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56
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 ..."
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Cited by 190 (2 self)
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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.
Sizeestimation framework with applications to transitive closure and reachability
 Journal of Computer and System Sciences
, 1997
"... Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min{mn, n2.38}) time ..."
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Cited by 157 (21 self)
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Computing the transitive closure in directed graphs is a fundamental graph problem. We consider the more restricted problem of computing the number of nodes reachable from every node and the size of the transitive closure. The fastest known transitive closure algorithms run in O(min{mn, n2.38}) time, where n is the number of nodes and m the number of edges in the graph. We present an O(m) time randomized (Monte Carlo) algorithm that estimates, with small relative error, the sizes of all reachability sets and the transitive closure. Another ramification of our estimation scheme is a Õ(m) time algorithm for estimating sizes of neighborhoods in directed graphs with nonnegative edge lengths. Our sizeestimation algorithms are much faster than performing the respective explicit computations. 1
Tutorial on maximum likelihood estimation.
 Journal of Mathematical Psychology,
, 2003
"... Abstract In this paper, I provide a tutorial exposition on maximum likelihood estimation (MLE). The intended audience of this tutorial are researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method. Unlike leastsquares estimation which is primarily a ..."
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Cited by 115 (3 self)
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Abstract In this paper, I provide a tutorial exposition on maximum likelihood estimation (MLE). The intended audience of this tutorial are researchers who practice mathematical modeling of cognition but are unfamiliar with the estimation method. Unlike leastsquares estimation which is primarily a descriptive tool, MLE is a preferred method of parameter estimation in statistics and is an indispensable tool for many statistical modeling techniques, in particular in nonlinear modeling with nonnormal data. The purpose of this paper is to provide a good conceptual explanation of the method with illustrative examples so the reader can have a grasp of some of the basic principles. r
How to Fit a Response Time Distribution
"... Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data, response time distributions in particular. However, techniques for fitting distributions vary widely and little is known about the efficacy of different techniques. In this article, ..."
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Cited by 89 (1 self)
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Among the most valuable tools in behavioral science is statistically fitting mathematical models of cognition to data, response time distributions in particular. However, techniques for fitting distributions vary widely and little is known about the efficacy of different techniques. In this article, we assessed several fitting techniques by simulating six widely cited models of response time and using the fitting procedures to recover model parameters. The techniques include the maximization of likelihood and leastsquares fits of the theoretical distributions to different empirical estimates of the simulated distributions. A running example was used to illustrate the different estimation and fitting procedures. The simulation studies revealed that empirical density estimates are biased even for very large sample sizes. Some fitting techniques yielded more accurate and less variable parameter estimates than others. Methods that involved leastsquares fits to density estimates generally yielded very poor parameter estimates. How to Fit a Response Time Distribution The importance of considering the entire response time (RT) distribution in testing formal models of cognition is now widely appreciated. Fitting a model to mean RT alone can mask important details of the data that examination of the entire distribution would reveal, such as the behavior of fast and slow responses across the conditions of an experiment (e.g., Heathcote, Popiel & Mewhort, 1991), the extent of facilitation between perceptual channels (Miller, 1982), and the effects of practice on RT quantiles (Logan, 1992). Techniques for testing hypotheses based on the RT distribution have been developed (Townsend, 1990). In addition, the RT distribution provides an important meeting ground between theory and da...
Learning Action Strategies for Planning Domains
 ARTIFICIAL INTELLIGENCE
, 1997
"... This paper reports on experiments where techniques of supervised machine learning are applied to the problem of planning. The input to the learning algorithm is composed of a description of a planning domain, planning problems in this domain, and solutions for them. The output is an efficient algori ..."
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Cited by 86 (3 self)
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This paper reports on experiments where techniques of supervised machine learning are applied to the problem of planning. The input to the learning algorithm is composed of a description of a planning domain, planning problems in this domain, and solutions for them. The output is an efficient algorithm  a strategy  for solving problems in that domain. We test the strategy on an independent set of planning problems from the same domain, so that success is measured by its ability to solve complete problems. A system, L2Act, has been developed in order to perform these experiments. We have experimented with the blocks world domain, and the logistics domain, using strategies in the form of a generalization of decision lists, where the rules on the list are existentially quantified first order expressions. The learning algorithm is a variant of Rivest`s [39] algorithm, improved with several techniques that reduce its time complexity. As the experiments demonstrate, generalization is a...
RandomSet Methods Identify Distinct Aspects of the Enrichment Signal in GeneSet Analysis,” The Annals of Applied Statistics
, 2007
"... A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biologi ..."
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Cited by 45 (4 self)
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A prespecified set of genes may be enriched, to varying degrees, for genes that have altered expression levels relative to two or more states of a cell. Knowing the enrichment of gene sets defined by functional categories, such as gene ontology (GO) annotations, is valuable for analyzing the biological signals in microarray expression data. A common approach to measuring enrichment is by crossclassifying genes according to membership in a functional category and membership on a selected list of significantly altered genes. A small Fisher’s exact test pvalue, for example, in this 2 × 2 table is indicative of enrichment. Other category analysis methods retain the quantitative genelevel scores and measure significance by referring a categorylevel statistic to a permutation distribution associated with the original differential expression problem. We describe a class of randomset scoring methods that measure distinct components of the enrichment signal. The class includes Fisher’s test based on selected genes and also tests that average genelevel evidence across the category. Averaging and selection methods are compared empirically using Affymetrix data on expression in nasopharyngeal cancer tissue, and theoretically using a location model of differential expression. We find that each method has a domain of superiority in the state space of enrichment problems, and that both methods have benefits in practice. Our analysis also addresses two problems related to multiplecategory inference, namely, that equally enriched categories are not detected with equal probability if they are of different sizes, and also that there is dependence among category statistics owing to shared genes. Randomset enrichment calculations do not require Monte Carlo for implementation. They are made available in the R package allez.
Feature selection in face recognition: A sparse representation perspective
, 2007
"... In this paper, we examine the role of feature selection in face recognition from the perspective of sparse representation. We cast the recognition problem as finding a sparse representation of the test image features w.r.t. the training set. The sparse representation can be accurately and efficientl ..."
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Cited by 36 (1 self)
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In this paper, we examine the role of feature selection in face recognition from the perspective of sparse representation. We cast the recognition problem as finding a sparse representation of the test image features w.r.t. the training set. The sparse representation can be accurately and efficiently computed by ℓ 1minimization. The proposed simple algorithm generalizes conventional face recognition classifiers such as nearest neighbors and nearest subspaces. Using face recognition under varying illumination and expression as an example, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficient and whether the sparse representation is correctly found. We conduct extensive experiments to validate the significance of imposing sparsity using the Extended Yale B database and the AR database. Our thorough evaluation shows that, using conventional features such as Eigenfaces and facial parts, the proposed algorithm achieves much higher recognition accuracy on face images with variation in either illumination or expression. Furthermore, other unconventional features such as severely downsampled images and randomly projected features perform almost equally well with the increase of feature dimensions. The differences in performance between different features become insignificant as the featurespace dimension is sufficiently large.
The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results
, 1994
"... • Although there is a growing understanding of the importance of statistical power considerations when designing studies and of the value of confidence intervals when interpreting data, confusion exists about the reverse arrangement: the role of confidence intervals in study design and of power in ..."
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Cited by 31 (0 self)
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• Although there is a growing understanding of the importance of statistical power considerations when designing studies and of the value of confidence intervals when interpreting data, confusion exists about the reverse arrangement: the role of confidence intervals in study design and of power in interpretation. Confidence intervals should play an important role when setting sample size, and power should play no role once the data have been collected, but exactly the opposite procedure is widely practiced. In this commentary, we present the reasons why the calculation of power after a study is over is inappropriate and how confidence intervals can be used during both study design and study interpretation. Med. 1994;121:200206. From Johns Hopkins University School of Medicine, Baltimore, Maryland; and the University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania. For current author addresses, see end of text. Ann Intern The increasing statistical sophistication of medical researchers has heightened their awareness of the importance of having appropriate statistical power in a clinical experiment. Power is the probability that, given a specified true difference between two groups, the quantitative results of a study will be deemed statistically significant. Freiman and colleagues (1) sensitized researchers to the possibility that many socalled "negative" trials of medical interventions might have too few participants to produce statistically significant findings even if clinically important effects actually existed. These authors calculated the statistical power of 71 "negative" studies that compared two treatments. They showed that for most of the studies, the power to detect a 50% improvement in success rates was quite low. This kind of analysis has been applied in various specialty fields, with similar results (26). Studies with low statistical power have sample sizes that are too small, producing results that have high statistical variability (low precision). Confidence intervals are a convenient way to express that variability. Numerous articles, commentaries, and editorials (713) have appeared in the biomedical literature during the past decade showing how confidence intervals are informative data summaries that can be used in addition to or instead of P values in reporting statistical results. Although there is a growing understanding of the role of power in designing studies and the role of confidence intervals in study interpretation, confusion exists about the reverse arrangement, the role of confidence intervals in designing studies and of power estimates in interpreting study findings. Confidence intervals should play an important role when setting sample size, and power should play no role once the data have been collected, but exactly the opposite is widely practiced. When "no significant difference" between two compared treatments is reported, a common question posed in journal clubs, on rounds, in letters to the editor, and in reviews of manuscripts is, "What was the power of the study to detect the observed difference?" A widely used instrument for assessing the quality of a clinical trial penalizes studies if post hoc power calculations of this type are omitted Although several writers Confidence Intervals A confidence interval can be thought of as the set of true but unknown differences that are statistically compatible with the observed difference. The standard convention for this statistical compatibility is the twosided 95% confidence interval. A confidence interval is typically reported in the following way: "There was a 10% (95% CI, 2% to 18%) difference in mortality." This means that even though the observed mortality difference was 10% (for example, 70% compared with 60%), the data are statistically compatible with a true mortality difference as small as 2% or as large as 18%. True differences that lie outside the 95% confidence interval are not impossible; they merely have less statistical evidence supporting them than values within it. The 200
Stochastic approximation algorithms for partition function estimation of Gibbs random fields
 IEEE Trans. Inform. Theory
, 1997
"... Abstract—We present an analysis of recently proposed Monte Carlo algorithms for estimating the partition function of a Gibbs random field. We show that this problem reduces to estimating one or more expectations of suitable functionals of the Gibbs states with respect to properly chosen Gibbs distri ..."
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Abstract—We present an analysis of recently proposed Monte Carlo algorithms for estimating the partition function of a Gibbs random field. We show that this problem reduces to estimating one or more expectations of suitable functionals of the Gibbs states with respect to properly chosen Gibbs distributions. As expected, the resulting estimators are consistent. Certain generalizations are also provided. We study computational complexity with respect to grid size and show that Monte Carlo partition function estimation algorithms can be classified into two categories: EType algorithms that are of exponential complexity and PType algorithms that are of polynomial complexity, Turing reducible to the problem of sampling from the Gibbs distribution. EType algorithms require estimating a single expectation, whereas, PType algorithms require estimating a number of expectations with respect to Gibbs distributions which are chosen to be sufficiently “close ” to each other. In the latter case, the required number of expectations is of polynomial order with respect to grid size. We compare computational complexity by using both theoretical results and simulation experiments. We determine the most efficient EType and PType algorithms and conclude that PType algorithms are more appropriate for partition function estimation. We finally suggest a practical and efficient PType algorithm for this task. Index Terms—Computational complexity, Gibbs random fields, importance sampling, Monte Carlo simulations, partition function estimation, stochastic approximation. I.