Abstract
We define a new Bayesian predictor called the posterior weighted median (PWM) and compare its performance to several other predictors includ- ing the Bayes model average under squared error loss, the Barbieri-Berger me- dian model predictor, the stacking predictor, and the model average predictor based on Akaike's information criterion. We argue that PWM generally gives better performance than other predictors over a range of M-complete problems. This range is between the M-closed-M-complete boundary and the M-complete- M-open boundary. Indeed, as a problem gets closer to M-open, it seems that M-complete predictive methods begin to break down. Our comparisons rest on extensive simulations and real data examples. As a separate issue, we introduce the concepts of the 'Bail out effect' and the 'Bail in effect'. These occur when a predictor gives not just poor results but defaults to the simplest model ('bails out') or to the most complex model ('bails in') on the model list. Either can occur inM-complete problems when the complexity of the data generator is too high for the predictor scheme to accommodate.
Original language | English (US) |
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Pages (from-to) | 647-690 |
Number of pages | 44 |
Journal | Bayesian Analysis |
Volume | 8 |
Issue number | 3 |
DOIs | |
State | Published - 2013 |
Keywords
- Basis selection
- Ensemble methods
- M-complete
- Model list selection
- Model selection
- Prediction
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics