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Elias Chaibub Neto - One of the best experts on this subject based on the ideXlab platform.
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speeding up non parametric bootstrap computations for statistics based on Sample moments in small Moderate Sample Size applications
PLOS ONE, 2015Co-Authors: Elias Chaibub NetoAbstract:In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on Sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of Sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a reSampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s Sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying Sample Sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/Moderate Sample Sizes. The same results were observed in the comparison with the straightforward implementation, except for large Sample Sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling.
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Speeding Up Non-Parametric Bootstrap Computations for Statistics Based on Sample Moments in Small/Moderate Sample Size Applications
2015Co-Authors: Elias Chaibub NetoAbstract:In this paper we propose a vectorized implementation of the non-parametric bootstrap for statistics based on Sample moments. Basically, we adopt the multinomial sampling formulation of the non-parametric bootstrap, and compute bootstrap replications of Sample moment statistics by simply weighting the observed data according to multinomial counts instead of evaluating the statistic on a reSampled version of the observed data. Using this formulation we can generate a matrix of bootstrap weights and compute the entire vector of bootstrap replications with a few matrix multiplications. Vectorization is particularly important for matrix-oriented programming languages such as R, where matrix/vector calculations tend to be faster than scalar operations implemented in a loop. We illustrate the application of the vectorized implementation in real and simulated data sets, when bootstrapping Pearson’s Sample correlation coefficient, and compared its performance against two state-of-the-art R implementations of the non-parametric bootstrap, as well as a straightforward one based on a for loop. Our investigations spanned varying Sample Sizes and number of bootstrap replications. The vectorized bootstrap compared favorably against the state-of-the-art implementations in all cases tested, and was remarkably/considerably faster for small/Moderate Sample Sizes. The same results were observed in the comparison with the straightforward implementation, except for large Sample Sizes, where the vectorized bootstrap was slightly slower than the straightforward implementation due to increased time expenditures in the generation of weight matrices via multinomial sampling.
Catherine A Pilachowski - One of the best experts on this subject based on the ideXlab platform.
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a Moderate Sample Size multielement analysis of the globular cluster m12 ngc 6218
The Astronomical Journal, 2006Co-Authors: Christian Johnson, Catherine A PilachowskiAbstract:We present chemical abundances of several proton-capture, α-, Fe-peak, and neutron-capture elements and radial velocities for 21 red giant branch (RGB) and asymptotic giant branch members of the Galactic globular cluster M12. Abundances are based on equivalent width measurements and synthetic spectral analyses of Moderate-resolution spectra (R ~ 15,000) obtained with the 3.5 m WIYN telescope and Hydra multifiber spectrograph. The stars observed range from the RGB tip (M = -2.47) down to about 0.50 mag above the level of the horizontal branch (M = +0.11). Our spectroscopic analysis suggests that M12 is a Moderately metal-poor cluster with [Fe/H] = -1.54 (σ = 0.09). While the Na abundances exhibit a range of 0.90 dex, Mg and Al abundances are enhanced by 0.37 and 0.54 dex and are nearly constant at all RGB luminosities, in contrast to the blue horizontal-branch cluster M13. The α- and Fe-peak elements indicate that M12 has undergone a similar chemical enrichment history to that of globular clusters and field stars of comparable metallicity, with [α/Fe] = +0.33 (σ = 0.11). M12 also appears to be slightly r-process-rich, with [Eu/Ba,La] = +0.22 (σ = 0.18).
Florian Schlagenhauf - One of the best experts on this subject based on the ideXlab platform.
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risk factors for addiction and their association with model based behavioral control
Frontiers in Behavioral Neuroscience, 2016Co-Authors: Andrea Reiter, Lorenz Deserno, Tilmann Wilbertz, Hansjochen Heinze, Florian SchlagenhaufAbstract:Addiction shows familial aggregation and previous endophenotype research suggests that healthy relatives of addicted individuals share altered behavioral and cognitive characteristics with individuals suffering from addiction. In this study we asked whether impairments in behavioral control proposed for addiction, namely a shift from goal-directed, model-based toward habitual model-free control, extends toward an unaffected Sample (n=20) of adult children of alcohol-dependent fathers as compared to a Sample without any personal or family history of alcohol addiction (n=17). Using a sequential decision-making task designed to investigate model-free and model-based control combined with a computational modeling analysis, we did not find any evidence for altered behavioral control in individuals with positive family history of alcohol addiction. Independent of family history of alcohol dependence, we however observed that the interaction of two different risk factors of addiction, namely impulsivity and cognitive capacities, predicts the balance of model-free and model-based behavioral control. Post-hoc tests showed an association of model-based behavior with cognitive capacity in the lower, but not in the higher impulsive group of the original Sample. In an independent Sample of particularly high vs. low impulsive individuals, we confirmed the interaction effect of cognitive capacities and high vs. low impulsivity on model-based control. In the confirmation Sample, a positive association of omega with cognitive capacity was observed in high-impulsive individuals. Due to the Moderate Sample Size of the study, further investigation of the association of risk factors for addiction with model-based behavior in larger Sample Sizes is warranted.
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risk factors for addiction and their association with model based behavioral control
Frontiers in Behavioral Neuroscience, 2016Co-Authors: Andrea M F Reiter, Lorenz Deserno, Tilmann Wilbertz, Hansjochen Heinze, Florian SchlagenhaufAbstract:Addiction shows familial aggregation and previous endophenotype research suggests that healthy relatives of addicted individuals share altered behavioral and cognitive characteristics with individuals suffering from addiction. In this study we asked whether impairments in behavioral control proposed for addiction, namely a shift from goal-directed, model-based toward habitual, model-free control, extends toward an unaffected Sample (n = 20) of adult children of alcohol-dependent fathers as compared to a Sample without any personal or family history of alcohol addiction (n = 17). Using a sequential decision-making task designed to investigate model-free and model-based control combined with a computational modeling analysis, we did not find any evidence for altered behavioral control in individuals with a positive family history of alcohol addiction. Independent of family history of alcohol dependence, we however observed that the interaction of two different risk factors of addiction, namely impulsivity and cognitive capacities, predicts the balance of model-free and model-based behavioral control. Post-hoc tests showed a positive association of model-based behavior with cognitive capacity in the lower, but not in the higher impulsive group of the original Sample. In an independent Sample of particularly high- vs. low-impulsive individuals, we confirmed the interaction effect of cognitive capacities and high vs. low impulsivity on model-based control. In the confirmation Sample, a positive association of omega with cognitive capacity was observed in highly impulsive individuals, but not in low impulsive individuals. Due to the Moderate Sample Size of the study, further investigation of the association of risk factors for addiction with model-based behavior in larger Sample Sizes is warranted.
Woochul Lim - One of the best experts on this subject based on the ideXlab platform.
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bootstrap guided information criterion for reliability analysis using small Sample Size information
World Congress of Structural and Multidisciplinary Optimisation, 2017Co-Authors: Eshan Amalnerkar, Tae Hee Lee, Woochul LimAbstract:Several methods for reliability analysis have been established and applied to engineering fields bearing in mind uncertainties as a major contributing factor. Small Sample Size based reliability analysis can be very beneficial when rising uncertainty from statistics of interest such as mean and standard deviation are considered. Model selection and evaluation methods like Akaike Information Criteria (AIC) have demonstrated efficient output for reliability analysis. However, information criterion based on maximum likelihood can provide better model selection and evaluation in small Sample Size scenario by considering the well-known measure of bootstrapping for curtailing uncertainty with resampling. Our purpose is to utilize the capabilities of bootstrap resampling in information criterion based reliability analysis to check for uncertainty arising from statistics of interest for small Sample Size problems. In this study, therefore, a unique and efficient simulation scheme is proposed which contemplates the best model selection frequency devised from information criterion to be combined with reliability analysis. It is also beneficial to compute the spread of reliability values as against solitary fixed values with desirable statistics of interest under replication based approach. The proposed simulation scheme is verified using a number of small and Moderate Sample Size focused mathematical example with AIC based reliability analysis for comparison and Monte Carlo simulation (MCS) for accuracy. The results show that the proposed simulation scheme favors the statistics of interest by reducing the spread and hence the uncertainty in small Sample Size based reliability analysis when compared with conventional methods whereas Moderate Sample Size based reliability analysis did not show any considerable favor.
Arne C Bathke - One of the best experts on this subject based on the ideXlab platform.
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small Sample performance and underlying assumptions of a bootstrap based inference method for a general analysis of covariance model with possibly heteroskedastic and nonnormal errors
Statistical Methods in Medical Research, 2019Co-Authors: Georg Zimmermann, Markus Pauly, Arne C BathkeAbstract:It is well known that the standard F test is severely affected by heteroskedasticity in unbalanced analysis of covariance models. Currently available potential remedies for such a scenario are based on heteroskedasticity-consistent covariance matrix estimation (HCCME). However, the HCCME approach tends to be liberal in small Samples. Therefore, in the present paper, we propose a combination of HCCME and a wild bootstrap technique, with the aim of improving the small-Sample performance. We precisely state a set of assumptions for the general analysis of covariance model and discuss their practical interpretation in detail, since this issue may have been somewhat neglected in applied research so far. We prove that these assumptions are sufficient to ensure the asymptotic validity of the combined HCCME-wild bootstrap analysis of covariance. The results of our simulation study indicate that our proposed test remedies the problems of the analysis of covariance F test and its heteroskedasticity-consistent alternatives in small to Moderate Sample Size scenarios. Our test only requires very mild conditions, thus being applicable in a broad range of real-life settings, as illustrated by the detailed discussion of a dataset from preclinical research on spinal cord injury. Our proposed method is ready-to-use and allows for valid hypothesis testing in frequently encountered settings (e.g., comparing group means while adjusting for baseline measurements in a randomized controlled clinical trial).
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small Sample performance and underlying assumptions of a bootstrap based inference method for a general analysis of covariance model with possibly heteroskedastic and nonnormal errors
arXiv: Methodology, 2017Co-Authors: Georg Zimmermann, Markus Pauly, Arne C BathkeAbstract:It is well known that the standard F test is severely affected by heteroskedasticity in unbalanced analysis of covariance (ANCOVA) models. Currently available potential remedies for such a scenario are based on heteroskedasticity-consistent covariance matrix estimation (HCCME). However, the HCCME approach tends to be liberal in small Samples. Therefore, in the present manuscript, we propose a combination of HCCME and a wild bootstrap technique, with the aim of improving the small-Sample performance. We precisely state a set of assumptions for the general ANCOVA model and discuss their practical interpretation in detail, since this issue may have been somewhat neglected in applied research so far. We prove that these assumptions are sufficient to ensure the asymptotic validity of the combined HCCME-wild bootstrap ANCOVA. The results of our simulation study indicate that our proposed test remedies the problems of the ANCOVA F test and its heteroskedasticity-consistent alternatives in small to Moderate Sample Size scenarios. Our test only requires very mild conditions, thus being applicable in a broad range of real-life settings, as illustrated by the detailed discussion of a dataset from preclinical research on spinal cord injury. Our proposed method is ready-to-use and allows for valid hypothesis testing in frequently encountered settings (e.g., comparing group means while adjusting for baseline measurements in a randomized controlled clinical trial).