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  1. Department of Genetics SK-50, University of Washington, Seattle WA 98195
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Journal Article: Publisher's Accepted Manuscript
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Additional Journal Information:
Journal Volume: 39; Journal Issue: 4; Related Information: CHORUS Timestamp: 2017-10-20 17:33:41; Journal ID: ISSN 0014-3820
Country of Publication:
United States

Citation Formats

Felsenstein, Joseph. CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP. United States: N. p., 2017. Web. doi:10.1111/j.1558-5646.1985.tb00420.x.
Felsenstein, Joseph. CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP. United States. doi:10.1111/j.1558-5646.1985.tb00420.x.
Felsenstein, Joseph. 2017. "CONFIDENCE LIMITS ON PHYLOGENIES: AN APPROACH USING THE BOOTSTRAP". United States. doi:10.1111/j.1558-5646.1985.tb00420.x.
author = {Felsenstein, Joseph},
abstractNote = {},
doi = {10.1111/j.1558-5646.1985.tb00420.x},
journal = {Evolution},
number = 4,
volume = 39,
place = {United States},
year = 2017,
month = 5

Journal Article:
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This content will become publicly available on May 31, 2018
Publisher's Accepted Manuscript

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  • The recently-developed statistical method known as the bootstrap can be used to place confidence intervals on phylogenies. It involves resampling points from one's own data, with replacement, to create a series of bootstrap samples of the same size as the original data. Each of these is analyzed, and the variation among the resulting estimates taken to indicate the size of the error involved in making estimates from the original data. In the case of phylogenies, it is argued that the proper method of resampling is to keep all of the original species while sampling characters with replacement, under the assumptionmore » that the characters have been independently drawn by the systematist and have evolved independently. Majority-rule consensus trees can be used to construct a phylogeny showing all of the inferred monophyletic groups that occurred in a majority of the bootstrap samples. If a group shows up 95% of the time or more, the evidence for it is taken to be statistically significant. Existing computer programs can be used to analyze different bootstrap samples by using weights on the characters, the weight of a character being how many times it was drawn in bootstrap sampling. When all characters are perfectly compatible, as envisioned by Hennig, bootstrap sampling becomes unnecessary; the bootstrap method would show significant evidence for a group if it is defined by three or more characters. 8 references, 2 figures, 1 table.« less
  • A simple method of calculating confidence limits for radioimmunoassay data is presented. The method involves the use of the within-assay variation in dose estimate of three routine quality-control specimens, measured in repeated assays, to estimate the confidence limits for results on unknown samples. Results for control specimens are combined by calculating the unique quadratic curve fitting a graph of within-assay standard deviation vs mean value for each control. This method requires no special data accumulation or advanced computing equipment. For cortisol, lutropin, and thyroxine radioimmunassays, confidence limits calculated in this way have been compared with three calculated from the variancemore » of the response variable B/Bq in repeated standard curves. Both methods agree well with actual limits observed when plasma pools containing a wide range of hormone concentrations are assayed repeatedly.« less
  • The Maximum, bootstrap and Bayes methods for calculating lower s-confidence limits on reliability by means of binomial component analysis are presently compared, using Monte Carlo simulations for 20 examples ranging in complexity from simple to moderate. The Maximus method is generally superior for moderate to large series systems of reliable components with small quantities of test data/component, and for small series systems of repeated components. The bootstrap method is generally superior for highly reliable and redundant systems, while the Bayes method is generally superior for moderate to large series systems of reliable components with moderate to large numbers of componentmore » tests, and small series systems of reliable nonrepeated components. 29 references.« less
  • We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter space by intelligently targeting likelihood evaluations so as to quickly and accurately characterize the likelihood surface in both low- and high-likelihood regions. We compare our algorithm to Bayesian credible limits derived by the well-tested Markov Chain Monte Carlo (MCMC) algorithm using both multi-modal toy likelihood functions and the seven yr Wilkinson Microwave Anisotropy Probe cosmic microwave background likelihood function. We find that our algorithm correctly identifies themore » location, general size, and general shape of high-likelihood regions in parameter space while being more robust against multi-modality than MCMC.« less
  • Reliability of ceramic components is usually obtained in terms of failure probability from Finite Element stress analysis and subsequent numerical integration of the stress field. Due to scatter in the material parameters that enter the numerical integration, the uncertainty in the resulting failure probabilities depends strongly on the quality and abundance of the underlying data base. Material parameters that enter the calculation are obtained at different levels of, e.g. temperature or loading rate. It would be helpful to have a framework which allows efficient allocation of specimens to different types of experiments with respect to minimizing the resulting scatter inmore » the failure probability predictions.For the prediction of confidence intervals for the failure probability, we use bootstrap resampling methods based on observed samples for material strength measurements. For the description of temperature dependent material behavior we have implemented two methods for regression neural networks, namely D. J. C. MacKay's Gaussian approximation method and also Markov Chain Monte Carlo Method of R. M. Neal.This procedure allows also a 'pooling' of the data -- in our case we obtain one large room temperature sample from various samples at different temperatures -- leading to reduced prediction uncertainty. Using the regression network, we can generate a relation between the strength data base and the corresponding reliability prediction uncertainty. In order to investigate the influence of different data bases, we use a parametric bootstrap approach to generate artificial samples from the original data. Imposing weights to different samples, a procedure is obtained which detects the relevance of specific samples to the uncertainties in the final failure probability prediction.Thus strategies can be proposed for efficient allocation of available specimens to selected experimental conditions.« less