Conservative prior distributions for variance parameters in hierarchical models

By Paul Gustafson, Shahadut Hossain, Ying C. MacNab. 2006

1,920 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service use (2010, methodology): “However, this choice can be deceptively informative because it concentrates most of the prior mass near zero, which, as Gelman (2006) notes, can lead to unstable posterior estimates since the posterior becomes improper as → 0.”
Kernel-Based Just-In-Time Learning for Passing Expectation Propagation Messages (2015, methodology): “To take one example, the inverse gamma prior, which is widely used as a convenient conjugate prior for the variance, has quite pathological behaviour (Gelman, 2006).”
Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models (2006, result): “2, but our quasi-likelihood conclusions are consistent with broad theoretical predictions made by Engel (1998) and Lee and Nelder (2001), and our Bayesian calibration findings are in line with those in other multilevel settings we have examined (e.”
Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution (2012, result): “We found very little difference between results using either of these priors in the examples presented here, but both Browne and Draper (2006) and Gelman (2006) provide useful criticisms and alternatives regarding the effects of using these priors for small sample sizes.”
Struggles with survey weighting and regression modeling (2007, methodology): “Models 4 and 5 are similar to the classical fits because age and education have only four categories, so there is little information available for partial pooling of these effects (see Gelman, 2006).”
Fitting multilevel multivariate models with missing data in responses and covariates that may include interactions and non‐linear terms (2014, methodology): “…0:001/, p.σ2e /∼Γ−1.0:001, 0:001/: In the literature there are several commonly used diffuse priors for such models (see Browne and Draper (2006) and Gelman (2006) for discussion on this) but this is not of prime interest in this paper and the data set is sufficiently large for the…”
Robustifying Generalized Linear Mixed Models Using a New Class of Mixtures of Multivariate Polya Trees (2009, background): “Other choices of prior distributions for the dispersion parameter τ were discussed in Gelman (2006) and can be easily implemented in our context.”
Moving beyond noninformative priors: why and how to choose weakly informative priors in Bayesian analyses (2019, methodology): “An noninformative prior on σB with large ν yields a standard mixed-effects model with random parameters (Gelman 2006).”
Spatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors (2007, background): “Alternative to gamma priors are discussed by, for example, Natarajan and Kass (2000) and Gelman (2006).”
Calibrated Bayes, an alternative inferential paradigm for official statistics (2012, methodology): “Fully Bayes methods based on weak priors on the variance components propagate uncertainty and avoid estimates on the boundary of the parameter space, though care is need with the choice of prior distribution for 2 (Gelman 2006).”
Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics (2009, background): “But it can notoriously difficult to choose among noninformative priors; and, even more importantly, seemingly noninformative distributions can sometimes have strong and undesirable implications, as I have found in my own experience (Gelman, 1996, 2006).”
Bivariate Binomial Spatial Modeling of Loa loa Prevalence in Tropical Africa (2008, methodology): “Alternatives to gamma priors have been discussed by, for example, Natarajan and Kass (2000) and Gelman (2006). These have the advantage of requiring less care in the choice of the hyperparameters.”
Design-Comparable Effect Sizes in Multiple Baseline Designs (2014, background): “Other approaches to model fitting may offer some advantage and should be investigated further, including in particular fully Bayesian methods with weakly informative priors (Baldwin & Fellingham, 2013; Gelman, 2006) or related varieties of penalized likelihood methods (Chung, Rabe-Hesketh, Dorie, Ge”
On the half-cauchy prior for a global scale parameter (2011, methodology): “All these desirable features are summarized by Gelman (2006). Our results give a quite different, classical justification for this prior in high-dimensional settings: its excellent quadratic risk properties.”