Statistics and Computing

, Volume 17, Issue 3, pp 235–244 | Cite as

Manipulating and summarizing posterior simulations using random variable objects

Article

Abstract

Practical Bayesian data analysis involves manipulating and summarizing simulations from the posterior distribution of the unknown parameters. By manipulation we mean computing posterior distributions of functions of the unknowns, and generating posterior predictive distributions. The results need to be summarized both numerically and graphically.

We introduce, and implement in R, an object-oriented programming paradigm based on a random variable object type that is implicitly represented by simulations. This makes it possible to define vector and array objects that may contain both random and deterministic quantities, and syntax rules that allow to treat these objects like any numeric vectors or arrays, providing a solution to various problems encountered in Bayesian computing involving posterior simulations.

We illustrate the use of this new programming environment with examples of Bayesian computing, demonstrating missing-value imputation, nonlinear summary of regression predictions, and posterior predictive checking.

Keywords

Bayesian inference Bayesian data analysis Object-oriented programming Posterior simulation Random variable objects 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Statistical MethodologyNovartis Pharma AGBaselSwitzerland
  2. 2.Department of StatisticsColumbia UniversityNew YorkUSA

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