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Bayesian Regularisation for Effective Variable Selection

Learn about Bayesian and hierarchical modeling for effective variable selection and improved prediction in high-dimensional data. Understand the importance of regularization techniques to avoid overfitting and enhance model performance.

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Bayesian Regularisation for Effective Variable Selection

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  1. No Such Thing as a Neutral Model Ewan Keith – Ministry of Defence Ewan.keith100@mod.uk

  2. Bayesian Modeling

  3. Bayesian Modeling

  4. Regularisation • Very large number of predictor variables can cause difficulties. • Multiple Comparisons risk unreliable hypothesis tests • Complete failure in P > N cases • Often increases the risks of co-linearity

  5. Regularisation

  6. Regularisation Source: Robert Tibshirani - http://statweb.stanford.edu/~tibs/ftp/covtest-talk.pdf

  7. Regularisation • Regularisation is very useful • Efficient variable selection in high dimensions • Enables treatment of poorly posed problems • As a general rule, provides better fit • Is objective?

  8. Bayesian Regularisation

  9. Bayesian Regularisation

  10. Hierarchical Modelling

  11. Hierarchical Modelling

  12. Hierarchical Modelling • Halfway between complete pooling and no-pooling • Weighted average between the two • Results in biased, ‘half-way’ estimates • Typically provides better prediction of future data than unbiased estimates

  13. Efron & Morris 1975 Mean Squared Error Source: Simon Jackman http://jackman.stanford.edu/classes/350C/07/randomeffects.pdf

  14. What about Bayesian Priors? • Hierarchical modelling is just the use of shared priors • Such as a common distribution for multiple averages • Values are shrunk towards the middle of this ‘higher’ distribution • Which values share priors is an analyst decision, not data driven

  15. No Such thing as an Impartial Model • ‘These are special cases where subjective input is useful, generally it should be avoided so we should not use Bayesian modelling.’ • From the first to last stage of fitting models (of any kind) we’re involved in subjective decision making.

  16. No Such thing as an Impartial Model

  17. No Such Thing as a Neutral Model Ewan Keith – Ministry of Defence Ewan.keith100@mod.uk

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