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Multiple regression

Multiple regression. Data: Multiple linear regression. Variable selection. Goal Find the “best” subset of predictors Problem possible models How to search in the model space? What criterion to evaluate different models?. Stochastic search variable selection (SSVS).

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Multiple regression

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  1. Multiple regression • Data: • Multiple linear regression

  2. Variable selection • Goal • Find the “best” subset of predictors • Problem • possible models • How to search in the model space? • What criterion to evaluate different models?

  3. Stochastic search variable selection (SSVS) • Use a set of binary indicator variables to represent sub-models (George & McCulloch 1993) • Bayesian: find the posterior distribution of • Ranking predictors by • Now, it is an estimation problem! • Bayesian: posterior = prior x likelihood (data)

  4. A Bayesian hierarchical model

  5. Prior distribution of

  6. Gibbs sampler for SSVS

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