Probable Inference, the Law of Succession, and Statistical Inference
01 Jun 1927-Journal of the American Statistical Association (Taylor & Francis Group)-Vol. 22, Iss: 158, pp 209-212
TL;DR: In this article, Probable Inference, the Law of Succession, and Statistical Inference are discussed, with a focus on the law of succession in probabilistic inference.
Abstract: (1927). Probable Inference, the Law of Succession, and Statistical Inference. Journal of the American Statistical Association: Vol. 22, No. 158, pp. 209-212.
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Conrad L. Schoch1, Keith A. Seifert, Sabine M. Huhndorf2, Vincent Robert3 +157 more•Institutions (59)
TL;DR: Among the regions of the ribosomal cistron, the internal transcribed spacer (ITS) region has the highest probability of successful identification for the broadest range of fungi, with the most clearly defined barcode gap between inter- and intraspecific variation.
Abstract: Six DNA regions were evaluated as potential DNA barcodes for Fungi, the second largest kingdom of eukaryotic life, by a multinational, multilaboratory consortium. The region of the mitochondrial cytochrome c oxidase subunit 1 used as the animal barcode was excluded as a potential marker, because it is difficult to amplify in fungi, often includes large introns, and can be insufficiently variable. Three subunits from the nuclear ribosomal RNA cistron were compared together with regions of three representative protein-coding genes (largest subunit of RNA polymerase II, second largest subunit of RNA polymerase II, and minichromosome maintenance protein). Although the protein-coding gene regions often had a higher percent of correct identification compared with ribosomal markers, low PCR amplification and sequencing success eliminated them as candidates for a universal fungal barcode. Among the regions of the ribosomal cistron, the internal transcribed spacer (ITS) region has the highest probability of successful identification for the broadest range of fungi, with the most clearly defined barcode gap between inter- and intraspecific variation. The nuclear ribosomal large subunit, a popular phylogenetic marker in certain groups, had superior species resolution in some taxonomic groups, such as the early diverging lineages and the ascomycete yeasts, but was otherwise slightly inferior to the ITS. The nuclear ribosomal small subunit has poor species-level resolution in fungi. ITS will be formally proposed for adoption as the primary fungal barcode marker to the Consortium for the Barcode of Life, with the possibility that supplementary barcodes may be developed for particular narrowly circumscribed taxonomic groups.
4,116 citations
TL;DR: Criteria appropriate to the evaluation of various proposed methods for interval estimate methods for proportions include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use.
Abstract: Simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals. Criteria appropriate to the evaluation of various proposed methods include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use, whether by tables, software or formulae. Seven methods for the single proportion are evaluated on 96,000 parameter space points. Intervals based on tail areas and the simpler score methods are recommended for use. In each case, methods are available that aim to align either the minimum or the mean coverage with the nominal 1 -alpha.
3,825 citations
TL;DR: For example, this paper showed that using the adjusted Wald test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes, and that the 95% score interval has similar behavior as the adjusted-Wald interval obtained after adding two "successes" and two "failures" to the sample.
Abstract: For interval estimation of a proportion, coverage probabilities tend to be too large for “exact” confidence intervals based on inverting the binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion ± z-score × estimated standard error). Wilson's suggestion of inverting the related score test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes. The 95% score interval has similar behavior as the adjusted Wald interval obtained after adding two “successes” and two “failures” to the sample. In elementary courses, with the score and adjusted Wald methods it is unnecessary to provide students with awkward sample size guidelines.
3,276 citations
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...Wilson (1927), has the form...
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TL;DR: In this paper, the problem of interval estimation of a binomial proportion is revisited, and a number of natural alternatives are presented, each with its motivation and con- text, each interval is examined for its coverage probability and its length.
Abstract: We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the stan- d ardWaldconfid ence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinter- val are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted . This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and con- text. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equal- tailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.
2,893 citations
Cites background or methods from "Probable Inference, the Law of Succ..."
...The score interval for the binomial case seems to have been introduced in Wilson (1927); so we call it the Wilson interval....
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...This confidence interval has the form CIW = X+ κ2/2 n+ κ2 ± κn1/2 n+ κ2 p̂q̂+ κ 2/ 4n 1/2 (4) This interval was apparently introduced by Wilson (1927) and we will call this interval the Wilson interval....
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TL;DR: This paper presents a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and shows that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios.
2,756 citations
Cites methods from "Probable Inference, the Law of Succ..."
...Confidence intervals (95%) were computed using the Wilson method (Wilson, 1927)....
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...%) were computed using the Wilson method (Wilson, 1927)....
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