• Abstract: We consider an approximate posterior approach to making joint probabilistic inference on the action and the associated risk in classification. The posterior probability is based on an empirical likelihood (EL), which imposes a moment restriction relating the action to the resulting risk, but does not otherwise require a probability model for the underlying data generating process. We illustrate with examples how this framework can be used to describe the EL-posterior distribution of actions to take in order to achieve a low risk, or conversely, to describe the posterior distribution of the resulting risk for a given action. A theoretical study on the frequentist properties reveals that the ELposterior concentrates around the true risk-action relation with high probability for large data size, and that the actions can be generated from this posterior to reliably control the true resulting risk. Finally, an application to the German credit data is presented.

• Paper: pdf file

• Data set: German Credit Data
  http://archive.ics.uci.edu/ml/datasets/Statlog+(German+Credit+Data)

• Slides: pdf file

• Related literature:

  Lazar N. (2003)
  Bayesian empirical likelihood.
  Biometrica. 90, 319-326.

  Schennach S. (2005)
  Bayesian exponentially tilted empirical likelihood.
  Biometrica. 92, 31-46

• Presentations:

  2010

  • Rutgers University, Department of Statistics and Biostatistics