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Reversible jump methods for generalised linear models and generalised linear mixed models

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Abstract

A reversible jump algorithm for Bayesian model determination among generalised linear models, under relatively diffuse prior distributions for the model parameters, is proposed. Orthogonal projections of the current linear predictor are used so that knowledge from the current model parameters is used to make effective proposals. This idea is generalised to moves of a reversible jump algorithm for model determination among generalised linear mixed models. Therefore, this algorithm exploits the full flexibility available in the reversible jump method. The algorithm is demonstrated via two examples and compared to existing methods.

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Authors and Affiliations

  1. School of Mathematics, University of Southampton, Southampton, UK

    Jonathan J. Forster

  2. Oxford Nanopore Technologies Ltd., Edmund Cartwright House, 4 Robert Robinson Avenue, Oxford Science Park, Oxford, UK

    Roger C. Gill

  3. S3RI, University of Southampton, Southampton, UK

    Antony M. Overstall

Authors
  1. Jonathan J. Forster
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  2. Roger C. Gill
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  3. Antony M. Overstall
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Correspondence to Antony M. Overstall.

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Forster, J.J., Gill, R.C. & Overstall, A.M. Reversible jump methods for generalised linear models and generalised linear mixed models. Stat Comput 22, 107–120 (2012). https://doi.org/10.1007/s11222-010-9210-3

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  • DOI: https://doi.org/10.1007/s11222-010-9210-3

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