A Bayesian Formulation of Exploratory Data Analysis and Goodness‐of‐fit Testing *

By Andrew Gelman. 2003

254 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d732134e86626059e7b3c31a03c1fa1b8a0cb1aa

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Citations in the corpus

EDA for HLM: Visualization when Probabilistic Inference Fails (2005, background): “4), Gelman (2003, 2004), and Gelman et al. (2004, chap.”
Statistical Model Criticism using Kernel Two Sample Tests (2015, background): “This claimed inadequacy of posterior predictive p-values was rebutted [30] and while their usefulness is becoming more accepted (see e.g. introduction of [31]) it would appear there is still confusion on the subject [32].”
Shape restricted regression with random Bernstein polynomials (2007, methodology): “The method of this paper can also be used to assess the validity of the shape restriction on the regression function, by considering the predictive posterior assessment proposed by Gelman et al. [14] and Gelman [13]; in fact, we have implemented this assessment and found it quite satisfactory.”
Philosophy and the practice of Bayesian statistics (2010, unknown): “…of model checking, then, is not to demonstrate the foregone conclusion of falsity as such, but rather to learn how, in particular, this model fails (Gelman, 2003).13 When we find such particular failures, they tell us how the model must be improved; when severe tests cannot find them, the…”
Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics (2009, methodology): “It is in this sense that graphical methods and exploratory data analysis can be viewed as explicitly Bayesian, as tools for comparing posterior predictions to data (Gelman, 2003).”
Two simple examples for understanding posterior p-values whose distributions are far from uniform (2013, background): “A u-value can be averaged over the distribution of θ to give it a Bayesian flavor, but it is fundamentally not Bayesian, in that it cannot necessarily be interpreted as a posterior probability (Gelman, 2003).”
Parameterization and Bayesian Modeling (2004, methodology): “In Gelman and King (1990), we modeled similar data from many other elections to study the properties of the electoral system under various assumptions about electoral swings.”
Bayesian Workflow (2020, methodology): “Indeed all parameters in inference can be viewed as some quantities to predict, and all of our modeling can be viewed as having exploratory goals (Gelman, 2003).”
The Prior Can Often Only Be Understood in the Context of the Likelihood (2017, background): “Incoherence is an unavoidable aspect of much real-world data analysis; and, indeed, one might argue that as scientists we learn the most from the anomalies and reassessments associated with episodes of incoherence [8,9].”
Home range size of adult Indo-Pacific bottlenose dolphins (Tursiops aduncus) in a coastal and estuarine system is habitat and sex-specific (2016, methodology): “Additionally, to confirm adequate model fit a goodness-of-fit P-value was computed through a posterior predictive check based on sum of squared Pearson residuals (Gelman 2003).”