Results 1  10
of
152
Interval estimation for a binomial proportion
 Statist. Sci
, 2001
"... Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that t ..."
Abstract

Cited by 185 (2 self)
 Add to MetaCart
Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence 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 Waldinterval 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 context. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equaltailedJeffreys 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. Key words and phrases: Bayes, binomial distribution, confidence intervals, coverage probability, Edgeworth expansion, expected length, Jeffreys prior, normal approximation, posterior.
Likelihood
, 1992
"... *This article is a preliminary version of what will be published in the International Encyclopedia of the Social and Behavioral Sciences, and was written while Professor Edwards was visiting CIMAT, March 819, 1999. A statistical model for phenomena in the sciences or social sciences is a mathemat ..."
Abstract

Cited by 63 (0 self)
 Add to MetaCart
*This article is a preliminary version of what will be published in the International Encyclopedia of the Social and Behavioral Sciences, and was written while Professor Edwards was visiting CIMAT, March 819, 1999. A statistical model for phenomena in the sciences or social sciences is a mathematical construct which associates a probability with each of the possible outcomes. If the data are discrete, such as the numbers of people falling into various classes, the model will be a discrete probability distribution, but if the data consist of measurements or other numbers which may take any values in a continuum, the model will be a continuous probability distribution. When two different models, or perhaps two variants of the same model differing only in the value of some adjustable parameter(s), are to be compared as explanations for the same observed outcome, the probability of obtaining this particular outcome can be calculated for each and is then known as likelihood for the model or parameter value(s) given the data. Probabilities and likelihoods are easily (and frequently) confused, and it is for this
Severe Testing as a Basic Concept in a NeymanPearson Philosophy of Induction
 BRITISH JOURNAL FOR THE PHILOSOPHY OF SCIENCE
, 2006
"... Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and longstanding problems of N–P tests s ..."
Abstract

Cited by 50 (21 self)
 Add to MetaCart
Despite the widespread use of key concepts of the Neyman–Pearson (N–P) statistical paradigm—type I and II errors, significance levels, power, confidence levels—they have been the subject of philosophical controversy and debate for over 60 years. Both current and longstanding problems of N–P tests stem from unclarity and confusion, even among N–P adherents, as to how a test’s (predata) error probabilities are to be used for (postdata) inductive inference as opposed to inductive behavior. We argue that the relevance of error probabilities is to ensure that only statistical hypotheses that have passed severe or probative tests are inferred from the data. The severity criterion supplies a metastatistical principle for evaluating proposed statistical inferences, avoiding classic fallacies from tests that are overly sensitive, as well as those not sensitive enough to particular errors and discrepancies.
The DempsterShafer calculus for statisticians
 International Journal of Approximate Reasoning
, 2007
"... The DempsterShafer (DS) theory of probabilistic reasoning is presented in terms of a semantics whereby every meaningful formal assertion is associated with a triple (p, q, r) where p is the probability “for ” the assertion, q is the probability “against” the assertion, and r is the probability of “ ..."
Abstract

Cited by 46 (1 self)
 Add to MetaCart
(Show Context)
The DempsterShafer (DS) theory of probabilistic reasoning is presented in terms of a semantics whereby every meaningful formal assertion is associated with a triple (p, q, r) where p is the probability “for ” the assertion, q is the probability “against” the assertion, and r is the probability of “don’t know”. Arguments are presented for the necessity of “don’t know”. Elements of the calculus are sketched, including the extension of a DS model from a margin to a full state space, and DS combination of independent DS uncertainty assessments on the full space. The methodology is applied to inference and prediction from Poisson counts, including an introduction to the use of jointree model structure to simplify and shorten computation. The relation of DS theory to statistical significance testing is elaborated, introducing along the way the new concept of “dull ” null hypothesis. Key words: DempsterShafer; belief functions; state space; Poisson model; jointree computation; statistical significance; dull null hypothesis 1
Inference and Hierarchical Modeling in the Social Sciences
, 1995
"... this paper I (1) examine three levels of inferential strength supported by typical social science datagathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (2) reconsider the use of HMs in school effective ..."
Abstract

Cited by 44 (6 self)
 Add to MetaCart
this paper I (1) examine three levels of inferential strength supported by typical social science datagathering methods, and call for a greater degree of explicitness, when HMs and other models are applied, in identifying which level is appropriate; (2) reconsider the use of HMs in school effectiveness studies and metaanalysis from the perspective of causal inference; and (3) recommend the increased use of Gibbs sampling and other Markovchain Monte Carlo (MCMC) methods in the application of HMs in the social sciences, so that comparisons between MCMC and betterestablished fitting methodsincluding full or restricted maximum likelihood estimation based on the EM algorithm, Fisher scoring or iterative generalized least squaresmay be more fully informed by empirical practice.
Predicting linear Bcell epitopes using string kernels
, 2008
"... The identification and characterization of Bcell epitopes play an important role in vaccine design, immunodiagnostic tests, and antibody production. Therefore, computational tools for reliably predicting linear Bcell epitopes are highly desirable. We evaluated Support Vector Machine (SVM) classifi ..."
Abstract

Cited by 38 (3 self)
 Add to MetaCart
The identification and characterization of Bcell epitopes play an important role in vaccine design, immunodiagnostic tests, and antibody production. Therefore, computational tools for reliably predicting linear Bcell epitopes are highly desirable. We evaluated Support Vector Machine (SVM) classifiers trained utilizing five different kernel methods using fivefold crossvalidation on a homologyreduced data set of 701 linear Bcell epitopes, extracted from Bcipep database, and 701 nonepitopes, randomly extracted from SwissProt sequences. Based on the results of our computational experiments, we propose BCPred, a novel method for predicting linear Bcell epitopes using the subsequence kernel. We show that the predictive performance of BCPred (AUC 0.758) outperforms 11 SVMbased classifiers developed and evaluated in our experiments as well as our implementation of AAP (AUC 0.7), a recently proposed method for predicting linear Bcell epitopes using amino acid pair antigenicity. Furthermore, we compared BCPred with AAP and ABCPred, a method that uses recurrent neural networks, using two data sets of unique Bcell epitopes that had been previously used to evaluate ABCPred. Analysis of the data sets used and the results of this comparison show that conclusions about the relative performance of different Bcell epitope prediction methods drawn on the basis of experiments using data sets of unique Bcell epitopes are likely to yield overly optimistic estimates of performance of evaluated methods. This argues for the use of carefully homologyreduced data sets in comparing Bcell epitope prediction methods to avoid misleading conclusions about how different methods compare to each other. Our homologyreduced data set and implementations of BCPred as well as the APP method are publicly available through
A tutorial on conformal prediction
 Journal of Machine Learning Research
, 2008
"... Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability ε, together with a method that makes a prediction ˆy of a label y, it produces a set of labels, typically containing ˆy, that also contains y with probability 1 − ε. Con ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
(Show Context)
Conformal prediction uses past experience to determine precise levels of confidence in new predictions. Given an error probability ε, together with a method that makes a prediction ˆy of a label y, it produces a set of labels, typically containing ˆy, that also contains y with probability 1 − ε. Conformal prediction can be applied to any method for producing ˆy: a nearestneighbor method, a supportvector machine, ridge regression, etc. Conformal prediction is designed for an online setting in which labels are predicted successively, each one being revealed before the next is predicted. The most novel and valuable feature of conformal prediction is that if the successive examples are sampled independently from the same distribution, then the successive predictions will be right 1 − ε of the time, even though they are based on an accumulating data set rather than on independent data sets. In addition to the model under which successive examples are sampled independently, other online compression models can also use conformal prediction. The widely used Gaussian linear model is one of these. This tutorial presents a selfcontained account of the theory of conformal prediction and works through several numerical examples. A more comprehensive treatment of the topic is provided in
Misinterpretations of significance. A problem students share with their teachers
 Methods of Psychological Research Online
, 2000
"... ..."
Intuitions about sample size; The empirical law of large numbers
 Journal of Behavioral Decision Making
, 1997
"... According to Jacob Bernoulli, even the “stupidest man ” knows that the larger one’s sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Twoandahalf centuries later, psychologists empirically tested people’s intuitions about sample s ..."
Abstract

Cited by 29 (5 self)
 Add to MetaCart
According to Jacob Bernoulli, even the “stupidest man ” knows that the larger one’s sample of observations, the more confidence one can have in being close to the truth about the phenomenon observed. Twoandahalf centuries later, psychologists empirically tested people’s intuitions about sample size. One group of such studies found participants attentive to sample size; another found participants ignoring it. We suggest an explanation for a substantial part of these inconsistent findings. We propose the hypothesis that human intuition conforms to the “empirical law of large numbers ” and distinguish between two kinds of tasks—one that can be solved by this intuition (frequency distributions) and one for which it is not sufficient (sampling distributions). A review of the literature reveals that this distinction can explain a substantial part of the apparently inconsistent results. Key Words: sample size; law of large numbers; sampling distribution; frequency distribution. Jacob Bernoulli, who formulated the first version of the law of large numbers, asserted in a letter to Leibniz that “even the stupidest man knows by some instinct of nature per se and by no previous instruction ” that the greater the number of confirming observations, the surer the conjecture (Gigerenzer et al., 1989, p. 29). Twoandahalf centuries later, psychologists began to study whether people actually take into account information about sample size in judgements of various kinds. The results turned out to be contradictory: One group of studies seemed to confirm, a second to disconfirm the “instinct of nature ” assumed by Bernoulli. In this paper, we propose an explanation that accounts for a substantial part of the contradictory results reported in the literature.