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Cited by 145Statistical Methods and InferenceMarkov Chains and Monte Carlo MethodsStatistical Methods and Bayesian Inference

The DOI matches its Crossref record; 32 of the 32 references it cites were found in a registry or an index.

Prediction via Orthogonalized Model Mixing

Clyde, Merlise, Desimone, Heather, Parmigiani, Giovanni·1996·Journal of the American Statistical Association
DOI 10.1080/01621459.1996.10476989
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Abstract

We introduce an approach and algorithms for model mixing in large prediction problems with correlated predictors. We focus on the choice of predictors in linear models, and mix over possible subsets of candidate predictors. Our approach is based on expressing the space of models in terms of an orthogonalization of the design matrix. Advantages are both statistical and computational. Statistically, orthogonalization often leads to a reduction in the number of competing models by eliminating correlations. Computationally, large model spaces cannot be enumerated; recent approaches are based on sampling models with high posterior probability via Markov chains. Based on orthogonalization of the space of candidate predictors, we can approximate the posterior probabilities of models by products of predictor-specific terms. This leads to an importance sampling function for sampling directly from the joint distribution over the model space, without resorting to Markov chains. Compared to the latter, orthogonalized model mixing by importance sampling is faster in sampling models and is also more efficient in finding models that contribute significantly to the prediction. Further advantages are in the speed of convergence and the availability of more reliable convergence diagnostic tools. We illustrate these in practice, using a data set on prediction of crime rates. The model space is small enough so that enumeration of all models is available for comparison and convergence checks. Als…

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Research works printed but not linked: 6

  1. Bennett , I. and Wakefield , J. 1994 . “Covariate Modelling in Population Pharmacokinetics models,” , Imperial College, Dept. of Mathematics . TR-94–19
  2. Clyde , M. A. and Parmigiani , G. 1996 . “Orthogonalizations and Priors for Orthogonalized Model Mixing,” . In “Modeling and Prediction: Honoring Seymour Geisser” , Edited by: Johnson , W. , Lee , J. and Zellner , A. Springer . (forthcoming)
  3. Higdon , D. 1994 . “Spatial Applications of Markov Chain Monte Carlo for Bayesian Inference,” , Ph.D. thesis University of Washington, Dept. of Statistics .
  4. Menius , A. J. , Rocque , W. , Emptage , M. R. and Young , S. S. “Space Filling Experimental Design for Determining Protein Construct Storage Conditions,” . Proceedings of the 26th Symposium on the Interface . pp. 106 – 110 .
  5. Raftery , A. E. , Madigan , D. M. and Volinsky , C. T. 1996 . “Accounting for Model Uncertainty in Survival Analysis Improves Predictive Performance” . In Bayesian Statistics 5 , Edited by: Bernardo , J. M. , Berger , J. O. , Dawid , A. P. and Smith , A. F. M. 323 – 350 . Oxford : University Press . (with discussion)
  6. Rao , C. R. 1964 . “The Use and Interpretation of Principal Components in Applied Research,” . Sankhya , 26 : 329 – 358 . Ser. A

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Metadata

Authors
Clyde, M., Desimone, H., & Parmigiani, G.
Affiliations
Duke University (US)
ORCID
Venue
Journal of the American Statistical Association
Publisher
Informa UK Limited
Published
1996-09
Volume
91
Issue
435
Pages
1197-1208
ISSN
  • 0162-1459 (ISSN-L)
  • 1537-274X
DOI
10.1080/01621459.1996.10476989
OpenAlex
W2033149996
Cited by
145
References
32
Citations by year
2026: 1 · 2025: 1 · 2024: 3 · 2023: 1 · 2022: 3 · 2021: 4 · 2020: 1 · 2019: 2 · 2018: 8 · 2017: 1 · 2016: 5 · 2015: 4 · 2014: 6 · 2013: 3 · 2012: 9
FWCI
4.47
Type
journal article
Language
en
Open access
closed
Locations
Journal of the American Statistical Association (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords
orthogonalization, correlated predictors, model selection, importance sampling, posterior model probabilities, linear models, model space exploration, prediction intervals, crime rate prediction, storage conditions

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