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Weak Informativity . . . Prior Relative to Another
, 2009
"... A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization of this information, we provide an approach to characterizing the amount of information a prior puts into an analysis, when compared to a ..."
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A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization of this information, we provide an approach to characterizing the amount of information a prior puts into an analysis, when compared
Avoiding Boundary Estimates in Linear Mixed Models Through Weakly Informative Priors
"... Variance parameters in mixed or multilevel models can be difficult to estimate, especially when the number of groups is small. We propose a maximum penalized likelihood approach which is equivalent to estimating variance parameters by their marginal posterior mode, given a weakly informative prior ..."
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Cited by 2 (0 self)
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prior distribution. By choosing the prior from the gamma family with at least 1 degree of freedom, we ensure that the prior density is zero at the boundary and thus the marginal posterior mode of the grouplevel variance will be positive. The use of a weakly informative prior allows us to stabilize our
Weakly Informative Prior for Covariance Matrices 1 Running head: WEAKLY INFORMATIVE PRIOR FOR COVARIANCE MATRICES Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models
"... When fitting hierarchical regression models, maximum likelihood estimation has computational (and, for some users, philosophical) advantages compared with full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (Σ) of grouplevel varying coefficients are o ..."
Examining the Role of a Noninformative Prior Function Through Weakly Informative Prior Densities
"... A noninformative prior function is discussed from the standpoint of a weakly informative prior density, though it has been pursued in relation only to the sampling densities. We note that a weakly informative prior density is useful for examining a noinformative prior function. Some disadvantages ..."
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A noninformative prior function is discussed from the standpoint of a weakly informative prior density, though it has been pursued in relation only to the sampling densities. We note that a weakly informative prior density is useful for examining a noinformative prior function. Some disadvantages
Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models
"... When fitting hierarchical regression models, maximum likelihood (ML) estimation has computational (and, for some users, philosophical) advantages compared to full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (S) of grouplevel varying coefficients a ..."
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Cited by 1 (0 self)
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definite. Furthermore, the resulting uncertainty for the fixed coefficients is less underestimated than under classical ML or restricted maximum likelihood estimation. We also suggest an extension of our method that can be used when stronger prior information is available for some of the variances
Prior distributions for variance parameters in hierarchical models
 Bayesian Analysis
, 2006
"... Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new foldednoncentralt family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors i ..."
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Cited by 430 (15 self)
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Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new foldednoncentralt family of conditionally conjugate priors for hierarchical standard deviation parameters, and then consider noninformative and weakly informative priors
Bayesian Analysis (.)., Number., pp. 1–18 Weakly Informative Prior for Point Estimation of Covariance Matrices in Hierarchical Models
"... Abstract. When fitting hierarchical regression models, maximum likelihood estimation has computational (and, for some users, philosophical) advantages compared with full Bayesian inference, but when the number of groups is small, estimates of the covariance matrix (Σ) of grouplevel varying coeffici ..."
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definite. Furthermore, the resulting uncertainty for the fixed coefficients is less underestimated than under classical maximum likelihood or restricted maximum likelihood. We also suggest an extension of our method that can be used when stronger prior information is available for some of the variances
Bayesian Data Analysis
, 1995
"... I actually own a copy of Harold Jeffreys’s Theory of Probability but have only read small bits of it, most recently over a decade ago to confirm that, indeed, Jeffreys was not too proud to use a classical chisquared pvalue when he wanted to check the misfit of a model to data (Gelman, Meng and Ste ..."
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Cited by 2194 (63 self)
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the following: (1) in thinking about prior distributions, we should go beyond Jeffreys’s principles and move toward weakly informative priors; (2) it is natural for those of us who work in social and computational sciences to favor complex models, contra Jeffreys’s preference for simplicity; and (3) a key
Some informational aspects of visual perception
 Psychol. Rev
, 1954
"... The ideas of information theory are at present stimulating many different areas of psychological inquiry. In providing techniques for quantifying situations which have hitherto been difficult or impossible to quantify, they suggest new and more precise ways of conceptualizing these situations (see M ..."
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Cited by 643 (2 self)
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The ideas of information theory are at present stimulating many different areas of psychological inquiry. In providing techniques for quantifying situations which have hitherto been difficult or impossible to quantify, they suggest new and more precise ways of conceptualizing these situations (see
A Language Modeling Approach to Information Retrieval
, 1998
"... Models of document indexing and document retrieval have been extensively studied. The integration of these two classes of models has been the goal of several researchers but it is a very difficult problem. We argue that much of the reason for this is the lack of an adequate indexing model. This sugg ..."
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Cited by 1154 (42 self)
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. This suggests that perhaps a better indexing model would help solve the problem. However, we feel that making unwarranted parametric assumptions will not lead to better retrieval performance. Furthermore, making prior assumptions about the similarity of documents is not warranted either. Instead, we propose
Results 1  10
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36,509