andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1477 knowledge-graph by maker-knowledge-mining
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Introduction: Since we’ve been discussing prior distributions on covariance matrices, I will recommend this recent article (coauthored with Tomoki Tokuda, Ben Goodrich, Iven Van Mechelen, and Francis Tuerlinckx) on their visualization: We present some methods for graphing distributions of covariance matrices and demonstrate them on several models, including the Wishart, inverse-Wishart, and scaled inverse-Wishart families in different dimensions. Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and three-dimensional plots to reveal multivariate structure. Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. Our visualization methods are available through the R package VisCov.
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1 Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and three-dimensional plots to reveal multivariate structure. [sent-2, score-1.948]
2 Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. [sent-3, score-2.396]
3 Our visualization methods are available through the R package VisCov. [sent-4, score-0.404]
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Introduction: Since we’ve been discussing prior distributions on covariance matrices, I will recommend this recent article (coauthored with Tomoki Tokuda, Ben Goodrich, Iven Van Mechelen, and Francis Tuerlinckx) on their visualization: We present some methods for graphing distributions of covariance matrices and demonstrate them on several models, including the Wishart, inverse-Wishart, and scaled inverse-Wishart families in different dimensions. Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and three-dimensional plots to reveal multivariate structure. Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. Our visualization methods are available through the R package VisCov.
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Introduction: In response to our recent posting of Amazon’s offer of Bayesian Data Analysis 3rd edition at 40% off, some people asked what was in this new edition, with more information beyond the beautiful cover image and the brief paragraph I’d posted earlier. Here’s the table of contents. The following sections have all-new material: 1.4 New introduction of BDA principles using a simple spell checking example 2.9 Weakly informative prior distributions 5.7 Weakly informative priors for hierarchical variance parameters 7.1-7.4 Predictive accuracy for model evaluation and comparison 10.6 Computing environments 11.4 Split R-hat 11.5 New measure of effective number of simulation draws 13.7 Variational inference 13.8 Expectation propagation 13.9 Other approximations 14.6 Regularization for regression models C.1 Getting started with R and Stan C.2 Fitting a hierarchical model in Stan C.4 Programming Hamiltonian Monte Carlo in R And the new chapters: 20 Basis function models 2
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Introduction: I’ve had a couple of email conversations in the past couple days on dependence in multivariate prior distributions. Modeling the degrees of freedom and scale parameters in the t distribution First, in our Stan group we’ve been discussing the choice of priors for the degrees-of-freedom parameter in the t distribution. I wrote that also there’s the question of parameterization. It does not necessarily make sense to have independent priors on the df and scale parameters. In some sense, the meaning of the scale parameter changes with the df. Prior dependence between correlation and scale parameters in the scaled inverse-Wishart model The second case of parameterization in prior distribution arose from an email I received from Chris Chatham pointing me to this exploration by Matt Simpson of the scaled inverse-Wishart prior distribution for hierarchical covariance matrices. Simpson writes: A popular prior for Σ is the inverse-Wishart distribution [ not the same as the
Introduction: Since we’re talking about the scaled inverse Wishart . . . here’s a recent message from Chris Chatham: I have been reading your book on Bayesian Hierarchical/Multilevel Modeling but have been struggling a bit with deciding whether to model my multivariate normal distribution using the scaled inverse Wishart approach you advocate given the arguments at this blog post [entitled "Why an inverse-Wishart prior may not be such a good idea"]. My reply: We discuss this in our book. We know the inverse-Wishart has problems, that’s why we recommend the scaled inverse-Wishart, which is a more general class of models. Here ‘s an old blog post on the topic. And also of course there’s the description in our book. Chris pointed me to the following comment by Simon Barthelmé: Using the scaled inverse Wishart doesn’t change anything, the standard deviations of the invidual coefficients and their covariance are still dependent. My answer would be to use a prior that models the stan
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Introduction: Since we’ve been discussing prior distributions on covariance matrices, I will recommend this recent article (coauthored with Tomoki Tokuda, Ben Goodrich, Iven Van Mechelen, and Francis Tuerlinckx) on their visualization: We present some methods for graphing distributions of covariance matrices and demonstrate them on several models, including the Wishart, inverse-Wishart, and scaled inverse-Wishart families in different dimensions. Our visualizations follow the principle of decomposing a covariance matrix into scale parameters and correlations, pulling out marginal summaries where possible and using two and three-dimensional plots to reveal multivariate structure. Visualizing a distribution of covariance matrices is a step beyond visualizing a single covariance matrix or a single multivariate dataset. Our visualization methods are available through the R package VisCov.
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