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A Bayesian Framework for the Analysis of Microarray Expression Data: Regularized tTest and Statistical Inferences of Gene Changes
 Bioinformatics
, 2001
"... Motivation: DNA microarrays are now capable of providing genomewide patterns of gene expression across many different conditions. The first level of analysis of these patterns requires determining whether observed differences in expression are significant or not. Current methods are unsatisfactory ..."
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Cited by 491 (6 self)
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with neighboring genes. An additional hyperparameter, inversely related to the number of empirical observations, determines the strength of the background variance. Simulations show that these point estimates, combined with a ttest, provide a systematic inference approach that compares favorably with simple t
Statistical Inference
"... In the process of developing a conditiopallydependent item response theory (IRT) model, the problem arose of modeling an underlying multivariate normal (MVN) response process with general correlation among the items. Without the assumption of conditional independence, for which the underlying MVN c ..."
*Statistical Inference
"... Probabilitybased inference in complex networks of interdependent variables is an active topic in statistical research, spurred by such diverse applications as forecasting, pedigree analysis, troubleshooting, and medical diagnosis. This paper concerns the role of Bayesian inference networks for upda ..."
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Probabilitybased inference in complex networks of interdependent variables is an active topic in statistical research, spurred by such diverse applications as forecasting, pedigree analysis, troubleshooting, and medical diagnosis. This paper concerns the role of Bayesian inference networks
Statistical Inference
"... Up to now we’ve been looking exclusively at the problem of estimation, of trying to identify the value θ ∈ Θ of an uncertain parameter on the basis of an observation x ∈ X of a random vector from some probability distribution x ∼ f(x  θ) that depends on θ. Today we begin a new quest: again on the b ..."
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Up to now we’ve been looking exclusively at the problem of estimation, of trying to identify the value θ ∈ Θ of an uncertain parameter on the basis of an observation x ∈ X of a random vector from some probability distribution x ∼ f(x  θ) that depends on θ. Today we begin a new quest: again on the basis of an observed value x ∼ f(x  θ), we seek to discover whether an assertion about θ is true or false. We can think about hypotheses (or “assertions ” about θ) simply as subsets H0 ⊂ Θ, interpreted as the set of θ ∈ Θ for which the assertion or hypothesis is true; thus we would like to discover, on the basis of an observed value x ∈ X, whether or not θ ∈ H0. Some times we will consider an alternative hypothesis H1 ⊂ Θ with H0 ∩ H1 = ∅; evidently the largest possible alternative would be H0 c = {θ ∈ Θ: θ / ∈ H0}. There are many approaches to the problem of testing hypotheses. We will consider two variations of Frequentist approach, both the NeymanPearson fixedlevel approach and Fisher’s significance testing approach (reporting Pvalues), and also the Bayesian approach, in both the decisiontheoretic and posterior probability versions. 2. Fixedlevel Frequentist [NeymanPearson] If we feel constrained to answer the question “Is θ ∈ H0? ” with a simple yes or no, then we may also divide X up into two sets, the “rejection region ” or “critical region ” R ⊂ X of those possible outcomes x ∈ X for which we will 1 conclude that H0 is false, and its complement R c = X\R, the outcomes that will not lead us to reject H0. Notice that there are four possibilities: 1. Reject a True Hypothesis: θ ∈ H0, and x ∈ R; 2. Accept a False Hypothesis: θ ∈ H1, and x / ∈ R; 3. Reject a False Hypothesis: θ ∈ H1, and x ∈ R;
Statistical Inference as Default Reasoning
"... Classical statistical inference is nonmonotonic in nature. We show how it can be form~ized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics, the justifications ..."
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Classical statistical inference is nonmonotonic in nature. We show how it can be form~ized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics
Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality
, 1998
"... We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance ..."
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Cited by 261 (32 self)
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We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance
Statistics and causal inference.
 J. Am. Statist. Assoc.,
, 1986
"... Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is address ..."
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Cited by 734 (0 self)
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Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question
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