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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.
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.
Fundamentally, the difference between the Bayesian approach and the sampling-theory approach above is that in the sampling-theory approach the parameter is taken as fixed, and then probability distributions of a statistic are considered, based on the predicted sampling distribution of the data. For a Bayesian, however, it is the data which are ...
A Bayesian account appears in Gelman et al. (2003). An alternative parametric approach is to assume that the residuals follow a mixture of normal distributions ( Daemi et al. 2019 ); in particular, a contaminated normal distribution in which the majority of observations are from a specified normal distribution, but a small proportion are from a ...
Bayesian inference (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available.