cointegration vectors. The fast double boot...
More on analytic bootstrap for O( N) models
Dey, Parijat; Kaviraj, Apratim; Sen, Kallol
2016-06-01
This note is an extension of a recent work on the analytical bootstrapping of O( N) models. An additonal feature of the O( N) model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor ( T μν ) and the ϕ i ϕ i scalar, we also have other minimal twist operators as the spin-1 current J μ and the symmetric-traceless scalar in the case of O( N). We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the O( N) model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the ɛ-expansion are an exact match with our n = 0 case. A plausible holographic setup for the special case when N = 2 is also mentioned which mimics the calculation in the CFT.
Bootstrap current in low aspect ratio tokamaks using Maschke equilibrium model
A study of relevant aspects of equilibrium and bootstrap current in low-aspect-ratio tokamaks is made using the Maschke equilibrium model, which provides analytic and exact solution of the Grad-Shafranov equation. The current profile in the Maschke model is parabolic, which is a good approximation for actual experimentally observed ones. The results are compared with the Soloviev equilibrium model, that has the current profile almost flat. It is shown that the bootstrap current depends on the geometrical parameter of the plasma column, that is, elongation. The bootstrap current increases with the inverse aspect ratio for elongated cross-section of the plasma column. (author). 6 refs., 2 figs
Splicing and bootstrapping methods for coupling primary DORT/TORT models to secondary TORT models
Two computer programmes are provided in the DOORS package which enable the user to splice or bootstrap models together. TORSED couples a DORT RZ calculation with an XYZ TORT calculation, and TORSET couples two XYZ TORT models. Each of these codes maps directional flux from the internal boundary of one problem to an external boundary of the other problem. This bootstrapping approach allows the solution of problems too large to be treated as one unit. The technique, also referred to as splicing, can allow details of a small section of a problem to be changed repeatedly without recalculating the flux environment surrounding the section. (author)
Bootstrap Methods in Econometrics
MacKinnon, James G.
2006-01-01
There are many bootstrap methods that can be used for econometric analysis. In certain circumstances, such as regression models with independent and identically distributed error terms, appropriately chosen bootstrap methods generally work very well. However, there are many other cases, such as regression models with dependent errors, in which bootstrap methods do not always work well. This paper discusses a large number of bootstrap methods that can be useful in econometrics. Applications to...
Mitterpach, Róbert
2012-01-01
Aim of this thesis is to introduce the reader to the basic bootstrap techniques used in econometrics, to present their variations and importance. Results of the ordinary least squares model, residual bootstrap and case resampling bootstrap will be presented and compared on cross-sectional data and time series from small numbered random subsample from the available data. Bootstrap was shown to improve numerical performance of ordinary least squares model.
A bootstrap based space-time surveillance model with an application to crime occurrences
Kim, Youngho; O'Kelly, Morton
2008-06-01
This study proposes a bootstrap-based space-time surveillance model. Designed to find emerging hotspots in near-real time, the bootstrap based model is characterized by its use of past occurrence information and bootstrap permutations. Many existing space-time surveillance methods, using population at risk data to generate expected values, have resulting hotspots bounded by administrative area units and are of limited use for near-real time applications because of the population data needed. However, this study generates expected values for local hotspots from past occurrences rather than population at risk. Also, bootstrap permutations of previous occurrences are used for significant tests. Consequently, the bootstrap-based model, without the requirement of population at risk data, (1) is free from administrative area restriction, (2) enables more frequent surveillance for continuously updated registry database, and (3) is readily applicable to criminology and epidemiology surveillance. The bootstrap-based model performs better for space-time surveillance than the space-time scan statistic. This is shown by means of simulations and an application to residential crime occurrences in Columbus, OH, year 2000.
Bootstrap, Wild Bootstrap and Generalized Bootstrap
Mammen, Enno
1995-01-01
Some modifications and generalizations of the bootstrap procedurehave been proposed. In this note we will consider the wild bootstrap and the generalized bootstrap and we will give two arguments why it makes sense touse these modifications instead of the original bootstrap. The firstargument is that there exist examples where generalized and wild bootstrapwork, but where the original bootstrap fails and breaks down. The secondargument will be based on higher order considerations. We will show...
Tiwari, Mukesh K.; Adamowski, Jan
2013-10-01
A new hybrid wavelet-bootstrap-neural network (WBNN) model is proposed in this study for short term (1, 3, and 5 day; 1 and 2 week; and 1 and 2 month) urban water demand forecasting. The new method was tested using data from the city of Montreal in Canada. The performance of the WBNN method was compared with the autoregressive integrated moving average (ARIMA) and autoregressive integrated moving average model with exogenous input variables (ARIMAX), traditional NNs, wavelet analysis-based NNs (WNN), bootstrap-based NNs (BNN), and a simple naïve persistence index model. The WBNN model was developed as an ensemble of several NNs built using bootstrap resamples of wavelet subtime series instead of raw data sets. The results demonstrated that the hybrid WBNN and WNN models produced significantly more accurate forecasting results than the traditional NN, BNN, ARIMA, and ARIMAX models. It was also found that the WBNN model reduces the uncertainty associated with the forecasts, and the performance of WBNN forecasted confidence bands was found to be more accurate and reliable than BNN forecasted confidence bands. It was found in this study that maximum temperature and total precipitation improved the accuracy of water demand forecasts using wavelet analysis. The performance of WBNN models was also compared for different numbers of bootstrap resamples (i.e., 25, 50, 100, 200, and 500) and it was found that WBNN models produced optimum results with different numbers of bootstrap resamples for different lead time forecasts with considerable variability.
Treyens, Pierre-Eric
2008-01-01
We consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Then, by using Edgeworth expansions, we compute the exact errors in the rejection probability (ERPs) for all one-restriction tests (asymptotic and bootstrap) which can occur in these linear models. More precisely, we show that the ERP is the same for the asymptotic test as for the classical parametric bootstrap test it is based on as soon as the third cumulant is nonnul. On the other sid...
Bootstrapping critical Ising model on three-dimensional real projective space
Nakayama, Yu
2016-01-01
Given a conformal data on a flat Euclidean space, we use crosscap conformal bootstrap equations to numerically solve the Lee-Yang model as well as the critical Ising model on a three-dimensional real projective space. We check the rapid convergence of our bootstrap program in two-dimensions from the exact solutions available. Based on the comparison, we estimate that our systematic error on the numerically solved one-point functions of the critical Ising model on a three-dimensional real projective space is less than one percent. Our method opens up a novel way to solve conformal field theories on non-trivial geometries.
Janitza, Silke; Binder, Harald; Boulesteix, Anne-Laure
2016-05-01
The bootstrap method has become a widely used tool applied in diverse areas where results based on asymptotic theory are scarce. It can be applied, for example, for assessing the variance of a statistic, a quantile of interest or for significance testing by resampling from the null hypothesis. Recently, some approaches have been proposed in the biometrical field where hypothesis testing or model selection is performed on a bootstrap sample as if it were the original sample. P-values computed from bootstrap samples have been used, for example, in the statistics and bioinformatics literature for ranking genes with respect to their differential expression, for estimating the variability of p-values and for model stability investigations. Procedures which make use of bootstrapped information criteria are often applied in model stability investigations and model averaging approaches as well as when estimating the error of model selection procedures which involve tuning parameters. From the literature, however, there is evidence that p-values and model selection criteria evaluated on bootstrap data sets do not represent what would be obtained on the original data or new data drawn from the overall population. We explain the reasons for this and, through the use of a real data set and simulations, we assess the practical impact on procedures relevant to biometrical applications in cases where it has not yet been studied. Moreover, we investigate the behavior of subsampling (i.e., drawing from a data set without replacement) as a potential alternative solution to the bootstrap for these procedures. PMID:26372408
The use of vector bootstrapping to improve variable selection precision in Lasso models.
Laurin, Charles; Boomsma, Dorret; Lubke, Gitta
2016-08-01
The Lasso is a shrinkage regression method that is widely used for variable selection in statistical genetics. Commonly, K-fold cross-validation is used to fit a Lasso model. This is sometimes followed by using bootstrap confidence intervals to improve precision in the resulting variable selections. Nesting cross-validation within bootstrapping could provide further improvements in precision, but this has not been investigated systematically. We performed simulation studies of Lasso variable selection precision (VSP) with and without nesting cross-validation within bootstrapping. Data were simulated to represent genomic data under a polygenic model as well as under a model with effect sizes representative of typical GWAS results. We compared these approaches to each other as well as to software defaults for the Lasso. Nested cross-validation had the most precise variable selection at small effect sizes. At larger effect sizes, there was no advantage to nesting. We illustrated the nested approach with empirical data comprising SNPs and SNP-SNP interactions from the most significant SNPs in a GWAS of borderline personality symptoms. In the empirical example, we found that the default Lasso selected low-reliability SNPs and interactions which were excluded by bootstrapping. PMID:27248122
Rubin, Donald B.
1981-01-01
The Bayesian bootstrap is the Bayesian analogue of the bootstrap. Instead of simulating the sampling distribution of a statistic estimating a parameter, the Bayesian bootstrap simulates the posterior distribution of the parameter; operationally and inferentially the methods are quite similar. Because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions, neither method should be applied wit...
The following applications of the statistical bootstrap model (SBM) to hadron production in hadron-hadron collisions are discussed: (1) the independent fireball production model (IFPM); (2) single particle distributions in the IFPM (thermodynamic model); (3) production of heavy particles and pairs of heavy particles; (4) two-particle distributions and correlations in the IFPM and the Bose effect; (5) large psub(perpendicular) phenomena and fireball models; (6) N anti N annihilation at rest in the SBM. (author)
Niska, Christoffer
2014-01-01
Practical and instruction-based, this concise book will take you from understanding what Bootstrap is, to creating your own Bootstrap theme in no time! If you are an intermediate front-end developer or designer who wants to learn the secrets of Bootstrap, this book is perfect for you.
Bootstrapping the portmanteau tests in weak auto-regressive moving average models
Zhu, Ke
2015-01-01
This paper uses a random weighting (RW) method to bootstrap the critical values for the Ljung-Box/Monti portmanteau tests and weighted Ljung-Box/Monti portmanteau tests in weak ARMA models. Unlike the existing methods, no user-chosen parameter is needed to implement the RW method. As an application, these four tests are used to check the model adequacy in power GARCH models. Simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests...
Daniel Grenouilleau
2006-01-01
The paper introduces an approximate dynamic factor model based on the extraction of principal components from a very large number of leading indicators stacked at various lags. The model is designed to produce short-term forecasts that are computed with the EM algorithm implemented with the first few eigenvectors ordered by descending eigenvalues. A cross-sectional bootstrap experiment is used to shed light on the sensitivity of the factor model to factor selection and to sampling uncertainty...
Bootstrap Results From the State Space From Representation of the Heath-Jarrow-Morton Model
Ram Bhar; Carl Chiarella
1996-01-01
This paper builds upon the authors' previous work on transformation of the Heath-Jarrow-Morton (HJM) model of the term structure of interest rates to state space form for a fairly general class of volatility specification including stochastic variables. Estimation of this volatility function is at the heart of the identification of the HJM model. The paper develops a bootstrap procedure for the HJM model cast into the non-linear filtering framework to analyse the statistical significance of t...
Forecasting Model for IPTV Service in Korea Using Bootstrap Ridge Regression Analysis
Lee, Byoung Chul; Kee, Seho; Kim, Jae Bum; Kim, Yun Bae
The telecom firms in Korea are taking new step to prepare for the next generation of convergence services, IPTV. In this paper we described our analysis on the effective method for demand forecasting about IPTV broadcasting. We have tried according to 3 types of scenarios based on some aspects of IPTV potential market and made a comparison among the results. The forecasting method used in this paper is the multi generation substitution model with bootstrap ridge regression analysis.
Violation of KNO scaling and the NBD phenomenon in the framework of the statistical bootstrap model
Kokoulina, E. S.; Kuvshinov, V. I.
1991-05-01
The connection is considered of multiplicity distributions in three stages: partonic, hadronization, and hadronic. An interpretation of the LoPHD parameter is found. It is shown that under specific hypotheses on the form of the mass spectrum, the statistical bootstrap model leads to the negative binomial distribution (NBD) at the hadronic stage of development of the multiple production process with specific analytic dependences of the parameters of the NBD.
Theoretical and computational analyses of bootstrapped tokamaks with oscillating field current drive (OFCD) have been developed using a nonlinear magnetic helicity model. Assuming a rigid current profile, the conditions for optimal tokamak steady-state operation are derived and are shown to agree with the results of computer calculations. Generalized limit formulae for the toroidal plasma beta and bootstrap current fraction are also obtained. The results of the analyses indicate that steady-state bootstrapped tokamak operation with high toroidal plasma beta can best be achieved in tight aspect ratio A → 1 reactors with OFCD supplying as much as a quarter of the total toroidal plasma current. (author)
Chen, Xuan; Goodwin, Barry K.
2012-01-01
Our study focuses on modeling wildfire damage in the State of Florida. The approach is to evaluate wildfire risks in a spatio-temporal framework. A block bootstrapping method has been proposed to construct a statistical model accounting for explanatory variables while adjusting for spatial and temporal autocorrelation. Although the bootstrap (Efron 1979) method can handle independent observations well, the strong autocorrelation of wildfire risks brings about a major challenge. Motivated by b...
Bootstrap data methodology for sequential hybrid model building
Volponi, Allan J. (Inventor); Brotherton, Thomas (Inventor)
2007-01-01
A method for modeling engine operation comprising the steps of: 1. collecting a first plurality of sensory data, 2. partitioning a flight envelope into a plurality of sub-regions, 3. assigning the first plurality of sensory data into the plurality of sub-regions, 4. generating an empirical model of at least one of the plurality of sub-regions, 5. generating a statistical summary model for at least one of the plurality of sub-regions, 6. collecting an additional plurality of sensory data, 7. partitioning the second plurality of sensory data into the plurality of sub-regions, 8. generating a plurality of pseudo-data using the empirical model, and 9. concatenating the plurality of pseudo-data and the additional plurality of sensory data to generate an updated empirical model and an updated statistical summary model for at least one of the plurality of sub-regions.
Pragmatic Bootstrapping: A Neural Network Model of Vocabulary Acquisition
Caza, Gregory A.; Knott, Alistair
2012-01-01
The social-pragmatic theory of language acquisition proposes that children only become efficient at learning the meanings of words once they acquire the ability to understand the intentions of other agents, in particular the intention to communicate (Akhtar & Tomasello, 2000). In this paper we present a neural network model of word learning which…
Siana Halim; Herman Mallian
2006-01-01
The Bootstrap is a lively research area. A lot Of ideas are around and have let to quiet different proposals. In this paper we sketch briefly some Bootstrap methods for independent and dependent data. Finally we give an Bootstrap example for constructing confidence interval in the forecasting for stationer data. Abstract in Bahasa Indonesia : Bootstrap merupakan area penelitian yang terus berkembang. Ada banyak ide dan proposal-proposal yang berbeda telah diberikan oleh para peneliti. Namun d...
Echeverri, Alejandro Castedo; Serone, Marco
2016-01-01
We study the numerical bounds obtained using a conformal-bootstrap method - advocated in ref. [1] but never implemented so far - where different points in the plane of conformal cross ratios $z$ and $\\bar z$ are sampled. In contrast to the most used method based on derivatives evaluated at the symmetric point $z=\\bar z =1/2$, we can consistently "integrate out" higher-dimensional operators and get a reduced simpler, and faster to solve, set of bootstrap equations. We test this "effective" bootstrap by studying the 3D Ising and $O(n)$ vector models and bounds on generic 4D CFTs, for which extensive results are already available in the literature. We also determine the scaling dimensions of certain scalar operators in the $O(n)$ vector models, with $n=2,3,4$, which have not yet been computed using bootstrap techniques.
Test of bootstrap current models using high-βp EAST-demonstration plasmas on DIII-D
Magnetic measurements together with kinetic profile and motional Stark effect measurements are used in full kinetic equilibrium reconstructions to test the Sauter and NEO bootstrap current models in a DIII-D high-βp EAST-demonstration experiment. This aims at developing on DIII-D a high bootstrap current scenario to be extended on EAST for a demonstration of true steady-state at high performance and uses EAST-similar operational conditions: plasma shape, plasma current, toroidal magnetic field, total heating power and current ramp-up rate. It is found that the large edge bootstrap current in these high-βp plasmas allows the use of magnetic measurements to clearly distinguish the two bootstrap current models. In these high collisionality and high-βp plasmas, the Sauter model overpredicts the peak of the edge current density by about 30%, while the first-principle kinetic NEO model is in close agreement with the edge current density of the reconstructed equilibrium. These results are consistent with recent work showing that the Sauter model largely overestimates the edge bootstrap current at high collisionality (Belli et al 2014 Plasma Phys. Control. Fusion 56 045006). (paper)
A bootstrapping soft shrinkage approach for variable selection in chemical modeling.
Deng, Bai-Chuan; Yun, Yong-Huan; Cao, Dong-Sheng; Yin, Yu-Long; Wang, Wei-Ting; Lu, Hong-Mei; Luo, Qian-Yi; Liang, Yi-Zeng
2016-02-18
In this study, a new variable selection method called bootstrapping soft shrinkage (BOSS) method is developed. It is derived from the idea of weighted bootstrap sampling (WBS) and model population analysis (MPA). The weights of variables are determined based on the absolute values of regression coefficients. WBS is applied according to the weights to generate sub-models and MPA is used to analyze the sub-models to update weights for variables. The optimization procedure follows the rule of soft shrinkage, in which less important variables are not eliminated directly but are assigned smaller weights. The algorithm runs iteratively and terminates until the number of variables reaches one. The optimal variable set with the lowest root mean squared error of cross-validation (RMSECV) is selected. The method was tested on three groups of near infrared (NIR) spectroscopic datasets, i.e. corn datasets, diesel fuels datasets and soy datasets. Three high performing variable selection methods, i.e. Monte Carlo uninformative variable elimination (MCUVE), competitive adaptive reweighted sampling (CARS) and genetic algorithm partial least squares (GA-PLS) are used for comparison. The results show that BOSS is promising with improved prediction performance. The Matlab codes for implementing BOSS are freely available on the website: http://www.mathworks.com/matlabcentral/fileexchange/52770-boss. PMID:26826688
Different bootstrap current formulations are implemented in a self-consistent equilibrium calculation obtained from a direct variational technique in fixed boundary tokamak plasmas. The total plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schlueter, and the neoclassical Ohmic and bootstrap currents. The Ohmic component is calculated in terms of the neoclassical conductivity, compared here among different expressions, and the loop voltage determined consistently in order to give the prescribed value of the total plasma current. A comparison among several bootstrap current models for different viscosity coefficient calculations and distinct forms for the Coulomb collision operator is performed for a variety of plasma parameters of the small aspect ratio tokamak ETE (Experimento Tokamak Esferico) at the Associated Plasma Laboratory of INPE, in Brazil. We have performed this comparison for the ETE tokamak so that the differences among all the models reported here, mainly regarding plasma collisionality, can be better illustrated. The dependence of the bootstrap current ratio upon some plasma parameters in the frame of the self-consistent calculation is also analysed. We emphasize in this paper what we call the Hirshman-Sigmar/Shaing model, valid for all collisionality regimes and aspect ratios, and a fitted formulation proposed by Sauter, which has the same range of validity but is faster to compute than the previous one. The advantages or possible limitations of all these different formulations for the bootstrap current estimate are analysed throughout this work. (author)
Andrade, Maria Celia Ramos; Ludwig, Gerson Otto [Instituto Nacional de Pesquisas Espaciais (INPE), Sao Jose dos Campos, SP (Brazil). Lab. Associado de Plasma]. E-mail: mcr@plasma.inpe.br
2004-07-01
Different bootstrap current formulations are implemented in a self-consistent equilibrium calculation obtained from a direct variational technique in fixed boundary tokamak plasmas. The total plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schlueter, and the neoclassical Ohmic and bootstrap currents. The Ohmic component is calculated in terms of the neoclassical conductivity, compared here among different expressions, and the loop voltage determined consistently in order to give the prescribed value of the total plasma current. A comparison among several bootstrap current models for different viscosity coefficient calculations and distinct forms for the Coulomb collision operator is performed for a variety of plasma parameters of the small aspect ratio tokamak ETE (Experimento Tokamak Esferico) at the Associated Plasma Laboratory of INPE, in Brazil. We have performed this comparison for the ETE tokamak so that the differences among all the models reported here, mainly regarding plasma collisionality, can be better illustrated. The dependence of the bootstrap current ratio upon some plasma parameters in the frame of the self-consistent calculation is also analysed. We emphasize in this paper what we call the Hirshman-Sigmar/Shaing model, valid for all collisionality regimes and aspect ratios, and a fitted formulation proposed by Sauter, which has the same range of validity but is faster to compute than the previous one. The advantages or possible limitations of all these different formulations for the bootstrap current estimate are analysed throughout this work. (author)
Survey bootstrap and bootstrap weights
Stas Kolenikov
2008-01-01
In this presentation, I will review the bootstrap for complex surveys with designs featuring stratification, clustering, and unequal probability weights. I will present the Stata module bsweights, which creates the bootstrap weights for designs specified through and supported by svy. I will also provide simple demonstrations highlighting the use of the procedure and its syntax. I will discuss various tuning parameters and their impact on the performance of the procedure, and I will give argum...
On the Model-Based Bootstrap with Missing Data: Obtaining a "P"-Value for a Test of Exact Fit
Savalei, Victoria; Yuan, Ke-Hai
2009-01-01
Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) for general covariance structure models and applied to structural equation modeling by Bollen and Stine…
Bo E. Honoré; Hu, Luojia
2015-01-01
The bootstrap is a convenient tool for calculating standard errors of the parameters of complicated econometric models. Unfortunately, the fact that these models are complicated often makes the bootstrap extremely slow or even practically infeasible. This paper proposes an alternative to the bootstrap that relies only on the estimation of one-dimensional parameters. The paper contains no new difficult math. But we believe that it can be useful.
Convex and Monotonic Bootstrapped Kriging
Kleijnen, Jack P.C.; Mehdad, E.; Beers, W.C.M. van
2012-01-01
Abstract: Distribution-free bootstrapping of the replicated responses of a given discreteevent simulation model gives bootstrapped Kriging (Gaussian process) metamodels; we require these metamodels to be either convex or monotonic. To illustrate monotonic Kriging, we use an M/M/1 queueing simulation with as output either the mean or the 90% quantile of the transient-state waiting times, and as input the traffic rate. In this example, monotonic bootstrapped Kriging enables better sensitivity a...
Wild Bootstrap Versus Moment-Oriented Bootstrap
Sommerfeld, Volker
1997-01-01
We investigate the relative merits of a “moment-oriented” bootstrap method of Bunke (1997) in comparison with the classical wild bootstrap of Wu (1986) in nonparametric heteroscedastic regression situations. The “moment-oriented” bootstrap is a wild bootstrap based on local estimators of higher order error moments that are smoothed by kernel smoothers. In this paper we perform an asymptotic comparison of these two dierent bootstrap procedures. We show that the moment-oriented bootstrap is in ...
Hounyo, Ulrich
-studentized statistics, our results justify using the bootstrap to esitmate the covariance matrix of a broad class of covolatility estimators. The bootstrap variance estimator is positive semi-definite by construction, an appealing feature that is not always shared by existing variance estimators of the integrated...
Pfiffner, H. J.
1969-01-01
Circuit can sample a number of transducers in sequence without drawing from them. This bootstrap unloader uses a differential amplifier with one input connected to a circuit which is the equivalent of the circuit to be unloaded, and the other input delivering the proper unloading currents.
Bhaumik, Snig
2015-01-01
If you are a web developer who designs and develops websites and pages using HTML, CSS, and JavaScript, but have very little familiarity with Bootstrap, this is the book for you. Previous experience with HTML, CSS, and JavaScript will be helpful, while knowledge of jQuery would be an extra advantage.
Bootstrap Sequential Determination of the Co-integration Rank in VAR Models
Guiseppe, Cavaliere; Rahbæk, Anders; Taylor, A.M. Robert
empirical rejection frequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the co-integrating rank based on these bootstrap tests need to be consistent, in the sense...... we fill this gap in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlo simulations show the proposed procedure performs well in practice....
Point Set Denoising Using Bootstrap-Based Radial Basis Function
Ramli, Ahmad; Abd. Majid, Ahmad
2016-01-01
This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study. PMID:27315105
Sensitivity Analysis to Efficiency Scores : How to Bootstrap in Nonparametric Frontier Models
Simar, Léopold; Wilson, Paul
1995-01-01
Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, ... ) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data generating process in this complex framework and to propose a reaso...
Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models
Simar, Léopold; Paul W. Wilson
1998-01-01
Efficiency scores of production units are generally measured relative to an estimated production frontier. Nonparametric estimators (DEA, FDH, \\cdots ) are based on a finite sample of observed production units. The bootstrap is one easy way to analyze the sensitivity of efficiency scores relative to the sampling variations of the estimated frontier. The main point in order to validate the bootstrap is to define a reasonable data-generating process in this complex framework and to propose a re...
Beran, Rudolf
1994-01-01
This essay is organized around the theoretical and computationalproblem of constructing bootstrap confidence sets, with forays into relatedtopics. The seven section headings are: Introduction; The Bootstrap World;Bootstrap Confidence Sets; Computing Bootstrap Confidence Sets; Quality ofBootstrap Confidence Sets; Iterated and Two-step Boostrap; Further Resources.
Elvarsson, B. P.; Taylor, L.; Trenkel, Verena; Kupca, V.; Stefansson, G.
2014-01-01
Statistical models of marine ecosystems use a variety of data sources to estimate parameters using composite or weighted likelihood functions with associated weighting issues and questions on how to obtain variance estimates. Regardless of the method used to obtain point estimates, a method is required for variance estimation. A bootstrap technique is introduced for the evaluation of uncertainty in such models, taking into account inherent spatial and temporal correlations in the datasets, wh...
Kapetanios, George; Weeks, Melvyn J.
2003-01-01
We consider an alternative use of simulation in the context of using the Likelihood-Ratio statistic to test non-nested models. To date simulation has been used to estimate the Kullback-Leibler measure of closeness between two densities, which in turn ?mean adjusts? the Likelihood-Ratio statistic. Given that this adjustment is still based upon asymptotic arguments, an alternative procedure is to utilise bootstrap procedures to construct the empirical density. To our knowledge this study re...
Bootstrap Sequential Determination of the Co-integration Rank in VAR Models
Cavaliere, Giuseppe; Rahbek, Anders; Taylor, A. M. Robert
empirical rejection frequencies often very much in excess of the nominal level. As a consequence, bootstrap versions of these tests have been developed. To be useful, however, sequential procedures for determining the co-integrating rank based on these bootstrap tests need to be consistent, in the sense...... that the probability of selecting a rank smaller than (equal to) the true co-integrating rank will converge to zero (one minus the marginal significance level), as the sample size diverges, for general I(1) processes. No such likelihood-based procedure is currently known to be available. In this paper...... we fill this gap in the literature by proposing a bootstrap sequential algorithm which we demonstrate delivers consistent cointegration rank estimation for general I(1) processes. Finite sample Monte Carlo simulations show the proposed procedure performs well in practice....
Chaos Expansion Based Bootstrap Filter To Calibrate CO2 Injection Models
Oladyshkin, Sergey; Schröder, Patrick; Class, Holger; Nowak, Wolfgang
2013-04-01
dependence of the model on these multipliers with the response surface. Step two consists of Bayesian updating in order to match the reduced model to past or real-time observations of system behavior (e.g. past production data or pressure at monitoring wells during a certain time period). In this step we apply Bootstrap filtering on the response surface constructed in step one. Bootstrap filtering is a fully non-linear and Bayesian approach to the inverse problem in history matching, more accurate than Ensemble Kalman filters. As a specific methodological focus, ensuring that the expansion remains optimal even if the updated parameter values are far from their prior expansion, we will iterate between Step 1 and Step 2, so that the PCE expansion will be repeated successively. This may be interpreted as a high-order expansion equivalent to successive linearization.
The bootstrap current in tokamaks
The properties of the Hirshman equation for the bootstrap in the tokamak and the difference between it and the simpler Hinton-Hazeltine equation are discussed. The Hirshman model, which takes into account finite-aspect-ratio effects, is used to calculate the bootstrap current in the plasma in a circular cross section with Te = Ti. Approximate upper and lower bounds on the bootstrap current are obtained. These restrict the range of variation of the current as the temperature and density profiles vary. 16 refs., 9 figs
A Score Based Approach to Wild Bootstrap Inference
Patrick M. Kline; Andres Santos
2010-01-01
We propose a generalization of the wild bootstrap of Wu (1986) and Liu (1988) based upon perturbing the scores of M-estimators. This "score bootstrap" procedure avoids recomputing the estimator in each bootstrap iteration, making it substantially less costly to compute than the conventional nonparametric bootstrap, particularly in complex nonlinear models. Despite this computational advantage, in the linear model, the score bootstrap studentized test statistic is equivalent to that of the con...
Magno, Alexandre
2013-01-01
A practical, step-by-step tutorial on developing websites for mobile using Bootstrap.This book is for anyone who wants to get acquainted with the new features available in Bootstrap 3 and who wants to develop websites with the mobile-first feature of Bootstrap. The reader should have a basic knowledge of Bootstrap as a frontend framework.
Poland, David; Simmons-Duffin, David
2016-06-01
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008. We report on some of the main results and ideas from this renaissance, focusing on new determinations of critical exponents and correlation functions in the three-dimensional Ising and O(N) models.
Bootstrap inference in econometrics
James G. MacKinnon
2002-01-01
The astonishing increase in computer performance over the past two decades has made it possible for economists to base many statistical inferences on simulated, or bootstrap, distributions rather than on distributions obtained from asymptotic theory. In this paper, I review some of the basic ideas of bootstrap inference. I discuss Monte Carlo tests, several types of bootstrap test, and bootstrap confidence intervals. Although bootstrapping often works well, it does not do so in every case.
Bootstrap current in a tokamak
Kessel, C.E.
1994-03-01
The bootstrap current in a tokamak is examined by implementing the Hirshman-Sigmar model and comparing the predicted current profiles with those from two popular approximations. The dependences of the bootstrap current profile on the plasma properties are illustrated. The implications for steady state tokamaks are presented through two constraints; the pressure profile must be peaked and {beta}{sub p} must be kept below a critical value.
Bootstrap current in a tokamak
The bootstrap current in a tokamak is examined by implementing the Hirshman-Sigmar model and comparing the predicted current profiles with those from two popular approximations. The dependences of the bootstrap current profile on the plasma properties are illustrated. The implications for steady state tokamaks are presented through two constraints; the pressure profile must be peaked and βp must be kept below a critical value
Applications of threshold models and the weighted bootstrap for Hungarian precipitation data
Varga, László; Rakonczai, Pál; Zempléni, András
2016-05-01
This paper presents applications of the peaks-over-threshold methodology for both the univariate and the recently introduced bivariate case, combined with a novel bootstrap approach. We compare the proposed bootstrap methods to the more traditional profile likelihood. We have investigated 63 years of the European Climate Assessment daily precipitation data for five Hungarian grid points, first separately for the summer and winter months, then aiming at the detection of possible changes by investigating 20 years moving windows. We show that significant changes can be observed both in the univariate and the bivariate cases, the most recent period being the most dangerous in several cases, as some return values have increased substantially. We illustrate these effects by bivariate coverage regions.
Model Specification Searches in Structural Equation Modeling Using Tabu Search.
Marcoulides, George A.; Drezner, Zvi; Schumacker, Randall E.
1998-01-01
Introduces an alternative structural equation modeling (SEM) specification search approach based on the Tabu search procedure. Using data with known structure, the procedure is illustrated, and its capabilities for specification searches in SEM are demonstrated. (Author/SLD)
The bootstrap current for three electron cyclotron resonance heated plasma scenarios in a quasihelically symmetric stellarator (the Helically Symmetric Experiment) are analyzed and compared to a neoclassical transport code PENTA. The three conditions correspond to 50 kW input power with a resonance that is off-axis, 50 kW on-axis heating and 100 kW on-axis heating. When the heating location was moved from off-axis to on-axis with 50 kW heating power, the stored energy and the extrapolated steady-state current were both observed to increase. When the on-axis heating power was increased from 50 kW to 100 kW, the stored energy continued to increase while the bootstrap current slightly decreased. This trend is qualitatively in agreement with the calculations which indicate that a large positive electric field for the 100 kW case was driving the current negative in a small region close to the magnetic axis and accounting for the decrease in the total integrated current. This trend in the calculations is only observed to occur when momentum conservation between particle species is included. Without momentum conservation, the calculated bootstrap current increases monotonically. We show that the magnitude of the bootstrap current as calculated by PENTA agrees better with the experiment when momentum conservation between plasma species is included in the calculation. The total current was observed in all cases to flow in a direction to unwind the transform, unlike in a tokamak in which the bootstrap current adds to the transform. The 3-D inductive response of the plasma is simulated to predict the evolution of the current profile during the discharge. The 3-D equilibrium reconstruction code V3FIT is used to reconstruct profiles of the plasma pressure and current constrained by measurements with a set of magnetic diagnostics. The reconstructed profiles are consistent with the measured plasma pressure profile and the simulated current profile when the
Bootstrapping phylogenies inferred from rearrangement data
Lin Yu
2012-08-01
Full Text Available Abstract Background Large-scale sequencing of genomes has enabled the inference of phylogenies based on the evolution of genomic architecture, under such events as rearrangements, duplications, and losses. Many evolutionary models and associated algorithms have been designed over the last few years and have found use in comparative genomics and phylogenetic inference. However, the assessment of phylogenies built from such data has not been properly addressed to date. The standard method used in sequence-based phylogenetic inference is the bootstrap, but it relies on a large number of homologous characters that can be resampled; yet in the case of rearrangements, the entire genome is a single character. Alternatives such as the jackknife suffer from the same problem, while likelihood tests cannot be applied in the absence of well established probabilistic models. Results We present a new approach to the assessment of distance-based phylogenetic inference from whole-genome data; our approach combines features of the jackknife and the bootstrap and remains nonparametric. For each feature of our method, we give an equivalent feature in the sequence-based framework; we also present the results of extensive experimental testing, in both sequence-based and genome-based frameworks. Through the feature-by-feature comparison and the experimental results, we show that our bootstrapping approach is on par with the classic phylogenetic bootstrap used in sequence-based reconstruction, and we establish the clear superiority of the classic bootstrap for sequence data and of our corresponding new approach for rearrangement data over proposed variants. Finally, we test our approach on a small dataset of mammalian genomes, verifying that the support values match current thinking about the respective branches. Conclusions Our method is the first to provide a standard of assessment to match that of the classic phylogenetic bootstrap for aligned sequences. Its
Quilty, John; Adamowski, Jan; Khalil, Bahaa; Rathinasamy, Maheswaran
2016-03-01
The input variable selection problem has recently garnered much interest in the time series modeling community, especially within water resources applications, demonstrating that information theoretic (nonlinear)-based input variable selection algorithms such as partial mutual information (PMI) selection (PMIS) provide an improved representation of the modeled process when compared to linear alternatives such as partial correlation input selection (PCIS). PMIS is a popular algorithm for water resources modeling problems considering nonlinear input variable selection; however, this method requires the specification of two nonlinear regression models, each with parametric settings that greatly influence the selected input variables. Other attempts to develop input variable selection methods using conditional mutual information (CMI) (an analog to PMI) have been formulated under different parametric pretenses such as k nearest-neighbor (KNN) statistics or kernel density estimates (KDE). In this paper, we introduce a new input variable selection method based on CMI that uses a nonparametric multivariate continuous probability estimator based on Edgeworth approximations (EA). We improve the EA method by considering the uncertainty in the input variable selection procedure by introducing a bootstrap resampling procedure that uses rank statistics to order the selected input sets; we name our proposed method bootstrap rank-ordered CMI (broCMI). We demonstrate the superior performance of broCMI when compared to CMI-based alternatives (EA, KDE, and KNN), PMIS, and PCIS input variable selection algorithms on a set of seven synthetic test problems and a real-world urban water demand (UWD) forecasting experiment in Ottawa, Canada.
Bootstrapping O( N ) vector models with four supercharges in 3 ≤ d ≤ 4
Chester, Shai M.; Iliesiu, Luca V.; Pufu, Silviu S.; Yacoby, Ran
2016-05-01
We analyze the conformal bootstrap constraints in theories with four super-charges and a global O( N ) × U(1) flavor symmetry in 3 ≤ d ≤ 4 dimensions. In particular, we consider the 4-point function of O( N )-fundamental chiral operators Z i that have no chiral primary in the O( N )-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of N + 1 chiral super-fields with superpotential W = X∑ i = 1 N Z i 2 as well as general bounds on SCFTs where ∑ i = 1 N Z i 2 vanishes in the chiral ring.
Efficient bootstrap with weakly dependent processes
Francesco Bravo; Federico Crudu
2012-01-01
The efficient bootstrap methodology is developed for overidentified moment conditions models with weakly dependent observation. The resulting bootstrap procedure is shown to be asymptotically valid and can be used to approximate the distributions of t-statistics, J statistic for overidentifying restrictions, and Wald, Lagrange multiplier and distance statistics for nonlinear hypotheses. The asymptotic validity of the efficient bootstrap based on a computationally less demanding approximate k-...
Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
Li, Zhijin
2016-01-01
We use the conformal bootstrap approach to explore $5D$ CFTs with $O(N)$ global symmetry, which contain $N$ scalars $\\phi_i$ transforming as $O(N)$ vector. Specifically, we study multiple four-point correlators of the leading $O(N)$ vector $\\phi_i$ and the $O(N)$ singlet $\\sigma$. The crossing symmetry of the four-point functions and the unitarity condition provide nontrivial constraints on the scaling dimensions ($\\Delta_\\phi$, $\\Delta_\\sigma$) of $\\phi_i$ and $\\sigma$. With reasonable assumptions on the gaps between scaling dimensions of $\\phi_i$ ($\\sigma$) and the next $O(N)$ vector (singlet) scalar, we are able to isolate the scaling dimensions $(\\Delta_\\phi$, $\\Delta_\\sigma)$ in small islands. In particular, for large $N=500$, the isolated region is highly consistent with the result obtained from large $N$ expansion. We also study the interacting $O(N)$ CFTs for $1\\leqslant N\\leqslant100$. Isolated regions on $(\\Delta_\\phi,\\Delta_\\sigma)$ plane are obtained using conformal bootstrap program with lower or...
Wöhling, T.; Schöniger, A.; Geiges, A.; Nowak, W.; Gayler, S.
2013-12-01
The objective selection of appropriate models for realistic simulations of coupled soil-plant processes is a challenging task since the processes are complex, not fully understood at larger scales, and highly non-linear. Also, comprehensive data sets are scarce, and measurements are uncertain. In the past decades, a variety of different models have been developed that exhibit a wide range of complexity regarding their approximation of processes in the coupled model compartments. We present a method for evaluating experimental design for maximum confidence in the model selection task. The method considers uncertainty in parameters, measurements and model structures. Advancing the ideas behind Bayesian Model Averaging (BMA), we analyze the changes in posterior model weights and posterior model choice uncertainty when more data are made available. This allows assessing the power of different data types, data densities and data locations in identifying the best model structure from among a suite of plausible models. The models considered in this study are the crop models CERES, SUCROS, GECROS and SPASS, which are coupled to identical routines for simulating soil processes within the modelling framework Expert-N. The four models considerably differ in the degree of detail at which crop growth and root water uptake are represented. Monte-Carlo simulations were conducted for each of these models considering their uncertainty in soil hydraulic properties and selected crop model parameters. Using a Bootstrap Filter (BF), the models were then conditioned on field measurements of soil moisture, matric potential, leaf-area index, and evapotranspiration rates (from eddy-covariance measurements) during a vegetation period of winter wheat at a field site at the Swabian Alb in Southwestern Germany. Following our new method, we derived model weights when using all data or different subsets thereof. We discuss to which degree the posterior mean outperforms the prior mean and all
Iliesiu, Luca; Kos, Filip; Poland, David; Pufu, Silviu S.; Simmons-Duffin, David; Yacoby, Ran
2016-03-01
We study the conformal bootstrap for a 4-point function of fermions in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing in fermion 4-point functions. Using these results, we find general bounds on the dimensions of operators appearing in the ψ × ψ OPE, and also on the central charge C T . We observe features in our bounds that coincide with scaling dimensions in the GrossNeveu models at large N . We also speculate that other features could coincide with a fermionic CFT containing no relevant scalar operators.
Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3 \\leq d \\leq4$
Chester, Shai M; Pufu, Silviu S; Yacoby, Ran
2015-01-01
We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N) \\times U(1)$ flavor symmetry in $3 \\leq d \\leq 4$ dimensions. In particular, we consider the 4-point function of $O(N)$-fundamental chiral operators $Z_i$ that have no chiral primary in the $O(N)$-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of $N+1$ chiral super-fields with superpotential $W = X \\sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTs where $\\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.
Kapoyannis, A S; Panagiotou, A D
1998-01-01
A recently constructed strangeness-including Statistical Bootstrap Model (S-SBM), which defines the limits of the hadronic phase and provides for a phase beyond, is further extended so as to include a factor that describes strangeness suppression. The model is then used to analyse the multiplicity data from collision experiments in which the colliding entities form isospin symmetric systems, the primary focus being on S+S interactions (NA35 collaboration). An optimal set of thermodynamical variables is extracted through a fit to both the inclusive full phase space and midrapidity data. The assumption that the measured particles originate from a thermally and partial-chemically equilibrated source described by the S-SBM is satisfactorily established. The proximity of the thermodynamical variables extracted from the S+S data to the limits of the hadronic phase is systematically investigated. Finally, experimental data from proton-antiproton collisions (UA5 collaboration) are similarly analysed.
Efficient bootstrap with weakly dependent processes
Bravo, Francesco; Crudu, Federico
2012-01-01
The efficient bootstrap methodology is developed for overidentified moment conditions models with weakly dependent observation. The resulting bootstrap procedure is shown to be asymptotically valid and can be used to approximate the distributions of t-statistics, the J-statistic for overidentifying
R.Manjula
2012-06-01
Full Text Available This Software product line engineering is an inter-disciplinary concept. It spans the dimensions of business, architecture, process, and the organization. Similarly, Education System engineering is also an inter-disciplinary concept, which spans the dimensions of academic, infrastructure, facilities, administration etc. Some of the potential benefits of this approach include continuous improvements in System quality and adhering to global standards. The increasing competency in IT and Educational Sectors necessitates a process maturity evaluation methodology. Accordingly, this paper presents an organizational maturity model for Education system for evaluating the maturity of multi- dimension factors and attributes of an Education System. Assessment questionnaires and a rating methodology comprise the framework of this Educational maturity model. The objective and design of the questionnaires are to collect information about the Education system engineering process from the multi perspectives of academic, infrastructure, administration, facilities etc. Furthermore, we conducted one case study and reported the assessment results using the organizational maturity model presented in this paper.
Bootstrapping structured page segmentation
Ma, Huanfeng; Doermann, David S.
2003-01-01
In this paper, we present an approach to the bootstrap learning of a page segmentation model. The idea evolves from attempts to segment dictionaries that often have a consistent page structure, and is extended to the segmentation of more general structured documents. In cases of highly regular structure, the layout can be learned from examples of only a few pages. The system is first trained using a small number of samples, and a larger test set is processed based on the training result. After making corrections to a selected subset of the test set, these corrected samples are combined with the original training samples to generate bootstrap samples. The newly created samples are used to retrain the system, refine the learned features and resegment the test samples. This procedure is applied iteratively until the learned parameters are stable. Using this approach, we do not need to initially provide a large set of training samples. We have applied this segmentation to many structured documents such as dictionaries, phone books, spoken language transcripts, and obtained satisfying segmentation performance.
Balogh, József; Morris, Robert
2011-01-01
Graph bootstrap percolation is a deterministic cellular automaton which was introduced by Bollob\\'as in 1968, and is defined as follows. Given a graph $H$, and a set $G \\subset E(K_n)$ of initially `infected' edges, we infect, at each time step, a new edge $e$ if there is a copy of $H$ in $K_n$ such that $e$ is the only not-yet infected edge of $H$. We say that $G$ percolates in the $H$-bootstrap process if eventually every edge of $K_n$ is infected. The extremal questions for this model, when $H$ is the complete graph $K_r$, were solved (independently) by Alon, Kalai and Frankl almost thirty years ago. In this paper we study the random questions, and determine the critical probability $p_c(n,K_r)$ for the $K_r$-process up to a poly-logarithmic factor. In the case $r = 4$ we prove a stronger result, and determine the threshold for $p_c(n,K_4)$.
Wild bootstrap of the mean in the infinite variance case
Giuseppe Cavaliere; Iliyan Georgiev; Robert Taylor, A. M.
2011-01-01
It is well known that the standard i.i.d. bootstrap of the mean is inconsistent in a location model with infinite variance (alfa-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the i.i.d. bootstrap owing to the fact ...
uniform bootstrap confidence bands for bounded influence curve estimators
Härdle, Wolfgang Karl; Ritov, Ya‘acov; Wang, Weining
2013-01-01
We consider theoretical bootstrap "coupling" techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of "coupling" bootstrap techniques are developed for additive models with both symmetric error distributions and further extension to the quantile regression framework. Our bootstrap method can be used in many situations like constructing con dence intervals and bands. We demonstrate the bootst...
Nonparametric bootstrap prediction
Fushiki, Tadayoshi; Komaki, Fumiyasu; Aihara, Kazuyuki
2005-01-01
Ensemble learning has recently been intensively studied in the field of machine learning. `Bagging' is a method of ensemble learning and uses bootstrap data to construct various predictors. The required prediction is then obtained by averaging the predictors. Harris proposed using this technique with the parametric bootstrap predictive distribution to construct predictive distributions, and showed that the parametric bootstrap predictive distribution gives asymptotically better prediction tha...
The Local Fractional Bootstrap
Bennedsen, Mikkel; Hounyo, Ulrich; Lunde, Asger;
new resampling method, the local fractional bootstrap, relies on simulating an auxiliary fractional Brownian motion that mimics the fine properties of high frequency differences of the Brownian semistationary process under the null hypothesis. We prove the first order validity of the bootstrap method...
Bootstrap Dynamical Symmetry Breaking
Wei-Shu Hou
2013-01-01
Full Text Available Despite the emergence of a 125 GeV Higgs-like particle at the LHC, we explore the possibility of dynamical electroweak symmetry breaking by strong Yukawa coupling of very heavy new chiral quarks Q . Taking the 125 GeV object to be a dilaton with suppressed couplings, we note that the Goldstone bosons G exist as longitudinal modes V L of the weak bosons and would couple to Q with Yukawa coupling λ Q . With m Q ≳ 700 GeV from LHC, the strong λ Q ≳ 4 could lead to deeply bound Q Q ¯ states. We postulate that the leading “collapsed state,” the color-singlet (heavy isotriplet, pseudoscalar Q Q ¯ meson π 1 , is G itself, and a gap equation without Higgs is constructed. Dynamical symmetry breaking is affected via strong λ Q , generating m Q while self-consistently justifying treating G as massless in the loop, hence, “bootstrap,” Solving such a gap equation, we find that m Q should be several TeV, or λ Q ≳ 4 π , and would become much heavier if there is a light Higgs boson. For such heavy chiral quarks, we find analogy with the π − N system, by which we conjecture the possible annihilation phenomena of Q Q ¯ → n V L with high multiplicity, the search of which might be aided by Yukawa-bound Q Q ¯ resonances.
Bootstrap current estimate in the ETE Tokamak
First estimates of the bootstrap current in the ETE small aspect ratio tokamak using the Hirshman single ion collisionless model show that we can expect from 25 to 55% of total bootstrap current depending on the optimization level of the plasma parameter profiles. Higher levels of bootstrap current are limited by peaked pressure profiles and βpol values which must be kept under a critical level due to stability conditions. Different methods for the trapped particle fraction calculation are also illustrated in this paper. (author). 7 refs., 5 figs., 1 tab
Investigating Mortality Uncertainty Using the Block Bootstrap
Xiaoming Liu
2010-01-01
Full Text Available This paper proposes a block bootstrap method for measuring mortality risk under the Lee-Carter model framework. In order to take account of all sources of risk (the process risk, the parameter risk, and the model risk properly, a block bootstrap is needed to cope with the spatial dependence found in the residuals. As a result, the prediction intervals we obtain for life expectancy are more accurate than the ones obtained from other similar methods.
Investigating Mortality Uncertainty Using the Block Bootstrap
Xiaoming Liu; W. John Braun
2010-01-01
This paper proposes a block bootstrap method for measuring mortality risk under the Lee-Carter model framework. In order to take account of all sources of risk (the process risk, the parameter risk, and the model risk) properly, a block bootstrap is needed to cope with the spatial dependence found in the residuals. As a result, the prediction intervals we obtain for life expectancy are more accurate than the ones obtained from other similar methods.
Bootstrap confidence intervals
Thomas J. DiCiccio; Efron, Bradley
1996-01-01
This article surveys bootstrap methods for producing good approximate confidence intervals. The goal is to improve by an order of magnitude upon the accuracy of the standard intervals $\\hat{\\theta} \\pm z^{(\\alpha)} \\hat{\\sigma}$, in a way that allows routine application even to very complicated problems. Both theory and examples are used to show how this is done. The first seven sections provide a heuristic overview of four bootstrap confidence interval procedures: $BC_a$, bootstrap-t , ABC a...
Horn, D.
2015-03-01
The quark model emerged from the Gell-Mann-Ne'eman flavor SU(3) symmetry. Its development, in the context of strong interactions, took place in a heuristic theoretical framework, referred to as the Bootstrap Era. Setting the background for the dominant ideas in strong interaction of the early 1960s, we outline some aspects of the constituent quark model. An independent theoretical development was the emergence of hadron duality in 1967, leading to a realization of the Bootstrap idea by relating hadron resonances (in the s-channel) with Regge pole trajectories (in t- and u-channels). The synthesis of duality with the quark-model has been achieved by duality diagrams, serving as a conceptual framework for discussing many aspects of hadron dynamics toward the end of the 1960s.
A Search Model of Discouragement
Rosholm, Michael; Toomet, Ott
psychological consequences of unemployement affecting search effectiveness. This model enables us to analyse the issue of discouragement, as the returns to search will gradually decline. Even so, the model is actually stationary from the point of view of the individual, which implies that many interesting...... to analyse theoretically the impact of changes in unemployment insurance and social assistance benefits, and we conduct some simulation exercises based on a calibrated model....
Chain ladder method: Bayesian bootstrap versus classical bootstrap
Peters, Gareth W.; Mario V. W\\"uthrich; Shevchenko, Pavel V.
2010-01-01
The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilising Markov chain Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. T...
Dynamics of bootstrap percolation
Prabodh Shukla
2008-08-01
Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first-order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed transition is characterized by power-law avalanches, while the continuous transition is characterized by truncated avalanches in a related sequential bootstrap process. We explain this behaviour on the basis of an analytical and numerical study of the avalanche distributions on a Bethe lattice.
Bootstrap percolation with inhibition
Einarsson, Hafsteinn; Lengler, Johannes; Panagiotou, Konstantinos; Mousset, Frank; Steger, Angelika
2014-01-01
Bootstrap percolation is a prominent framework for studying the spreading of activity on a graph. We begin with an initial set of active vertices. The process then proceeds in rounds, and further vertices become active as soon as they have a certain number of active neighbors. A recurring feature in bootstrap percolation theory is an `all-or-nothing' phenomenon: either the size of the starting set is so small that the process stops very soon, or it percolates (almost) completely. Motivated by...
Francq, Bernard G; Cartiaux, Olivier
2016-09-10
Resecting bone tumors requires good cutting accuracy to reduce the occurrence of local recurrence. This issue is considerably reduced with a navigated technology. The estimation of extreme proportions is challenging especially with small or moderate sample sizes. When no success is observed, the commonly used binomial proportion confidence interval is not suitable while the rule of three provides a simple solution. Unfortunately, these approaches are unable to differentiate between different unobserved events. Different delta methods and bootstrap procedures are compared in univariate and linear mixed models with simulations and real data by assuming the normality. The delta method on the z-score and parametric bootstrap provide similar results but the delta method requires the estimation of the covariance matrix of the estimates. In mixed models, the observed Fisher information matrix with unbounded variance components should be preferred. The parametric bootstrap, easier to apply, outperforms the delta method for larger sample sizes but it may be time costly. Copyright © 2016 John Wiley & Sons, Ltd. PMID:26990871
Wild cluster bootstrap confidence intervals
MacKinnon, James G.
2014-01-01
Confidence intervals based on cluster-robust covariance matrices can be constructed in many ways. In addition to conventional intervals obtained by inverting Wald (t) tests, the paper studies intervals obtained by inverting LM tests, studentized bootstrap intervals based on the wild cluster bootstrap, and restricted bootstrap intervals obtained by inverting bootstrap Wald and LM tests. It also studies the choice of an auxiliary distribution for the wild bootstrap, a modified covariance matrix...
Breakdown theory for bootstrap quantiles
Singh, Kesar
1998-01-01
A general formula for computing the breakdown point in robustness for the $t$th bootstrap quantile of a statistic $T_n$ is obtained. The answer depends on $t$ and the breakdown point of $T_n$. Since the bootstrap quantiles are vital ingredients of bootstrap confidence intervals, the theory has implications pertaining to robustness of bootstrap confidence intervals. For certain $L$ and $M$ estimators, a robustification of bootstrap is suggested via the notion of Winsorization.
Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
Esterlis, Ilya; Ramirez, David
2016-01-01
We use the numerical conformal bootstrap in two dimensions to search for finite, closed sub-algebras of the operator product expansion (OPE), without assuming unitarity. We find the minimal models as special cases, as well as additional lines of solutions that can be understood in the Coulomb gas formalism. All the solutions we find that contain the vacuum in the operator algebra are cases where the external operators of the bootstrap equation are degenerate operators, and we argue that this follows analytically from the expressions in arXiv:1202.4698 for the crossing matrices of Virasoro conformal blocks. Our numerical analysis is a special case of the "Gliozzi" bootstrap method, and provides a simpler setting in which to study technical challenges with the method. In the supplementary material, we provide a Mathematica notebook that automates the calculation of the crossing matrices and OPE coefficients for degenerate operators using the formulae of Dotsenko and Fateev.
Tie the straps: Uniform bootstrap con fidence bands for bounded influence curve estimators
Härdle, Wolfgang Karl; Ritov, Ya'Acov; Wang, Weining
2013-01-01
We consider theoretical bootstrap coupling techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of coupling bootstrap techniques are developed for additive models with both symmetric error distributions and further extension to the quantile regression framework. Our bootstrap method can be used in many situations like constructing con dence intervals and bands. We demonstrate the bootstrap ...
The alignment of bootstrap current in tokamak
By calculating the trapped particle fraction, solving the Grand-Shafranov equation describing plasma equilibrium, and using Harris model, the magnitude and alignment of the bootstrap current in tokamak are calculated and analysed under the conventional shear regimes and also the negative central shear regimes. The conclusion authors obtained are: through adjusting the profile parameters of plasma density, temperature and current, and the elongation k and triangularity d which describe the plasma shape, the alignment of bootstrap current profile with the equilibrium current profile can be produced; the negative central shear regimes are advantage ous to produce bootstrap current, and the profile of bootstrap current is well-aligned with the equilibrium current profile. By comparing authors' calculated results, the optimized parameters are obtained under the conventional shear and the negative central shear regimes
Search Models: Who Does the Looking?
Duffield, Judith A.
1996-01-01
Describes two search models for school libraries. Models include searches defined by the student but conducted by a trained searcher, and student-conducted searches which teach search skills. Decisions about which model (or combination) to use should be based on the available resources and the purposes for conducting the search. (AEF)
Conformal Bootstrap in Mellin Space
Gopakumar, Rajesh; Sen, Kallol; Sinha, Aninda
2016-01-01
We propose a new approach towards analytically solving for the dynamical content of Conformal Field Theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mellin representation of CFT amplitudes. We employ exchange Witten diagrams with built in crossing symmetry as our basic building blocks rather than the conventional conformal blocks in a particular channel. Demanding consistency with the operator product expansion (OPE) implies an infinite set of constraints on operator dimensions and OPE coefficients. We illustrate the power of this method in the epsilon expansion of the Wilson-Fisher fixed point by computing operator dimensions and, strikingly, OPE coefficients to higher orders in epsilon than currently available using other analytic techniques (including Feynman diagram calculations). Our results enable us to get a somewhat better agreement of certain observables in the 3d Ising model, with the precise numerical values that...
Bootstrapping Time Dilation Decoherence
Gooding, Cisco; Unruh, William G.
2015-10-01
We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer (Gooding and Unruh in Phys Rev D 90:044071, 2014). The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed "universal" decoherence mechanism attributed to gravitational time dilation (Pikovski et al in Nat Phys, 2015). We note that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, emphasizing that the effect can be attributed entirely to proper time differences, and thus is not necessarily related to gravity. Whereas the effect described in (Pikovski et al in Nat Phys, 2015) vanishes in the absence of an external gravitational field, our approach bootstraps the gravitational contribution to the time dilation decoherence by including self-interaction, yielding a fundamentally gravitational intrinsic decoherence effect.
Bootstrapping topology and systemic risk of complex network using the fitness model
Musmeci N.; Battiston S.; Caldarelli G.; Puliga M.; Gabrielli A.
2012-01-01
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the ...
Bootstrapping topology and systemic risk of complex network using the fitness model
Musmeci, Nicoló; Caldarelli, Guido; Puliga, Michelangelo; Gabrielli, Andrea
2012-01-01
We present a novel method to reconstruct complex network from partial information. We assume to know the links only for a subset of the nodes and to know some non-topological quantity (fitness) characterising every node. The missing links are generated on the basis of the latter quan- tity according to a fitness model calibrated on the subset of nodes for which links are known. We measure the quality of the reconstruction of several topological properties, such as the network density and the degree distri- bution as a function of the size of the initial subset of nodes. Moreover, we also study the resilience of the network to distress propagation. We first test the method on ensembles of synthetic networks generated with the Exponential Random Graph model which allows to apply common tools from statistical mechanics. We then test it on the empirical case of the World Trade Web. In both cases, we find that a subset of 10 % of nodes is enough to reconstruct the main features of the network along with its resili...
Metastability threshold for anisotropic bootstrap percolation in three dimensions
van Enter, Aernout
2011-01-01
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability threshold for a fairly general class of models. In our proofs we use an adaptation of the technique of dimensional reduction. We find that the order of the metastability threshold is generally determined by the "easiest growth direction" in the model. In contrast to the anisotropic bootstrap percolation in two dimensions, in three dimensions the order of the metatstability threshold for anisotropic bootstrap percolation can be equal to that of isotropic bootstrap percolation.
Temperature Corrected Bootstrap Algorithm
Comiso, Joey C.; Zwally, H. Jay
1997-01-01
A temperature corrected Bootstrap Algorithm has been developed using Nimbus-7 Scanning Multichannel Microwave Radiometer data in preparation to the upcoming AMSR instrument aboard ADEOS and EOS-PM. The procedure first calculates the effective surface emissivity using emissivities of ice and water at 6 GHz and a mixing formulation that utilizes ice concentrations derived using the current Bootstrap algorithm but using brightness temperatures from 6 GHz and 37 GHz channels. These effective emissivities are then used to calculate surface ice which in turn are used to convert the 18 GHz and 37 GHz brightness temperatures to emissivities. Ice concentrations are then derived using the same technique as with the Bootstrap algorithm but using emissivities instead of brightness temperatures. The results show significant improvement in the area where ice temperature is expected to vary considerably such as near the continental areas in the Antarctic, where the ice temperature is colder than average, and in marginal ice zones.
Conceptual Models for Search Engines
Hendry, D. G.; Efthimiadis, E. N.
Search engines have entered popular culture. They touch people in diverse private and public settings and thus heighten the importance of such important social matters as information privacy and control, censorship, and equitable access. To fully benefit from search engines and to participate in debate about their merits, people necessarily appeal to their understandings for how they function. In this chapter we examine the conceptual understandings that people have of search engines by performing a content analysis on the sketches that 200 undergraduate and graduate students drew when asked to draw a sketch of how a search engine works. Analysis of the sketches reveals a diverse range of conceptual approaches, metaphors, representations, and misconceptions. On the whole, the conceptual models articulated by these students are simplistic. However, students with higher levels of academic achievement sketched more complete models. This research calls attention to the importance of improving students' technical knowledge of how search engines work so they can be better equipped to develop and advocate policies for how search engines should be embedded in, and restricted from, various private and public information settings.
Bootstrap current fraction scaling for a tokamak reactor design study
Highlights: • New bootstrap current fraction scalings for systems codes were derived by solving the Hirshman–Sigmar model. • Nine self-consistent MHD equilibria were constructed in order to compare the bootstrap current fraction values. • Wilson formula most successfully predicted the bootstrap current fraction, but it requires current density profile index. • The new scaling formulas and IPDG accurately estimated the fBS values for the normal and weakly reversed shear tokamaks. - Abstract: We have derived new bootstrap current fraction scalings for systems codes by solving the Hirshman–Sigmar model, which is valid for arbitrary aspect ratios and collision conditions. The bootstrap current density calculation module in the ACCOME code was used with the matrix inversion method without the large aspect ratio assumption. Nine self-consistent MHD equilibria, which cover conventional, advanced and spherical tokamaks with normal or reversed shear, were constructed using numerical calculations in order to compare the bootstrap current fraction values with those of the new model and all six existing models. The Wilson formula successfully predicted the bootstrap current fraction, but it requires current density profile index for the calculation. The new scaling formulas and IPDG accurately estimated the bootstrap current fraction for the normal and weakly reversed shear tokamaks, regardless of the aspect ratio. However, none of the existing models except the Wilson formula can accurately estimate the bootstrap current fraction for the reversed shear tokamaks, which is promising for the advanced tokamak operation mode
Rejon-Barrera, Fernando; Robbins, Daniel
2016-01-01
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
A PARAMETRIC BOOTSTRAP USING THE FIRST FOURMOMENTS OF THE RESIDUALS
Pierre-Eric Treyens
2007-01-01
We consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Until now, within the framework of the bootstrap, we thought that the error in rejection probability (ERP) had the same rate of convergence with the parametric bootstrap or the nonparametric bootstrap. For linear data generating processes (DGP) we show in this paper that this assertion is false if skewness and/or kurtosis coefficients of the distribution of the disturbances are nonnull. ...
Introduction to the Bootstrap World
Boos, Dennis D.
2003-01-01
The bootstrap has made a fundamental impact on how we carry out statistical inference in problems without analytic solutions. This fact is illustrated with examples and comments that emphasize the parametric bootstrap and hypothesis testing.
Generalized bootstrap for estimating equations
Chatterjee, Snigdhansu; Bose, Arup
2005-01-01
We introduce a generalized bootstrap technique for estimators obtained by solving estimating equations. Some special cases of this generalized bootstrap are the classical bootstrap of Efron, the delete-d jackknife and variations of the Bayesian bootstrap. The use of the proposed technique is discussed in some examples. Distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained.
A strangeness and isospin asymmetry including statistical bootstrap model analysis of the multiparticle system produced in the Pb+Pb collision at 158 A GeV at CERN is presented. It is concluded that this interaction process has not crossed the deconfinement line. Direct comparisons with the results of similar analyses pertaining to nucleus-nucleus and p-p-bar collisions at CERN are made. The overall picture points to the S+S collision at 200 A GeV as a prime candidate of a process which has crossed the border separating the hadronic from the deconfined phase of matter. (author). Letter-to-the-editor
Cavaliere, Giuseppe; Nielsen, Morten Ørregaard; Taylor, A.M. Robert
Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should cointegrate with a unit slope on futures prices, does not hold. However, these statistical methods are...... fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed...
The bootstrap and Bayesian bootstrap method in assessing bioequivalence
Parametric method for assessing individual bioequivalence (IBE) may concentrate on the hypothesis that the PK responses are normal. Nonparametric method for evaluating IBE would be bootstrap method. In 2001, the United States Food and Drug Administration (FDA) proposed a draft guidance. The purpose of this article is to evaluate the IBE between test drug and reference drug by bootstrap and Bayesian bootstrap method. We study the power of bootstrap test procedures and the parametric test procedures in FDA (2001). We find that the Bayesian bootstrap method is the most excellent.
USEFULNESS OF BOOTSTRAPPING IN PORTFOLIO MANAGEMENT
Boris Radovanov
2012-12-01
Full Text Available This paper contains a comparison of in-sample and out-of-sample performances between the resampled efficiency technique, patented by Richard Michaud and Robert Michaud (1999, and traditional Mean-Variance portfolio selection, presented by Harry Markowitz (1952. Based on the Monte Carlo simulation, data (samples generation process determines the algorithms by using both, parametric and nonparametric bootstrap techniques. Resampled efficiency provides the solution to use uncertain information without the need for constrains in portfolio optimization. Parametric bootstrap process starts with a parametric model specification, where we apply Capital Asset Pricing Model. After the estimation of specified model, the series of residuals are used for resampling process. On the other hand, nonparametric bootstrap divides series of price returns into the new series of blocks containing previous determined number of consecutive price returns. This procedure enables smooth resampling process and preserves the original structure of data series.
Osmir José Lavoranti
2010-06-01
Full Text Available Reliable evaluation of the stability of genotypes and environment is of prime concern to plant breeders, but the lack of a comprehensive analysis of the structure of the GE interaction has been a stumbling block to the recommendation of varieties. The Additive Main Effects and Multiplicative Interaction (AMMI Model currently offers the good approach to interpretation and understanding of the GE interaction but lacks a way of assessing the stability of its estimates. The present contribution proposes the use of bootstrap resampling
in the AMMI Model, and applies it to obtain both a graphical and a numerical analysis of the phenotypic
stability of 20 Eucalyptus grandis progenies from Australia that were planted in seven environments in the Southern and Southeastern regions of Brazil. The results showed distinct behaviors of genotypes and
environments and the genotype x environment interaction was significant (p value < 0.01. The bootstrap coefficient of stability based on the squared Mahalanobis distance of the scores showed that genotypes and environments can be differentiated in terms of their stabilities. Graphical analysis of the AMMI biplot provided a better understanding of the interpretation of phenotypic stability. The proposed AMMI bootstrap eliminated the uncertainties regarding the identification of low scores in traditional analyses.As posições críticas dos estatísticos, que atuam em programas de melhoramento genético, referem-se à falta de uma análise criteriosa da estrutura da interação do genótipo com o ambiente (GE como um dos principais problemas para a recomendação de cultivares. A metodologia AMMI (additive main effects and multiplicative interaction analysis propõe ser mais eficiente que as análises usuais na interpretação e compreensão da interação GE, entretanto, à dificuldade de se interpretar a interação quando há baixa explicação do primeiro componente principal; à dificuldade de
Bootstrap Tests and Confidence Regions for Functions of a Covariance Matrix
Beran, Rudolf; Srivastava, Muni S.
1985-01-01
Bootstrap tests and confidence regions for functions of the population covariance matrix have the desired asymptotic levels, provided model restrictions, such as multiple eigenvalues in the covariance matrix, are taken into account in designing the bootstrap algorithm.
Bootstrap Percolation on Random Geometric Graphs
Bradonjić, Milan
2012-01-01
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of their neighbors according to a threshold rule. In a typical setting, bootstrap percolation starts by random and independent "activation" of nodes with a fixed probability $p$, followed by a deterministic process for additional activations based on the density of active nodes in each neighborhood ($\\th$ activated nodes). Here, we study bootstrap percolation on random geometric graphs in the regime when the latter are (almost surely) connected. Random geometric graphs provide an appropriate model in settings where the neighborhood structure of each node is determined by geographical distance, as in wireless {\\it ad hoc} ...
NI PUTU AYU DINITA TRISNAYANTI
2015-06-01
Full Text Available In this research bootstrap methods are used to determine the points inference of biplot figures on the analysis of AMMI. If the environmental factors are assumed to be random factors, then Mixed AMMI is used as a model of analysis. In the analysis of the stabilit, the main components score interaction used are KUI1 and KUI2. The purpose of this study is to determine the Biplot figures based on two scores these are KUI with the greatest diversity of Mixed AMMI models and the points inference by using the bootstrap method. The stable genotypes obtained from biplot AMMI2 are G1, G5, and G6. Based on points inference of each genotype, G1 and G5 can be regarded as the most stable genotype. This is because the distribution of G1 and G5 are the closest to the center point (0,0 and both of them have a small radius.
Unbiased Estimates of Variance Components with Bootstrap Procedures
Brennan, Robert L.
2007-01-01
This article provides general procedures for obtaining unbiased estimates of variance components for any random-model balanced design under any bootstrap sampling plan, with the focus on designs of the type typically used in generalizability theory. The results reported here are particularly helpful when the bootstrap is used to estimate standard…
A nonparametric hypothesis test via the Bootstrap resampling
Temel, Tugrul
2011-01-01
This paper adapts an already existing nonparametric hypothesis test to the bootstrap framework. The test utilizes the nonparametric kernel regression method to estimate a measure of distance between the models stated under the null hypothesis. The bootstraped version of the test allows to approximate errors involved in the asymptotic hypothesis test. The paper also develops a Mathematica Code for the test algorithm.
BOOTSTRAPPING FOR EXTRACTING RELATIONS FROM LARGE CORPORA
无
2008-01-01
A new approach of relation extraction is described in this paper. It adopts a bootstrapping model with a novel iteration strategy, which generates more precise examples of specific relation. Compared with previous methods, the proposed method has three main advantages: first, it needs less manual intervention; second, more abundant and reasonable information are introduced to represent a relation pattern; third, it reduces the risk of circular dependency occurrence in bootstrapping. Scalable evaluation methodology and metrics are developed for our task with comparable techniques over TianWang 100G corpus. The experimental results show that it can get 90% precision and have excellent expansibility.
Detrending bootstrap unit root tests
Smeekes, S.
2009-01-01
The role of detrending in bootstrap unit root tests is investigated. When bootstrapping, detrending must not only be done for the construction of the test statistic, but also in the first step of the bootstrap algorithm. It is argued that the two points should be treated separately. Asymptotic validity of sieve bootstrap ADF unit root tests is shown for test statistics based on full sample and recursive OLS and GLS detrending. It is also shown that the detrending method in the first step of t...
Chester, Shai M
2016-01-01
We initiate the conformal bootstrap study of Quantum Electrodynamics in $2+1$ space-time dimensions (QED$_{3}$) with $N$ flavors of charged fermions by focusing on the 4-point function of four monopole operators with the lowest unit of topological charge. We obtain upper bounds on the scaling dimension of the doubly-charged monopole operator, with and without assuming other gaps in the operator spectrum. Intriguingly, we find a (gap-dependent) kink in these bounds that comes reasonably close to the large $N$ extrapolation of the scaling dimensions of the singly-charged and doubly-charged monopole operators down to $N=4$ and $N=6$.
Applications of the Fast Double Bootstrap
MacKinnon, James G.
2006-01-01
The fast double bootstrap, or FDB, is a procedure for calculating bootstrap P values that is much more computationally efficient than the double bootstrap itself. In many cases, it can provide more accurate results than ordinary bootstrap tests. For the fast double bootstrap to be valid, the test statistic must be asymptotically independent of the random parts of the bootstrap data generating process. This paper presents simulation evidence on the performance of FDB tests in three cases of in...
Breakdown Point Theory for Implied Probability Bootstrap
Lorenzo Camponovo; Taisuke Otsu
2011-01-01
This paper studies robustness of bootstrap inference methods under moment conditions. In particular, we compare the uniform weight and implied probability bootstraps by analyzing behaviors of the bootstrap quantiles when outliers take arbitrarily large values, and derive the breakdown points for those bootstrap quantiles. The breakdown point properties characterize the situation where the implied probability bootstrap is more robust than the uniform weight bootstrap against outliers. Simulati...
The bootstrap fraction in TFTR
The TRANSP plasma analysis code is used to calculate the bootstrap current generated during neutral beam injection and ion cyclotron resonance frequency heating for a wide variety of TFTR discharges. An empirical scaling relation is given for the bootstrap current fraction using the ratio of the peakednesses of the thermal pressure and of the total current density. copyright 1997 American Institute of Physics
On sieve bootstrap prediction intervals.
Andrés M. Alonso; Peña, Daniel; Romo Urroz, Juan
2003-01-01
In this paper we consider a sieve bootstrap method for constructing nonparametric prediction intervals for a general class of linear processes. We show that the sieve bootstrap provides consistent estimators of the conditional distribution of future values given the observed data.
Ultrafast Approximation for Phylogenetic Bootstrap
Bui Quang Minh, [No Value; Nguyen, Thi; von Haeseler, Arndt
2013-01-01
Nonparametric bootstrap has been a widely used tool in phylogenetic analysis to assess the clade support of phylogenetic trees. However, with the rapidly growing amount of data, this task remains a computational bottleneck. Recently, approximation methods such as the RAxML rapid bootstrap (RBS) and
Explorations in Statistics: the Bootstrap
Curran-Everett, Douglas
2009-01-01
Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This fourth installment of Explorations in Statistics explores the bootstrap. The bootstrap gives us an empirical approach to estimate the theoretical variability among possible values of a sample statistic such as the…
Second Thoughts on the Bootstrap
Efron, Bradley
2003-01-01
This brief review article is appearing in the issue of Statistical Science that marks the 25th anniversary of the bootstrap. It concerns some of the theoretical and methodological aspects of the bootstrap and how they might influence future work in statistics.
A Novel Personalized Web Search Model
ZHU Zhengyu; XU Jingqiu; TIAN Yunyan; REN Xiang
2007-01-01
A novel personalized Web search model is proposed.The new system, as a middleware between a user and a Web search engine, is set up on the client machine. It can learn a user's preference implicitly and then generate the user profile automatically. When the user inputs query keywords, the system can automatically generate a few personalized expansion words by computing the term-term associations according to the current user profile, and then these words together with the query keywords are submitted to a popular search engine such as Yahoo or Google.These expansion words help to express accurately the user's search intention. The new Web search model can make a common search engine personalized, that is, the search engine can return different search results to different users who input the same keywords. The experimental results show the feasibility and applicability of the presented work.
Automatic bootstrapping and tracking of object contours.
Chiverton, John; Xie, Xianghua; Mirmehdi, Majid
2012-03-01
A new fully automatic object tracking and segmentation framework is proposed. The framework consists of a motion-based bootstrapping algorithm concurrent to a shape-based active contour. The shape-based active contour uses finite shape memory that is automatically and continuously built from both the bootstrap process and the active-contour object tracker. A scheme is proposed to ensure that the finite shape memory is continuously updated but forgets unnecessary information. Two new ways of automatically extracting shape information from image data given a region of interest are also proposed. Results demonstrate that the bootstrapping stage provides important motion and shape information to the object tracker. This information is found to be essential for good (fully automatic) initialization of the active contour. Further results also demonstrate convergence properties of the content of the finite shape memory and similar object tracking performance in comparison with an object tracker with unlimited shape memory. Tests with an active contour using a fixed-shape prior also demonstrate superior performance for the proposed bootstrapped finite-shape-memory framework and similar performance when compared with a recently proposed active contour that uses an alternative online learning model. PMID:21908256
A simple model of search engine pricing
Eliaz, Kfir; Spiegler, Ran
2009-01-01
We present a simple model of how a monopolistic search engine optimally determines the average quality of firms in its search pool. In our model, there is a continuum of consumers, who use the search engine’s pool, and there is a continuum of firms, whose entry to the pool is restricted by a price set by the search engine. We show that a monopolistic search engine may have an incentive to set a relatively low price that encouarges low-relevance advertisers to enter the searc...
Bootstrap consistency for general semiparametric M-estimation
Cheng, Guang
2010-10-01
Consider M-estimation in a semiparametric model that is characterized by a Euclidean parameter of interest and an infinite-dimensional nuisance parameter. As a general purpose approach to statistical inferences, the bootstrap has found wide applications in semiparametric M-estimation and, because of its simplicity, provides an attractive alternative to the inference approach based on the asymptotic distribution theory. The purpose of this paper is to provide theoretical justifications for the use of bootstrap as a semiparametric inferential tool. We show that, under general conditions, the bootstrap is asymptotically consistent in estimating the distribution of the M-estimate of Euclidean parameter; that is, the bootstrap distribution asymptotically imitates the distribution of the M-estimate. We also show that the bootstrap confidence set has the asymptotically correct coverage probability. These general onclusions hold, in particular, when the nuisance parameter is not estimable at root-n rate, and apply to a broad class of bootstrap methods with exchangeable ootstrap weights. This paper provides a first general theoretical study of the bootstrap in semiparametric models. © Institute of Mathematical Statistics, 2010.
Collier, Scott; Yin, Xi
2016-01-01
We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how "extremal spectra" which maximize the degeneracy at the gap can be determined numerically.
Bootstraping the general linear hypothesis test
Delicado, Pedro; Río, Manuel del, 1690-1766
1993-01-01
We discuss the use of bootstrap methodology in hypothesis testing, focusing on the classical F-test for linear hypotheses in the linear model. A modification of the F-statistics which allows for resampling under the null hypothesis is proposed. This approach is specifically considered in the one-way analysis of variance model. A simulation study illustrating the behaviour of our proposal is presented.
A Search Model for Imperfectly Detected Targets
Ahumada, Albert
2012-01-01
Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.
Accidental symmetries and the conformal bootstrap
Chester, Shai M.; Giombi, Simone; Iliesiu, Luca V.; Klebanov, Igor R.; Pufu, Silviu S.; Yacoby, Ran
2016-01-01
We study an N=2 supersymmetric generalization of the three-dimensional critical O( N) vector model that is described by N + 1 chiral superfields with superpotential W = g 1 X∑ i Z 1 2 + g 2 X 3. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to g 2 flowing to zero. This example is special in that the existence of an infrared fixed point with g 1 , g 2 ≠ 0, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the F-theorem excludes the models with g 1 , g 2 ≠ 0 for N > 5. The conformal bootstrap provides a stronger constraint and excludes such models for N > 2. We provide evidence that the g 2 = 0 models, which have the enhanced O( N) × U(1) symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the g 1 , g 2 ≠ 0 models by studying them perturbatively in the 4 - ɛ expansion.
The Talent Search Model of Gifted Identification
Assouline, Susan G.; Lupkowski-Shoplik, Ann
2012-01-01
The Talent Search model, founded at Johns Hopkins University by Dr. Julian C. Stanley, is fundamentally an above-level testing program. This simplistic description belies the enduring impact that the Talent Search model has had on the lives of hundreds of thousands of gifted students as well as their parents and teachers. In this article, we…
Incorporating opponent models into adversary search
Carmel, D.; Markovitch, S. [Technion, Haifa (Israel)
1996-12-31
This work presents a generalized theoretical framework that allows incorporation of opponent models into adversary search. We present the M* algorithm, a generalization of minimax that uses an arbitrary opponent model to simulate the opponent`s search. The opponent model is a recursive structure consisting of the opponent`s evaluation function and its model of the player. We demonstrate experimentally the potential benefit of using an opponent model. Pruning in M* is impossible in the general case. We prove a sufficient condition for pruning and present the {alpha}{beta}* algorithm which returns the M* value of a tree while searching only necessary branches.
The wild tapered block bootstrap
Hounyo, Ulrich
In this paper, a new resampling procedure, called the wild tapered block bootstrap, is introduced as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The method consists in tapering each overlapping block......-of-the-art block-based method in terms of asymptotic accuracy of variance estimation and distribution approximation. For stationary time series, the asymptotic validity, and the favorable bias properties of the new bootstrap method are shown in two important cases: smooth functions of means, and M-estimators. The...... estimator for the sample mean is shown to be robust against heteroskedasticity of the wild tapered block bootstrap. This easy to implement alternative bootstrap method works very well even for moderate sample sizes....
Linear algebra and bootstrap percolation
Balogh, József; Morris, Robert; Riordan, Oliver
2011-01-01
In $\\HH$-bootstrap percolation, a set $A \\subset [n]$ of initially `infected' vertices spreads by infecting vertices which are the only uninfected vertex in an edge of the hypergraph $\\HH \\subset \\P(n)$. A particular case of this is the $H$-bootstrap process, in which $\\HH$ encodes copies of $H$ in a graph $G$. We find the minimum size of a set $A$ that leads to complete infection when $G$ is a power of a complete graph and $H$ is a hypercube. The proof uses linear algebra, a technique that is new in bootstrap percolation, although standard in the study of weakly saturated graphs, which are equivalent to (edge) $H$-bootstrap percolation on a complete graph.
Bootstrapping Realized Multivariate Volatility Measures.
Donovon, Prosper; Goncalves, Silvia; Meddahi, Nour
2013-01-01
We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of Barndorff-Nielsen and Shephard (2004) show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent. This motivates our use of the bootstrap as an altern...
Deep Exploration via Bootstrapped DQN
Osband, Ian; Blundell, Charles; Pritzel, Alexander; Van Roy, Benjamin
2016-01-01
Efficient exploration in complex environments remains a major challenge for reinforcement learning. We propose bootstrapped DQN, a simple algorithm that explores in a computationally and statistically efficient manner through use of randomized value functions. Unlike dithering strategies such as epsilon-greedy exploration, bootstrapped DQN carries out temporally-extended (or deep) exploration; this can lead to exponentially faster learning. We demonstrate these benefits in complex stochastic ...
Bootstrap percolation on spatial networks
Jian Gao; Tao Zhou; Yanqing Hu
2015-01-01
Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active...
TASI Lectures on the Conformal Bootstrap
Simmons-Duffin, David
2016-01-01
These notes are from courses given at TASI and the Advanced Strings School in summer 2015. Starting from principles of quantum field theory and the assumption of a traceless stress tensor, we develop the basics of conformal field theory, including conformal Ward identities, radial quantization, reflection positivity, the operator product expansion, and conformal blocks. We end with an introduction to numerical bootstrap methods, focusing on the 2d and 3d Ising models.
Bootstrapping Deep Lexical Resources: Resources for Courses
Baldwin, Timothy
2007-01-01
We propose a range of deep lexical acquisition methods which make use of morphological, syntactic and ontological language resources to model word similarity and bootstrap from a seed lexicon. The different methods are deployed in learning lexical items for a precision grammar, and shown to each have strengths and weaknesses over different word classes. A particular focus of this paper is the relative accessibility of different language resource types, and predicted ``bang for the buck'' associated with each in deep lexical acquisition applications.
Bootstrapping quarks and gluons
Dual topological unitarization (DTU) - the approach to S-matrix causality and unitarity through combinatorial topology - is reviewed. Amplitudes associated with triangulated spheres are shown to constitute the core of particle physics. Each sphere is covered by triangulated disc faces corresponding to hadrons. The leading current candidate for the hadron-face triangulation pattern employs 3-triangle basic subdiscs whose orientations correspond to baryon number and topological color. Additional peripheral triangles lie along the hadron-face perimeter. Certain combinations of peripheral triangles with a basic-disc triangle can be identified as quarks, the flavor of a quark corresponding to the orientation of its edges that lie on the hadron-face perimeter. Both baryon number and flavor are additively conserved. Quark helicity, which can be associated with triangle-interior orientation, is not uniformly conserved and interacts with particle momentum, whereas flavor does not. Three different colors attach to the 3 quarks associated with a single basic subdisc, but there is no additive physical conservation law associated with color. There is interplay between color and quark helicity. In hadron faces with more than one basic subdisc, there may occur pairs of adjacent flavorless but colored triangles with net helicity +-1 that are identifiable as gluons. Broken symmetry is an automatic feature of the bootstrap. T, C and P symmetries, as well as up-down flavor symmetry, persist on all orientable surfaces
Monotonicity-preserving bootstrapped kriging metamodels for expensive simulations
Kleijnen, Jack P.C.; Beers, W.C.M. van
2013-01-01
Kriging (Gaussian process, spatial correlation) metamodels approximate the Input/Output (I/O) functions implied by the underlying simulation models; such metamodels serve sensitivity analysis and optimization, especially for computationally expensive simulations. In practice, simulation analysts often know that the I/O function is monotonic. To obtain a Kriging metamodel that preserves this known shape, this article uses bootstrapping (or resampling). Parametric bootstrapping assuming normali...
Bootstrapped Multinomial Logistic Regression on Apnea Detection Using ECG Data
Sanabila, Hadaiq R.; Fanany, Mohamad Ivan; Jatmiko, Wisnu; Arymurthy, Aniati Murni
2010-01-01
In designing a classification system, one of the most important considerations is how optimal the classifier will adapt and give best generalization when it is given data from unknown model distribution. Unlike linear regression, logistic regression has no simple formula to assess its generalization ability. In such cases, bootstrapping offers an advantage over analytical methods thanks to its simplicity. This paper presents an analysis of bootstrapped multinomial logistic regression appli...
Spectrum of local boundary operators from boundary form factor bootstrap
Szots, M
2007-01-01
Using the recently introduced boundary form factor bootstrap equations, we map the complete space of their solutions for the boundary version of the scaling Lee-Yang model and sinh-Gordon theory. We show that the complete space of solutions, graded by the ultraviolet behaviour of the form factors can be brought into correspondence with the spectrum of local boundary operators expected from boundary conformal field theory, which is a major evidence for the correctness of the boundary form factor bootstrap framework.
Double-bootstrap methods that use a single double-bootstrap simulation
Chang, Jinyuan; Hall, Peter
2014-01-01
We show that, when the double bootstrap is used to improve performance of bootstrap methods for bias correction, techniques based on using a single double-bootstrap sample for each single-bootstrap sample can be particularly effective. In particular, they produce third-order accuracy for much less computational expense than is required by conventional double-bootstrap methods. However, this improved level of performance is not available for the single double-bootstrap methods that have been s...
Model-based Tomographic Reconstruction Literature Search
Chambers, D H; Lehman, S K
2005-11-30
In the process of preparing a proposal for internal research funding, a literature search was conducted on the subject of model-based tomographic reconstruction (MBTR). The purpose of the search was to ensure that the proposed research would not replicate any previous work. We found that the overwhelming majority of work on MBTR which used parameterized models of the object was theoretical in nature. Only three researchers had applied the technique to actual data. In this note, we summarize the findings of the literature search.
Exploring Contextual Models in Chemical Patent Search
Urbain, Jay; Frieder, Ophir
We explore the development of probabilistic retrieval models for integrating term statistics with entity search using multiple levels of document context to improve the performance of chemical patent search. A distributed indexing model was developed to enable efficient named entity search and aggregation of term statistics at multiple levels of patent structure including individual words, sentences, claims, descriptions, abstracts, and titles. The system can be scaled to an arbitrary number of compute instances in a cloud computing environment to support concurrent indexing and query processing operations on large patent collections.
Geometric Models for Collaborative Search and Filtering
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both human and automated agents share control over a fleet of unmanned aerial vehicles (UAVs) with the goal of locating a missing subject as quickly as pos...
A Model-Driven Engineering Framework for Constrained Model Search
Kleiner, Mathias
2009-01-01
This document describes a formalization, a solver-independant methodology and implementation alternatives for realizing constrained model search in a model-driven engineering framework. The proposed approach combines model-driven engineering tools ((meta)model transformations, models to text, text to models) and constraint programming techniques. Based on previous research, motivations to model search are first introduced together with objectives and background context. A theory of model sear...
Simplified Models for LHC New Physics Searches
This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the 'Topologies for Early LHC Searches' workshop, held at SLAC in September of 2010, the purpose of which was to develop a set of representative models that can be used to cover all relevant phase space in experimental searches. Particular emphasis is placed on searches relevant for the first ∼ 50-500 pb-1 of data and those motivated by supersymmetric models. This note largely summarizes material posted at http://lhcnewphysics.org/, which includes simplified model definitions, Monte Carlo material, and supporting contacts within the theory community. We also comment on future developments that may be useful as more data is gathered and analyzed by the experiments.
Simplified Models for LHC New Physics Searches
Alves, Daniele; /SLAC; Arkani-Hamed, Nima; /Princeton, Inst. Advanced Study; Arora, Sanjay; /Rutgers U., Piscataway; Bai, Yang; /SLAC; Baumgart, Matthew; /Johns Hopkins U.; Berger, Joshua; /Cornell U., Phys. Dept.; Buckley, Matthew; /Fermilab; Butler, Bart; /SLAC; Chang, Spencer; /Oregon U. /UC, Davis; Cheng, Hsin-Chia; /UC, Davis; Cheung, Clifford; /UC, Berkeley; Chivukula, R.Sekhar; /Michigan State U.; Cho, Won Sang; /Tokyo U.; Cotta, Randy; /SLAC; D' Alfonso, Mariarosaria; /UC, Santa Barbara; El Hedri, Sonia; /SLAC; Essig, Rouven, (ed.); /SLAC; Evans, Jared A.; /UC, Davis; Fitzpatrick, Liam; /Boston U.; Fox, Patrick; /Fermilab; Franceschini, Roberto; /LPHE, Lausanne /Pittsburgh U. /Argonne /Northwestern U. /Rutgers U., Piscataway /Rutgers U., Piscataway /Carleton U. /CERN /UC, Davis /Wisconsin U., Madison /SLAC /SLAC /SLAC /Rutgers U., Piscataway /Syracuse U. /SLAC /SLAC /Boston U. /Rutgers U., Piscataway /Seoul Natl. U. /Tohoku U. /UC, Santa Barbara /Korea Inst. Advanced Study, Seoul /Harvard U., Phys. Dept. /Michigan U. /Wisconsin U., Madison /Princeton U. /UC, Santa Barbara /Wisconsin U., Madison /Michigan U. /UC, Davis /SUNY, Stony Brook /TRIUMF; /more authors..
2012-06-01
This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the 'Topologies for Early LHC Searches' workshop, held at SLAC in September of 2010, the purpose of which was to develop a set of representative models that can be used to cover all relevant phase space in experimental searches. Particular emphasis is placed on searches relevant for the first {approx} 50-500 pb{sup -1} of data and those motivated by supersymmetric models. This note largely summarizes material posted at http://lhcnewphysics.org/, which includes simplified model definitions, Monte Carlo material, and supporting contacts within the theory community. We also comment on future developments that may be useful as more data is gathered and analyzed by the experiments.
Simplified Models for LHC New Physics Searches
Alves, Daniele; Arora, Sanjay; Bai, Yang; Baumgart, Matthew; Berger, Joshua; Buckley, Matthew; Butler, Bart; Chang, Spencer; Cheng, Hsin-Chia; Cheung, Clifford; Chivukula, R.Sekhar; Cho, Won Sang; Cotta, Randy; D'Alfonso, Mariarosaria; El Hedri, Sonia; Essig, Rouven; Evans, Jared A.; Fitzpatrick, Liam; Fox, Patrick; Franceschini, Roberto; Freitas, Ayres; Gainer, James S.; Gershtein, Yuri; Gray, Richard; Gregoire, Thomas; Gripaios, Ben; Gunion, Jack; Han, Tao; Haas, Andy; Hansson, Per; Hewett, JoAnne; Hits, Dmitry; Hubisz, Jay; Izaguirre, Eder; Kaplan, Jared; Katz, Emanuel; Kilic, Can; Kim, Hyung-Do; Kitano, Ryuichiro; Koay, Sue Ann; Ko, Pyungwon; Krohn, David; Kuflik, Eric; Lewis, Ian; Lisanti, Mariangela; Liu, Tao; Liu, Zhen; Lu, Ran; Luty, Markus; Meade, Patrick; Morrissey, David; Mrenna, Stephen; Nojiri, Mihoko; Okui, Takemichi; Padhi, Sanjay; Papucci, Michele; Park, Michael; Park, Myeonghun; Perelstein, Maxim; Peskin, Michael; Phalen, Daniel; Rehermann, Keith; Rentala, Vikram; Roy, Tuhin; Ruderman, Joshua T.; Sanz, Veronica; Schmaltz, Martin; Schnetzer, Stephen; Schuster, Philip; Schwaller, Pedro; Schwartz, Matthew D.; Schwartzman, Ariel; Shao, Jing; Shelton, Jessie; Shih, David; Shu, Jing; Silverstein, Daniel; Simmons, Elizabeth; Somalwar, Sunil; Spannowsky, Michael; Spethmann, Christian; Strassler, Matthew; Su, Shufang; Tait, Tim; Thomas, Brooks; Thomas, Scott; Toro, Natalia; Volansky, Tomer; Wacker, Jay; Waltenberger, Wolfgang; Yavin, Itay; Yu, Felix; Zhao, Yue; Zurek, Kathryn
2012-01-01
This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the "Topologies for Early LHC Searches" workshop, held at SLAC in September of 2010, the purpose of which was to develop a...
Raquel Florez-Lopez; Juan Manuel Ramon-Jeronimo
2014-01-01
Credit risk models are commonly based on large internal data sets to produce reliable estimates of the probability of default (PD) that should be validated with time. However, in the real world, a substantial portion of the exposures is included in low-default portfolios (LDPs) in which the number of defaulted loans is usually much lower than the number of non-default observations. Modelling of these imbalanced data sets is particularly problematic with small portfolios in which the absence o...
A PARAMETRIC BOOTSTRAP USING THE FIRST FOUR
MOMENTS OF THE RESIDUALS
Treyens, Pierre-Eric
2007-01-01
We consider linear regression models and we suppose that disturbances are either Gaussian or non Gaussian. Until now, within the framework of the bootstrap, we thought that the error in rejection probability (ERP) had the same rate of convergence with the parametric bootstrap or the nonparametric bootstrap. For linear data generating processes (DGP) we show in this paper that this assertion is false if skewness and/or kurtosis coefficients of the distribution of the disturbances are nonnull. ...
Bootstrap bias-adjusted GMM estimators
Ramalho, Joaquim J.S.
2005-01-01
The ability of six alternative bootstrap methods to reduce the bias of GMM parameter estimates is examined in an instrumental variable framework using Monte Carlo analysis. Promising results were found for the two bootstrap estimators suggested in the paper.
Analytical bootstrap methods for censored data
Alan D. Hutson
2002-01-01
Analytic bootstrap estimators for the moments of survival quantities are derived. By using these expressions recommendations can be made as to the appropriateness of bootstrap estimation under censored data conditions.
The Bootstrap Approach for Testing Skewness Persistence
Krishnamurty Muralidhar
1993-01-01
This study presents a new methodology for testing changes in skewness between time periods (or samples) using the bootstrap method. A Monte Carlo simulation experiment was conducted to compare the effectiveness of the bootstrap method with the method suggested by Lau, Wingender and Lau (1989) to test skewness persistence. The results show the bootstrap method to be more powerful than the other method. The bootstrap method was also used to determine the persistence of skewness in stock returns...
Improving the Reliability of Bootstrap Tests
Russell Davidson; MacKinnon, James G.
2000-01-01
We first propose procedures for estimating the rejection probabilities for bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive as estimating rejection probabilities for asymptotic tersts. We then propose procedures for computing modified bootstrap P values that will often be more accurate than ordinary ones. These procedures are closely related to the double bootstrap, but they are far ...
Coefficient Omega Bootstrap Confidence Intervals: Nonnormal Distributions
Padilla, Miguel A.; Divers, Jasmin
2013-01-01
The performance of the normal theory bootstrap (NTB), the percentile bootstrap (PB), and the bias-corrected and accelerated (BCa) bootstrap confidence intervals (CIs) for coefficient omega was assessed through a Monte Carlo simulation under conditions not previously investigated. Of particular interests were nonnormal Likert-type and binary items.…
On the Asymptotic Accuracy of Efron's Bootstrap
Singh, Kesar
1981-01-01
In the non-lattice case it is shown that the bootstrap approximation of the distribution of the standardized sample mean is asymptotically more accurate than approximation by the limiting normal distribution. The exact convergence rate of the bootstrap approximation of the distributions of sample quantiles is obtained. A few other convergence rates regarding the bootstrap method are also studied.
The bootstrap and edgeworth expansion
Hall, Peter
1992-01-01
This monograph addresses two quite different topics, in the belief that each can shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. Chapter 1 is about the bootstrap, witih almost no mention of Edgeworth expansion; Chapter 2 is about Edgeworth expansion, with scarcely a word about the bootstrap; and Chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properites of the bootstrap. The book is aimed a a graduate level audience who has some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter (entitled "Details of Mathematical Rogour"), and so a mathematically able reader without knowledge of the rigorous theory of probability will have no trouble understanding the first four-fifths of the book. The book simultaneously fills two gaps in the literature; it provides a very readable graduate level account of t...
First estimate of bootstrap current in the ETE small aspect ratio tokamak
A first estimate of the bootstrap current in the ETE (Experimento Tokamak Esferico) small aspect ratio tokamak using the Hirshman single-ion collisionless model shows that we can expect a ratio of 15 to 30% of total bootstrap current in relation to the total equilibrium current depending on the optimization level of the plasma profile parameters. Bootstrap current levels basically depend on the βp values which must be kept under a critical level due to stability conditions and current alignment requirements. Preliminary studies of Shaing's predictions regarding bootstrap current calculations in collisional plasmas are briefly described and different methods for the trapped particle fraction calculation are also illustrated. (Author)
Frey, H. Christopher [North Carolina State University, Raleigh, NC (United States); Rhodes, David S. [North Carolina State University, Raleigh, NC (United States)
1999-04-30
This is Volume 1 of a two-volume set of reports describing work conducted at North Carolina State University sponsored by Grant Number DE-FG05-95ER30250 by the U.S. Department of Energy. The title of the project is “Quantitative Analysis of Variability and Uncertainty in Acid Rain Assessments.” The work conducted under sponsorship of this grant pertains primarily to two main topics: (1) development of new methods for quantitative analysis of variability and uncertainty applicable to any type of model; and (2) analysis of variability and uncertainty in the performance, emissions, and cost of electric power plant combustion-based NOx control technologies. These two main topics are reported separately in Volumes 1 and 2.
Feti, Andreea; Dudele, Aiga
2012-01-01
Bootstrapping plays a vital role in the life of small and medium-sized enter-prises. By providing a large variety of financing alternatives bootstrapping ensures the existence of entrepreneurship, even though, too less attention is paid to bootstrapping in the specific literature. Therefore, the master thesis strives to eliminate the gaps in the theory by bringing new insights in the field of bootstrapping.The purpose of the master thesis is to investigate the usage of boot-strapping methods ...
Model Unspecific Search in CMS
Schmitz Stefan Antonius
2012-06-01
Full Text Available We present the results of a model independent analysis, which systematically scans the data taken by CMS for deviations from the Standard Model predictions. Due to the minimal theoretical bias this approach is sensitive to a variety of models for new physics. Events with at least one electron or muon are classified according to their content of reconstructed objects (muons, electrons, photons, jets and missing transverse energy. A broad scan of three kinematic distributions in those classes is performed by identifying deviations from Standard Model expectations, accounting for systematic uncertainties.
Tabu search model selection for SVM.
Lebrun, Gilles; Charrier, Christophe; Lezoray, Olivier; Cardot, Hubert
2008-02-01
A model selection method based on tabu search is proposed to build support vector machines (binary decision functions) of reduced complexity and efficient generalization. The aim is to build a fast and efficient support vector machines classifier. A criterion is defined to evaluate the decision function quality which blends recognition rate and the complexity of a binary decision functions together. The selection of the simplification level by vector quantization, of a feature subset and of support vector machines hyperparameters are performed by tabu search method to optimize the defined decision function quality criterion in order to find a good sub-optimal model on tractable times. PMID:18344220
JuliBootS: a hands-on guide to the conformal bootstrap
Paulos, Miguel F
2014-01-01
We introduce {\\tt JuliBootS}, a package for numerical conformal bootstrap computations coded in {\\tt Julia}. The centre-piece of {\\tt JuliBootS} is an implementation of Dantzig's simplex method capable of handling arbitrary precision linear programming problems with continuous search spaces. Current supported features include conformal dimension bounds, OPE bounds, and bootstrap with or without global symmetries. The code is trivially parallelizable on one or multiple machines. We exemplify usage extensively with several real-world applications. In passing we give a pedagogical introduction to the numerical bootstrap methods.
Implementation of bootstrap current effects in the PIES code
The PIES code (Princeton Iterative Equilibrium Solver) has been modified to take into account the effects of bootstrap current. A simple bootstrap current model, applicable to tokamaks, is presently being employed. Pressure flattening, caused by the evolution of islands, has an important effect on the bootstrap current, which in turn has an important large effect on the island width. Analytic models have shown that the overall result of this interaction is, for negative shear, a destabilization of the islands. Recently, Chang et al., has shown that good agreement exists between the analytic expression proposed by reference and experiments on TFTR. Approximations used in this analytic expression, such as the expressions for Δ'(w), axe avoided in the calculations done with the PIES code. A comparison of the two results will be presented
Bootstrapped efficiency measures of oil blocks in Angola
This paper investigates the technical efficiency of Angola oil blocks over the period 2002-2007. A double bootstrap data envelopment analysis (DEA) model is adopted composed in the first stage of a DEA-variable returns to scale (VRS) model and then followed in the second stage by a bootstrapped truncated regression. Results showed that on average, the technical efficiency has fluctuated over the period of study, but deep and ultradeep oil blocks have generally maintained a consistent efficiency level. Policy implications are derived.
A bootstrap estimation scheme for chemical compositional data with nondetects
Palarea-Albaladejo, J; Martín-Fernández, J.A; Olea, Ricardo A.
2014-01-01
The bootstrap method is commonly used to estimate the distribution of estimators and their associated uncertainty when explicit analytic expressions are not available or are difficult to obtain. It has been widely applied in environmental and geochemical studies, where the data generated often represent parts of whole, typically chemical concentrations. This kind of constrained data is generically called compositional data, and they require specialised statistical methods to properly account for their particular covariance structure. On the other hand, it is not unusual in practice that those data contain labels denoting nondetects, that is, concentrations falling below detection limits. Nondetects impede the implementation of the bootstrap and represent an additional source of uncertainty that must be taken into account. In this work, a bootstrap scheme is devised that handles nondetects by adding an imputation step within the resampling process and conveniently propagates their associated uncertainly. In doing so, it considers the constrained relationships between chemical concentrations originated from their compositional nature. Bootstrap estimates using a range of imputation methods, including new stochastic proposals, are compared across scenarios of increasing difficulty. They are formulated to meet compositional principles following the log-ratio approach, and an adjustment is introduced in the multivariate case to deal with nonclosed samples. Results suggest that nondetect bootstrap based on model-based imputation is generally preferable. A robust approach based on isometric log-ratio transformations appears to be particularly suited in this context. Computer routines in the R statistical programming language are provided.
Simplified models for exotic BSM searches
Heisig, Jan; Lessa, Andre; Quertenmont, Loic
2015-12-01
Simplified models are a successful way of interpreting current LHC searches for models beyond the standard model (BSM). So far simplified models have focused on topologies featuring a missing transverse energy (MET) signature. However, in some BSM theories other, more exotic, signatures occur. If a charged particle becomes long-lived on collider time scales — as it is the case in parts of the SUSY parameter space — it leads to a very distinct signature. We present an extension of the computer package SModelS which includes simplified models for heavy stable charged particles (HSCP). As a physical application we investigate the CMSSM stau co-annihilation strip containing long-lived staus, which presents a potential solution to the Lithium problem. Applying both MET and HSCP constraints we show that, for low values of tan β, all this region of parameter space either violates Dark Matter constraints or is excluded by LHC searches.
Simplified Models for Exotic BSM Searches
Heisig, Jan; Quertenmont, Loic
2015-01-01
Simplified models are a successful way of interpreting current LHC searches for models beyond the standard model (BSM). So far simplified models have focused on topologies featuring a missing transverse energy (MET) signature. However, in some BSM theories other, more exotic, signatures occur. If a charged particle becomes long-lived on collider time scales - as it is the case in parts of the SUSY parameter space - it leads to a very distinct signature. We present an extension of the computer package SModelS which includes simplified models for heavy stable charged particles (HSCP). As a physical application we investigate the CMSSM stau co-annihilation strip containing long-lived staus, which presents a potential solution to the Lithium problem. Applying both MET and HSCP constraints we show that, for low values of $\\tan\\beta$, all this region of parameter space either violates Dark Matter constraints or is excluded by LHC searches.
The search for stable prognostic models in multiple imputed data sets
de Vet Henrica CW
2010-09-01
Full Text Available Abstract Background In prognostic studies model instability and missing data can be troubling factors. Proposed methods for handling these situations are bootstrapping (B and Multiple imputation (MI. The authors examined the influence of these methods on model composition. Methods Models were constructed using a cohort of 587 patients consulting between January 2001 and January 2003 with a shoulder problem in general practice in the Netherlands (the Dutch Shoulder Study. Outcome measures were persistent shoulder disability and persistent shoulder pain. Potential predictors included socio-demographic variables, characteristics of the pain problem, physical activity and psychosocial factors. Model composition and performance (calibration and discrimination were assessed for models using a complete case analysis, MI, bootstrapping or both MI and bootstrapping. Results Results showed that model composition varied between models as a result of how missing data was handled and that bootstrapping provided additional information on the stability of the selected prognostic model. Conclusion In prognostic modeling missing data needs to be handled by MI and bootstrap model selection is advised in order to provide information on model stability.
Bootstrap Current in Spherical Tokamaks
王中天; 王龙
2003-01-01
Variational principle for the neoclassical theory has been developed by including amomentum restoring term in the electron-electron collisional operator, which gives an additionalfree parameter maximizing the heat production rate. All transport coefficients are obtained in-cluding the bootstrap current. The essential feature of the study is that the aspect ratio affects thefunction of the electron-electron collision operator through a geometrical factor. When the aspectratio approaches to unity, the fraction of circulating particles goes to zero and the contribution toparticle flux from the electron-electron collision vanishes. The resulting diffusion coefficient is inrough agreement with Hazeltine. When the aspect ratio approaches to infinity, the results are inagreement with Rosenbluth. The formalism gives the two extreme cases a connection. The theoryis particularly important for the calculation of bootstrap current in spherical tokamaks and thepresent tokamaks, in which the square root of the inverse aspect ratio, in general, is not small.
Bootstrapping N=2 chiral correlators
Lemos, Madalena; Liendo, Pedro
2016-01-01
We apply the numerical bootstrap program to chiral operators in four-dimensional N=2 SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of N=2 SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.
Bootstrapping N=2 chiral correlators
Lemos, Madalena [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Liendo, Pedro [Humboldt-Univ. Berlin (Germany). IMIP
2015-12-15
We apply the numerical bootstrap program to chiral operators in four-dimensional N=2 SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of N=2 SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.
Bootstrapping N=2 chiral correlators
We apply the numerical bootstrap program to chiral operators in four-dimensional N=2 SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special emphasis to bootstrapping a specific theory: the simplest Argyres-Douglas fixed point with no flavor symmetry. In the second part we generalize our setup and consider correlators of fields with unequal dimension. This is an example of a mixed correlator and allows us to probe new regions in the parameter space of N=2 SCFTs. In particular, our results put constraints on relations in the Coulomb branch chiral ring and on the curvature of the Zamolodchikov metric.
On a generalized bootstrap principle
The S-matrices for non-simply-laced affine Toda field theories are considered in the context of a generalized bootstrap principle. The S-matrices, and in particular their poles, depend on a parameter whose range lies between the Coxeter numbers of dual pairs of the corresponding non-simply-laced algebras. It is proposed that only odd order poles in the physical strip with positive coefficients throughout this range should participate in the bootstrap. All other singularities have an explanation in principle in terms of a generalized Coleman-Thun mechanism. Besides the S-matrices introduced by Delius, Grisaru and Zanon, the missing case (F4(1), e6(2)), is also considered and provides many interesting examples of pole generation. (author)
Metastability Thresholds for Anisotropic Bootstrap Percolation in Three Dimensions
Van Enter, A.C.D.; Fey, A.
2012-01-01
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the orde
Metastability thresholds for anisotropic bootstrap percolation in three dimensions
Van Enter, A.C.D.; Fey, A.
2012-01-01
In this paper we analyze several anisotropic bootstrap percolation models in three dimensions. We present the order of magnitude for the metastability thresholds for a fairly general class of models. In our proofs, we use an adaptation of the technique of dimensional reduction. We find that the orde
Bootstrap clustering for graph partitioning
Gambette, Philippe; Guénoche, Alain
2011-01-01
Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this pr...
Conformal Bootstrap in Embedding Space
Fortin, Jean-François
2016-01-01
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation functions of four scalars. All remaining conformal blocks are simple derivatives of the minimal conformal block. With the help of the orthogonality properties of the conformal blocks, the analytic conformal bootstrap can be implemented directly in embedding space, leading to a Jacobi-like definition of conformal field theories.
Conformal bootstrap in embedding space
Fortin, Jean-François; Skiba, Witold
2016-05-01
It is shown how to obtain conformal blocks from embedding space with the help of the operator product expansion. The minimal conformal block originates from scalar exchange in a four-point correlation function of four scalars. All remaining conformal blocks are simple derivatives of the minimal conformal block. With the help of the orthogonality properties of the conformal blocks, the analytic conformal bootstrap can be implemented directly in embedding space, leading to a Jacobi-like definition of conformal field theories.
Bootstrapping High Dimensional Time Series
Zhang, Xianyang; Cheng, Guang
2014-01-01
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for mean vector; (2) specification testing on the second order property of time series such as white noise testing and bandedness testing of covariance matrix; (3) specification testing on the spectral property of time series. In theory, we first derive a Gaussi...
Modified Bootstrap Sensitometry In Radiography
Bednarek, Daniel R.; Rudin, Stephen
1981-04-01
A new modified bootstrap approach to sensitometry is presented which provides H and D curves that show almost exact agreement with those obtained using conventional methods. Two bootstrap techniques are described; both involve a combination of inverse-square and stepped-wedge modulation of the radiation field and provide intensity-scale sensitometric curves as appropriate for medical radiography. H and D curves obtained with these modified techniques are compared with those obtained for screen-film combinations using inverse-square sensitometry as well as with those obtained for direct x-ray film using time-scale sensitometry. The stepped wedge of the Wisconsin X-Ray Test Cassette was used in the bootstrap approach since it provides sufficient exposure latitude to encompass the useful density range of medical x-ray film. This approach makes radiographic sensitometry quick and convenient, allowing accurate characteristic curves to be obtained for any screen-film cassette using standard diagnostic x-ray equipment.
Bootstrapping Time Dilation Decoherence
Gooding, Cisco
2015-01-01
We present a general relativistic model of a spherical shell of matter with a perfect fluid on its surface coupled to an internal oscillator, which generalizes a model recently introduced by the authors to construct a self-gravitating interferometer [1]. The internal oscillator evolution is defined with respect to the local proper time of the shell, allowing the oscillator to serve as a local clock that ticks differently depending on the shell's position and momentum. A Hamiltonian reduction is performed on the system, and an approximate quantum description is given to the reduced phase space. If we focus only on the external dynamics, we must trace out the clock degree of freedom, and this results in a form of intrinsic decoherence that shares some features with a proposed "universal" decoherence mechanism attributed to gravitational time dilation [2]. We show that the proposed decoherence remains present in the (gravity-free) limit of flat spacetime, indicating that the effect can be attributed entirely to ...
Generalized Bootstrap Method for Assessment of Uncertainty in Semivariogram Inference
Olea, R.A.; Pardo-Iguzquiza, E.
2011-01-01
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. ?? 2010 International Association for Mathematical Geosciences.
Investigations of dipole localization accuracy in MEG using the bootstrap.
Darvas, F; Rautiainen, M; Pantazis, D; Baillet, S; Benali, H; Mosher, J C; Garnero, L; Leahy, R M
2005-04-01
We describe the use of the nonparametric bootstrap to investigate the accuracy of current dipole localization from magnetoencephalography (MEG) studies of event-related neural activity. The bootstrap is well suited to the analysis of event-related MEG data since the experiments are repeated tens or even hundreds of times and averaged to achieve acceptable signal-to-noise ratios (SNRs). The set of repetitions or epochs can be viewed as a set of independent realizations of the brain's response to the experiment. Bootstrap resamples can be generated by sampling with replacement from these epochs and averaging. In this study, we applied the bootstrap resampling technique to MEG data from somatotopic experimental and simulated data. Four fingers of the right and left hand of a healthy subject were electrically stimulated, and about 400 trials per stimulation were recorded and averaged in order to measure the somatotopic mapping of the fingers in the S1 area of the brain. Based on single-trial recordings for each finger we performed 5000 bootstrap resamples. We reconstructed dipoles from these resampled averages using the Recursively Applied and Projected (RAP)-MUSIC source localization algorithm. We also performed a simulation for two dipolar sources with overlapping time courses embedded in realistic background brain activity generated using the prestimulus segments of the somatotopic data. To find correspondences between multiple sources in each bootstrap, sample dipoles with similar time series and forward fields were assumed to represent the same source. These dipoles were then clustered by a Gaussian Mixture Model (GMM) clustering algorithm using their combined normalized time series and topographies as feature vectors. The mean and standard deviation of the dipole position and the dipole time series in each cluster were computed to provide estimates of the accuracy of the reconstructed source locations and time series. PMID:15784414
Theoretical comparisons of block bootstrap methods
Lahiri, S. N.
1999-01-01
In this paper, we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths. It is shown that, asymptotically, bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order. However, the variances of these bootstrap estimators may be different even in the first order. Expansions for the bias, the variance and the mean-squared error of different bloc...
Testing optimality in job search models
John W. Schindler
2001-01-01
This paper uses Bayesian techniques to compare three definitions of optimality for the basic job search model: the standard income-maximizing definition, an approximation to the standard definition, and a simple alternative. The important role of prior choice in these comparisons is illustrated. Using natural conjugate priors to represent hypothetical samples of data, we find that the simple alternative is preferred to the standard definition of optimality. However, using priors constructed f...
Finger Search in the Implicit Model
Brodal, Gerth Stølting; Nielsen, Jesper Asbjørn Sindahl; Truelsen, Jakob
2012-01-01
We address the problem of creating a dictionary with the finger search property in the strict implicit model, where no information is stored between operations, except the array of elements. We show that for any implicit dictionary supporting finger searches in q(t) = Ω(logt) time, the time to move...... the finger to another element is Ω(q− 1(logn)), where t is the rank distance between the query element and the finger. We present an optimal implicit static structure matching this lower bound. We furthermore present a near optimal implicit dynamic structure supporting search, change-finger, insert......, and delete in times $\\mathcal{O}(q(t))$, $\\mathcal{O}(q^{-1}(\\log n)\\log n)$, $\\mathcal{O}(\\log n)$, and $\\mathcal{O}(\\log n)$, respectively, for any q(t) = Ω(logt). Finally we show that the search operation must take Ω(logn) time for the special case where the finger is always changed to the element...
Multiquark hadrons in topological bootstrap
We use the lowest-order topological bootstrap framework to calculate hadron masses by imposing duality on an infinite sum of ladder graphs generated from spherical unitarity. By making a certain simple dynamical approximation, we derive an explicit generic Regge-trajectory formula for any given process. If we then make certain reasonable dynamical assumptions and require simultaneous consistency for entire sets of processes, we are able to calculate the masses of all the lowest meson, baryon and multiquark states involving u and d quarks, and the Regge trajectories associated with each of them. The only arbitrary parameter is the mass of the rho, which merely serves to set the mass scale
Advertising for attention in a consumer search model
Haan, M.A.; Moraga González, J.L.
2011-01-01
We model the idea that when consumers search for products, they first visit the firm whose advertising is most salient. The gains a firm derives from being visited early increase in search costs, so equilibrium advertising increases as search costs rise. As a result, higher search costs may decrease
Kleber Rogério Moreira Prado
2013-06-01
Full Text Available Current essay forwards a biodegradation model of a dye, used in the textile industry, based on a neural network propped by bootstrap remodeling. Bootstrapped neural network is set to generate estimates that are close to results obtained in an intrinsic experience in which a chemical process is applied. Pseudomonas oleovorans was used in the biodegradation of reactive Black 5. Results show a brief comparison between the information estimated by the proposed approach and the experimental data, with a coefficient of correlation between real and predicted values for a more than 0.99 biodegradation rate. Dye concentration and the solution’s pH failed to interfere in biodegradation index rates. A value above 90% of dye biodegradation was achieved between 1.000 and 1.841 mL 10 mL-1 of microorganism concentration and between 1.000 and 2.000 g 100 mL-1 of glucose concentration within the experimental conditions under analysis.
Standard Model Higgs Boson Searches at CDF
We present recent results from searches for a standard model Higgs boson by the CDF experiment at the Tevatron pp¯ collider with the full Run II data set. An excess of events above the expected background is observed and is the strongest in the associated production search channels where the Higgs is produced together with a W or Z boson, and then decays to a bottom-antibottom quark pair, with a global significance of 2.5σ. Both limits and best fit values of the Higgs production cross section are presented. For a Higgs mass of 125GeV/c2, the best agreement with data in the (σWH+σZH)×Br(H→bb¯)=291±113118fb
The (2, 0) superconformal bootstrap
Beem, Christopher; Lemos, Madalena; Rastelli, Leonardo; van Rees, Balt C.
2016-01-01
We develop the conformal bootstrap program for six-dimensional conformal field theories with (2, 0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward identities and describe the superconformal block decomposition of this correlator. We apply numerical bootstrap techniques to derive bounds on operator product expansion (OPE) coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. We also derive analytic results for the large spin spectrum using the light cone expansion of the crossing equation. Our principal result is strong evidence that the A1 theory realizes the minimal allowed central charge (c =25 ) for any interacting (2, 0) theory. This implies that the full stress tensor four-point function of the A1 theory is the unique unitary solution to the crossing symmetry equation at c =25 . For this theory, we estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2, 0) theory of central charge c . For large c , our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.
Bootstrap percolation on spatial networks
Gao, Jian; Zhou, Tao; Hu, Yanqing
2015-10-01
Bootstrap percolation is a general representation of some networked activation process, which has found applications in explaining many important social phenomena, such as the propagation of information. Inspired by some recent findings on spatial structure of online social networks, here we study bootstrap percolation on undirected spatial networks, with the probability density function of long-range links’ lengths being a power law with tunable exponent. Setting the size of the giant active component as the order parameter, we find a parameter-dependent critical value for the power-law exponent, above which there is a double phase transition, mixed of a second-order phase transition and a hybrid phase transition with two varying critical points, otherwise there is only a second-order phase transition. We further find a parameter-independent critical value around -1, about which the two critical points for the double phase transition are almost constant. To our surprise, this critical value -1 is just equal or very close to the values of many real online social networks, including LiveJournal, HP Labs email network, Belgian mobile phone network, etc. This work helps us in better understanding the self-organization of spatial structure of online social networks, in terms of the effective function for information spreading.
Bootstrap percolation in high dimensions
Balogh, Jozsef; Morris, Robert
2009-01-01
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A \\subset V(G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected neighbours. The set A is said to percolate if eventually all vertices are infected. Our aim is to understand this process on the grid, [n]^d, for arbitrary functions n = n(t), d = d(t) and r = r(t), as t -> infinity. The main question is to determine the critical probability p_c([n]^d,r) at which percolation becomes likely, and to give bounds on the size of the critical window. In this paper we study this problem when r = 2, for all functions n and d satisfying d \\gg log n. The bootstrap process has been extensively studied on [n]^d when d is a fixed constant and 2 \\le r \\le d, and in these cases p_c([n]^d,r) has recently been determined up to a factor of 1 + o(1) as n -> infinity. At the other end of the scale, Balogh and Bollobas determined p_c([2]^d,2) up to a constant factor, and...
A comparison of four different block bootstrap methods
Boris Radovanov; Aleksandra Marcikić
2014-01-01
The paper contains a description of four different block bootstrap methods, i.e., non-overlapping block bootstrap, overlapping block bootstrap (moving block bootstrap), stationary block bootstrap and subsampling. Furthermore, the basic goal of this paper is to quantify relative efficiency of each mentioned block bootstrap procedure and then to compare those methods. To achieve the goal, we measure mean square errors of estimation variance returns. The returns are calculated from 1250 daily ob...
A Bayesian Bootstrap for a Finite Population
Lo, Albert Y.
1988-01-01
A Bayesian bootstrap for a finite population is introduced; its small-sample distributional properties are discussed and compared with those of the frequentist bootstrap for a finite population. It is also shown that the two are first-order asymptotically equivalent.
Coefficient Alpha Bootstrap Confidence Interval under Nonnormality
Padilla, Miguel A.; Divers, Jasmin; Newton, Matthew
2012-01-01
Three different bootstrap methods for estimating confidence intervals (CIs) for coefficient alpha were investigated. In addition, the bootstrap methods were compared with the most promising coefficient alpha CI estimation methods reported in the literature. The CI methods were assessed through a Monte Carlo simulation utilizing conditions…
Bootstrapping Phylogenetic Trees: Theory and Methods
Holmes, Susan
2003-01-01
This is a survey of the use of the bootstrap in the area of systematic and evolutionary biology. I present the current usage by biologists of the bootstrap as a tool both for making inferences and for evaluating robustness, and propose a framework for thinking about these problems in terms of mathematical statistics.
Recent CMS searches for exotic phenomena beyond the Standard Model
Wulsin, H Wells
2015-01-01
The results of several recent CMS searches for exotic phenomena beyond the Standard Model are presented in this talk. Two searches look for new physics in a final state with a vector boson and missing transverse energy. Three searches target massive resonances decaying to a Higgs boson and a vector boson. Finally, preliminary results are presented for the first CMS search for exotic phenomena using $\\sqrt{s} = 13$ TeV data, the search for dijet resonances.
On Bootstrap Percolation in Living Neural Networks
Amini, Hamed
2009-01-01
Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks.
A neural network based reputation bootstrapping approach for service selection
Wu, Quanwang; Zhu, Qingsheng; Li, Peng
2015-10-01
With the concept of service-oriented computing becoming widely accepted in enterprise application integration, more and more computing resources are encapsulated as services and published online. Reputation mechanism has been studied to establish trust on prior unknown services. One of the limitations of current reputation mechanisms is that they cannot assess the reputation of newly deployed services as no record of their previous behaviours exists. Most of the current bootstrapping approaches merely assign default reputation values to newcomers. However, by this kind of methods, either newcomers or existing services will be favoured. In this paper, we present a novel reputation bootstrapping approach, where correlations between features and performance of existing services are learned through an artificial neural network (ANN) and they are then generalised to establish a tentative reputation when evaluating new and unknown services. Reputations of services published previously by the same provider are also incorporated for reputation bootstrapping if available. The proposed reputation bootstrapping approach is seamlessly embedded into an existing reputation model and implemented in the extended service-oriented architecture. Empirical studies of the proposed approach are shown at last.
Bootstrap-Based Regularization for Low-Rank Matrix Estimation
Josse, Julie; Wager, Stefan
2014-01-01
We develop a flexible framework for low-rank matrix estimation that allows us to transform noise models into regularization schemes via a simple bootstrap algorithm. Effectively, our procedure seeks an autoencoding basis for the observed matrix that is stable with respect to the specified noise model; we call the resulting procedure a stable autoencoder. In the simplest case, with an isotropic noise model, our method is equivalent to a classical singular value shrinkage estimator. For non-iso...
Search for the standard model Higgs boson
Buskulic, D.; de Bonis, I.; Decamp, D.; Ghez, P.; Goy, C.; Lees, J.-P.; Minard, M.-N.; Pietrzyk, B.; Ariztizabal, F.; Comas, P.; Crespo, J. M.; Delfino, M.; Efthymiopoulos, I.; Fernandez, E.; Fernandez-Bosman, M.; Gaitan, V.; Garrido, Ll.; Mattison, T.; Pacheco, A.; Padilla, C.; Pascual, A.; Creanza, D.; de Palma, M.; Farilla, A.; Iaselli, G.; Maggi, G.; Natali, S.; Nuzzo, S.; Quattromini, M.; Ranieri, A.; Raso, G.; Romano, F.; Ruggieri, F.; Selvaggi, G.; Silvestris, L.; Tempesta, P.; Zito, G.; Chai, Y.; Hu, H.; Huang, D.; Huang, X.; Lin, J.; Wang, T.; Xie, Y.; Xu, D.; Xu, R.; Zhang, J.; Zhang, L.; Zhao, W.; Blucher, E.; Bonvicini, G.; Boudreau, J.; Casper, D.; Drevermann, H.; Forty, R. W.; Ganis, G.; Gay, C.; Hagelberg, R.; Harvey, J.; Hilgart, J.; Jacobsen, R.; Jost, B.; Knobloch, J.; Lehraus, I.; Lohse, T.; Maggi, M.; Markou, C.; Martinez, M.; Mato, P.; Meinhard, H.; Minten, A.; Miotto, A.; Miguel, R.; Moser, H.-G.; Palazzi, P.; Pater, J. R.; Perlas, J. A.; Pusztaszeri, J.-F.; Ranjard, F.; Redlinger, G.; Rolandi, L.; Rothberg, J.; Ruan, T.; Saich, M.; Schlatter, D.; Schmelling, M.; Sefkow, F.; Tejessy, W.; Tomalin, I. R.; Veenhof, R.; Wachsmuth, H.; Wasserbaech, S.; Wiedenmann, W.; Wildish, T.; Witzeling, W.; Wotschack, J.; Ajaltouni, Z.; Badaud, F.; Bardadin-Otwinowska, M.; El Fellous, R.; Falvard, A.; Gay, P.; Guicheney, C.; Henrard, P.; Jousset, J.; Michel, B.; Montret, J.-C.; Pallin, D.; Perret, P.; Podlyski, F.; Proriol, J.; Prulhière, F.; Saadi, F.; Fearnley, T.; Hansen, J. B.; Hansen, J. D.; Hansen, J. R.; Hansen, P. H.; Møllerud, R.; Nilsson, B. S.; Kyriakis, A.; Simopoulou, E.; Siotis, I.; Vayaki, A.; Zachariadou, K.; Badier, J.; Blondel, A.; Bonneaud, G.; Brient, J. C.; Fouque, G.; Orteu, S.; Rougé, A.; Rumpf, M.; Tanaka, R.; Verderi, M.; Videau, H.; Candlin, D. J.; Parsons, M. I.; Veitch, E.; Focardi, E.; Moneta, L.; Parrini, G.; Corden, M.; Georgiopoulos, C.; Ikeda, M.; Levinthal, D.; Antonelli, A.; Baldini, R.; Bencivenni, G.; Bologna, G.; Bossi, F.; Campana, P.; Capon, G.; Cerutti, F.; Chiarella, V.; D'Ettorre-Piazzoli, B.; Felici, G.; Laurelli, P.; Mannocchi, G.; Murtas, F.; Murtas, G. P.; Passalacqua, L.; Pepe-Altarelli, M.; Picchi, P.; Colrain, P.; Ten Have, I.; Lynch, J. G.; Maitland, W.; Morton, W. T.; Raine, C.; Reeves, P.; Scarr, J. M.; Smith, K.; Thompson, A. S.; Turnbull, R. M.; Brandl, B.; Braun, O.; Geweniger, C.; Hanke, P.; Hepp, V.; Kluge, E. E.; Maumary, Y.; Putzer, A.; Rensch, B.; Stahl, A.; Tittel, K.; Wunsch, M.; Beuselinck, R.; Binnie, D. M.; Cameron, W.; Cattaneo, M.; Colling, D. J.; Dornan, P. J.; Greene, A. M.; Hassard, J. F.; Lieske, N. M.; Moutoussi, A.; Nash, J.; Patton, S.; Payne, D. G.; Phillips, M. J.; San Martin, G.; Sedgbeer, J. K.; Wright, A. G.; Girtler, P.; Kuhn, D.; Rudolph, G.; Vogl, R.; Bowdery, C. K.; Brodbeck, T. J.; Finch, A. J.; Foster, F.; Hughes, G.; Jackson, D.; Keemer, N. R.; Nuttall, M.; Patel, A.; Sloan, T.; Snow, S. W.; Whelan, E. P.; Kleinknecht, K.; Raab, J.; Renk, B.; Sander, H.-G.; Schmidt, H.; Steeg, F.; Walther, S. M.; Wanke, R.; Wolf, B.; Bencheikh, A. M.; Benchouk, C.; Bonissent, A.; Carr, J.; Coyle, P.; Drinkard, J.; Etienne, F.; Nicod, D.; Papalexiou, S.; Payre, P.; Roos, L.; Rousseau, D.; Schwemling, P.; Talby, M.; Adlung, S.; Assmann, R.; Bauer, C.; Blum, W.; Brown, D.; Cattaneo, P.; Dehning, B.; Dietl, H.; Dydak, F.; Frank, M.; Halley, A. W.; Jakobs, K.; Lauber, J.; Lütjens, G.; Lutz, G.; Männer, W.; Richter, R.; Schröder, J.; Schwarz, A. S.; Settles, R.; Seywerd, H.; Stierlin, U.; Stiegler, U.; Dennis, R. St.; Wolf, G.; Alemany, R.; Boucrot, J.; Callot, O.; Cordier, A.; Davier, M.; Duflot, L.; Grivaz, J.-F.; Heusse, Ph.; Jaffe, D. E.; Janot, P.; Kim, D. W.; Le Diberder, F.; Lefrançois, J.; Lutz, A.-M.; Schune, M.-H.; Veillet, J.-J.; Videau, I.; Zhang, Z.; Abbaneo, D.; Bagliesi, G.; Batignani, G.; Bottigli, U.; Bozzi, C.; Calderini, G.; Carpinelli, M.; Ciocci, M. A.; Dell'Orso, R.; Ferrante, I.; Fidecaro, F.; Foà, L.; Forti, F.; Giassi, A.; Giorgi, M. A.; Gregorio, A.; Ligabue, F.; Lusiani, A.; Manneli, E. B.; Marrocchesi, P. S.; Messineo, A.; Palla, F.; Rizzo, G.; Sanguinetti, G.; Spagnolo, P.; Steinberger, J.; Techini, R.; Tonelli, G.; Triggiani, G.; Vannini, C.; Venturi, A.; Verdini, P. G.; Walsh, J.; Betteridge, A. P.; Gao, Y.; Green, M. G.; March, P. V.; Mir, Ll. M.; Medcalf, T.; Quazi, I. S.; Strong, J. A.; West, L. R.; Botterill, D. R.; Clifft, R. W.; Edgecock, T. R.; Haywood, S.; Norton, P. R.; Thompson, J. C.; Bloch-Devaux, B.; Colas, P.; Duarte, H.; Emery, S.; Kozanecki, W.; Lançon, E.; Lemaire, M. C.; Locci, E.; Marx, B.; Perez, P.; Rander, J.; Renardy, J.-F.; Rosowsky, A.; Roussarie, A.; Schuller, J.-P.; Schwindling, J.; Si Mohand, D.; Vallage, B.; Johnson, R. P.; Litke, A. M.; Taylor, G.; Wear, J.; Ashman, J. G.; Babbage, W.; Booth, C. N.; Buttar, C.; Cartwright, S.; Combley, F.; Dawson, I.; Thompson, L. F.; Barberio, E.; Böhrer, A.; Brandt, S.; Cowan, G.; Grupen, C.; Lutters, G.; Rivera, F.; Schäfer, U.; Smolik, L.; Bosisio, L.; Della Marina, R.; Giannini, G.; Gobbo, B.; Ragusa, F.; Bellantoni, L.; Chen, W.; Conway, J. S.; Feng, Z.; Ferguson, D. P. S.; Gao, Y. S.; Grahl, J.; Harton, J. L.; Hayes, O. J.; Nachtman, J. M.; Pan, Y. B.; Saadi, Y.; Schmitt, M.; Scott, I.; Sharma, V.; Shi, Z. H.; Turk, J. D.; Walsh, A. M.; Weber, F. V.; Sau Lan Wu; Wu, X.; Zheng, M.; Zobernig, G.; Aleph Collaboration
1993-08-01
Using a data sample corresponding to about 1 233 000 hadronic Z decays collected by the ALEPH experiment at LEP, the reaction e+e- → HZ∗ has been used to search for the standard model Higgs boson, in association with missing energy when Z∗ → v v¯, or with a pair of energetic leptons when Z∗ → e+e-or μ +μ -. No signal was found and, at the 95% confidence level, mH exceeds 58.4 GeV/ c2.
Measuring productivity differences in equilibrium search models
Lanot, Gauthier; Neumann, George R.
1996-01-01
Equilibrium search models require unobserved heterogeneity in productivity to fit observed wage distribution data, but provide no guidance about the location parameter of the heterogeneity. In this paper we show that the location of the productivity heterogeneity implies a mode in a kernel density...... estimate of the wage distribution. The number of such modes and their location are identified using bump hunting techniques due to Silverman (1981). These techniques are applied to Danish panel data on workers and firms. These estimates are used to assess the importance of employer wage policy....
Search for symmetries beyond the Standard Model with ATLAS
Tal Hod, Noam; The ATLAS collaboration
2015-01-01
Searches for new physics beyond the Standard Model (SM) at the LHC are mainly driven by two approaches: a signature-based search where one looks for a deviation from the SM prediction in event yield or kinematic properties, and a more theory-oriented approach where the search is designed to look for specific signatures/topologies predicted by certain beyond standard model (BSM ) scenarios. Extensive searches for such signatures have been performed in ATLAS at LHC Run 1 in the context of Supersymmetry, Extended Gauge models, Technicolor, Little Higgs, Extra Dimensions, Left-Right symmetric models, and many other BSM scenarios. Highlights from these searches are presented.
The N=2 superconformal bootstrap
Beem, Christopher; Lemos, Madalena; Liendo, Pedro; Rastelli, Leonardo; van Rees, Balt C.
2016-03-01
In this work we initiate the conformal bootstrap program for N=2 super-conformal field theories in four dimensions. We promote an abstract operator-algebraic viewpoint in order to unify the description of Lagrangian and non-Lagrangian theories, and formulate various conjectures concerning the landscape of theories. We analyze in detail the four-point functions of flavor symmetry current multiplets and of N=2 chiral operators. For both correlation functions we review the solution of the superconformal Ward identities and describe their superconformal block decompositions. This provides the foundation for an extensive numerical analysis discussed in the second half of the paper. We find a large number of constraints for operator dimensions, OPE coefficients, and central charges that must hold for any N=2 superconformal field theory.
Bootstrapping Object Coreferencing on the Semantic Web
Wei Hu; Yu-Zhong Qu; Xing-Zhi Sun
2011-01-01
An object on the Semantic Web is likely to be denoted with several URIs by different parties.Object coreferencing is a process to identify "equivalent" URIs of objects for achieving a better Data Web.In this paper,we propose a bootstrapping approach for object coreferencing on the Semantic Web.For an object URI,we firstly establish a kernel that consists of semantically equivalent URIs from the same-as,(inverse) functional properties and (max-)cardinalities,and then extend the kernel with respect to the textual descriptions (e.g.,labels and local names) of URIs.We also propose a trustworthiness-based method to rank the coreferent URIs in the kernel as well as a similarity-based method for ranking the URIs in the extension of the kernel.We implement the proposed approach,called ObjectCoref,on a large-scale dataset that contains 76 million URIs collected by the Falcons search engine until 2008.The evaluation on precision,relative recall and response time demonstrates the feasibility of our approach.Additionally,we apply the proposed approach to investigate the popularity of the URI alias phenomenon on the current Semantic Web.
Bootstrapping Security Policies for Wearable Apps Using Attributed Structural Graphs
González-Tablas, Ana I.; Tapiador, Juan E.
2016-01-01
We address the problem of bootstrapping security and privacy policies for newly-deployed apps in wireless body area networks (WBAN) composed of smartphones, sensors and other wearable devices. We introduce a framework to model such a WBAN as an undirected graph whose vertices correspond to devices, apps and app resources, while edges model structural relationships among them. This graph is then augmented with attributes capturing the features of each entity together with user-defined tags. We...
Monojet Searches for MSSM Simplified Models
Arbey, A; Mahmoudi, F
2015-01-01
We explore the implications of monojet searches at hadron colliders in the MSSM. To quantify the impact of monojet searches, we consider simplified MSSM scenarios with neutralino dark matter. The monojet results of the LHC Run 1 are reinterpreted in the context of several MSSM simplified scenarios, and the complementarity with direct SUSY search results is highlighted. We also investigate the reach of monojet searches for the Run 2, as well as for future higher energy hadron colliders.
Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap
Davidson, Russell; MacKinnon, James
2006-01-01
Two procedures are proposed for estimating the rejection probabilities of bootstrap tests in Monte Carlo experiments without actually computing a bootstrap test for each replication. These procedures are only about twice as expensive (per replication) as estimating rejection probabilities for asymptotic tests. Then a new procedure is proposed for computing bootstrap P values that will often be more accurate than ordinary ones. This “fast double bootstrap” is closely related to the double boot...
Predicting disease risk using bootstrap ranking and classification algorithms.
Ohad Manor
Full Text Available Genome-wide association studies (GWAS are widely used to search for genetic loci that underlie human disease. Another goal is to predict disease risk for different individuals given their genetic sequence. Such predictions could either be used as a "black box" in order to promote changes in life-style and screening for early diagnosis, or as a model that can be studied to better understand the mechanism of the disease. Current methods for risk prediction typically rank single nucleotide polymorphisms (SNPs by the p-value of their association with the disease, and use the top-associated SNPs as input to a classification algorithm. However, the predictive power of such methods is relatively poor. To improve the predictive power, we devised BootRank, which uses bootstrapping in order to obtain a robust prioritization of SNPs for use in predictive models. We show that BootRank improves the ability to predict disease risk of unseen individuals in the Wellcome Trust Case Control Consortium (WTCCC data and results in a more robust set of SNPs and a larger number of enriched pathways being associated with the different diseases. Finally, we show that combining BootRank with seven different classification algorithms improves performance compared to previous studies that used the WTCCC data. Notably, diseases for which BootRank results in the largest improvements were recently shown to have more heritability than previously thought, likely due to contributions from variants with low minimum allele frequency (MAF, suggesting that BootRank can be beneficial in cases where SNPs affecting the disease are poorly tagged or have low MAF. Overall, our results show that improving disease risk prediction from genotypic information may be a tangible goal, with potential implications for personalized disease screening and treatment.
Top Partners Searches and Composite Higgs Models
Matsedonskyi, Oleksii; Wulzer, Andrea
2015-01-01
Colored fermionic partners of the top quark are well-known signatures of the Composite Higgs scenario and for this reason they have been and will be subject of an intensive experimental study at the LHC. Performing an assessment of the theoretical implications of this experimental effort is the goal of the present paper. We proceed by analyzing a set of simple benchmark models, characterized by simple two-dimensional parameter spaces where the results of the searches are conveniently visualized and their impact quantified. We only draw exclusion contours, in the hypothesis of no signal, but of course our formalism could equally well be used to report discoveries in a theoretically useful format.
Top partner searches and Composite Higgs models
Matsedonskyi, Oleksii [DESY Hamburg (Germany); Panico, Giuliano [Barcelona Univ. Autonoma (Spain). IFAE; Wulyer, Andrea [Padova Univ. (Italy). Dipt. di Fisica e Astronomia; INFN, Padova (Italy)
2015-12-15
Colored fermionic partners of the top quark are well-known signatures of the Composite Higgs scenario and for this reason they have been and will be subject of an intensive experimental study at the LHC. Performing an assessment of the theoretical implications of this experimental effort is the goal of the present paper. We proceed by analyzing a set of simple benchmark models, characterized by simple two-dimensional parameter spaces where the results of the searches are conveniently visualized and their impact quantified. We only draw exclusion contours, in the hypothesis of no signal, but of course our formalism could equally well be used to report discoveries in a theoretically useful format.