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Exploratory analysis of Bayesian models is an adaptation or extension of the exploratory data analysis approach to the needs and peculiarities of Bayesian modeling. In the words of Persi Diaconis: [16] Exploratory data analysis seeks to reveal structure, or simple descriptions in data. We look at numbers or graphs and try to find patterns.
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often ...
Andrew Eric Gelman (born February 11, 1965) is an American statistician and professor of statistics and political science at Columbia University. Gelman received bachelor of science degrees in mathematics and in physics from MIT , where he was a National Merit Scholar , in 1986.
Stan: A probabilistic programming language for Bayesian inference and optimization, Journal of Educational and Behavioral Statistics. Hoffman, Matthew D., Bob Carpenter, and Andrew Gelman (2012). Stan, scalable software for Bayesian modeling Archived 2015-01-21 at the Wayback Machine, Proceedings of the NIPS Workshop on Probabilistic Programming.
Exploring a forking decision-tree while analyzing data was at one point grouped with the multiple comparisons problem as an example of poor statistical method. However Gelman and Loken demonstrated [2] that this can happen implicitly by researchers aware of best practices who only make a single comparison and only evaluate their data once.
The technique was originally developed by Gelman and T. Little in 1997, [6] building upon ideas of Fay and Herriot [7] and R. Little. [8] It was subsequently expanded on by Park, Gelman, and Bafumi in 2004 and 2006. It was proposed for use in estimating US-state-level voter preference by Lax and Philips in 2009.
An approach to inverse uncertainty quantification is the modular Bayesian approach. [7] [17] The modular Bayesian approach derives its name from its four-module procedure. Apart from the current available data, a prior distribution of unknown parameters should be assigned. Module 1: Gaussian process modeling for the computer model
Bayesian Analysis] Michael Goldstein, David Wooff (2007) Bayes Linear Statistics, Theory & Methods, Wiley. ISBN 978-0-470-01562-9; de Finetti, B. (1931) "Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science," (translation of 1931 article) in Erkenntnis, volume 31, September 1989. The entire double issue is ...