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Bayesian model selection: a predictive approach with losses based on distances L1 and L2

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  • de la Horra, Julián
  • Rodríguez-Bernal, María Teresa

Abstract

A Bayesian model consists of two elements: a sampling model and a prior density. In this paper, we propose a new predictive approach for selecting a Bayesian model through a decision problem. The key idea in the paper is the loss function; we propose to measure the L1 distance (or the squared L2 distance) between the densities we can use for predicting future observations: sampling densities and posterior predictive densities. The method is also applied to the problem of variable selection in a regression model, showing a good behavior.

Suggested Citation

  • de la Horra, Julián & Rodríguez-Bernal, María Teresa, 2005. "Bayesian model selection: a predictive approach with losses based on distances L1 and L2," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 257-265, March.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:3:p:257-265
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    More about this item

    Keywords

    Posterior predictive density Posterior expected loss L1 distance L2 distance Bayesian model selection Variable selection;

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance
    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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