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Inference about constrained parameters using the elastic belief method,” Internat
 J. Approx. Reason
, 2011
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Generalized inferential models
, 2011
"... This paper generalizes the authors ’ inferential model (IM) framework for priorfree, posterior probabilistic inference about unknown parameters. This generalization is accomplished by focusing on an association model determined by the sampling distribution of a function of the data and parameter. Th ..."
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Cited by 3 (3 self)
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This paper generalizes the authors ’ inferential model (IM) framework for priorfree, posterior probabilistic inference about unknown parameters. This generalization is accomplished by focusing on an association model determined by the sampling distribution of a function of the data and parameter. The advantage is that the new association model is generally easier to work with than that determined by the full sampling distribution of the data, and that the generalized IM retains the desirable frequencycalibration property of the basic IM. An important special case is when this function of data and parameters is the likelihood. Illustrative examples and further properties of this likelihoodbased generalized IM are given, including extensions to handle marginal and conditional inference. The strengths of the proposed approach are showcased in two interesting marginal inference problems: the gamma mean model and a Gaussian variance components model.
A note on pvalues interpreted as plausibilities
 Statist. Sinica
, 2014
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Optimal inferential models for a Poisson mean
, 2014
"... Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging, even in the largesample case. Here we propose a new approa ..."
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Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging, even in the largesample case. Here we propose a new approach, based on the recently developed framework of inferential models (IMs). Specifically, we construct optimal, or at least approximately optimal, IMs for two important classes of assertions/hypotheses about the Poisson mean. For point assertions, we develop a novel recursive sorting algorithm to construct this optimal IM. Numerical comparisons of the proposed method to existing methods are given, for both the mean and the more challenging meanplusbackground problem.
Large Scale Multinomial Inferences and Its Applications in Genome Wide Association Studies
"... Abstract Statistical analysis of multinomial counts with a large number K of categories and a small number n of sample size is challenging to both frequentist and Bayesian methods and requires thinking about statistical inference at a very fundamental level. Following the framework of DempsterShafe ..."
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Abstract Statistical analysis of multinomial counts with a large number K of categories and a small number n of sample size is challenging to both frequentist and Bayesian methods and requires thinking about statistical inference at a very fundamental level. Following the framework of DempsterShafer theory of belief functions, a probabilistic inferential model is proposed for this “large K and small n” problem. The inferential model produces a probability triplet (p,q,r) for an assertion conditional on observed data. The probabilities p and q are for and against the truth of the assertion, whereas r = 1 − p − q is the remaining probability called the probability of “don’t know”. The new inference method is applied in a genomewide association study with very high dimensional count data, to identify association between genetic variants to the disease Rheumatoid Arthritis. 1
International Journal of Approximate Reasoning •• • (••••) •••–••• Contents lists available at SciVerse ScienceDirect International Journal of Approximate Reasoning
"... www.elsevier.com/locate/ijar Large scale two sample multinomial inferences and its ..."
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www.elsevier.com/locate/ijar Large scale two sample multinomial inferences and its
Likelihoodbased belief function: justification and some extensions to lowquality data
"... Given a parametric statistical model, evidential methods of statistical inference aim at constructing a belief function on the parameter space from observations. The two main approaches are Dempster’s method, which regards the observed variable as a function of the parameter and an auxiliary varia ..."
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Given a parametric statistical model, evidential methods of statistical inference aim at constructing a belief function on the parameter space from observations. The two main approaches are Dempster’s method, which regards the observed variable as a function of the parameter and an auxiliary variable with known probability distribution, and the likelihoodbased approach, which considers the relative likelihood as the contour function of a consonant belief function. In this paper, we revisit the latter approach and prove that it can be derived from three basic principles: the likelihood principle, compatibility with Bayes ’ rule and the minimal commitment principle. We then show how this method can be extended to handle lowquality data. Two cases are considered: observations that are only partially relevant to the population of interest, and data acquired through an imperfect observation process.