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Computational Statistics

, Volume 15, Issue 3, pp 355–371 | Cite as

Bayesian probabilistic extensions of a deterministic classification model

  • Iwin Leenen
  • Iven Van Mechelen
  • Andrew Gelman
Article

Summary

This paper extends deterministic models for Boolean regression within a Bayesian framework. For a given binary criterion variable Y and a set of k binary predictor variables X1,…, Xk, a Boolean regression model is a conjunctive (or disjunctive) logical combination consisting of a subset S of the X variables, which predicts Y. Formally, Boolean regression models include a specification of a k-dimensional binary indicator vector (θ1,…,θk) with θj = 1 iff XjS. In a probabilistic extension, a parameter π is added which represents the probability of the predicted value \({\hat y_i}\) and the observed value yi differing (for any observation i). Within a Bayesian framework, a posterior distribution of the parameters (θ1,…, θk, π) is looked for. The advantages of such a Bayesian approach include a proper account of the uncertainty in the model estimates and various possibilities for model checking (using posterior predictive checks). We illustrate this method with an example using real data.

Keywords

Bayesian Estimation Boolean Regression Logical Rule Analysis Posterior Predictive Checks 

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Copyright information

© Physica-Verlag 2000

Authors and Affiliations

  • Iwin Leenen
    • 1
  • Iven Van Mechelen
    • 1
  • Andrew Gelman
    • 2
  1. 1.Department of PsychologyUniversity of LeuvenLeuvenBelgium
  2. 2.Department of StatisticsColumbia UniversityNew YorkUSA

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