Bayesian Marginal Influence Assessment

Abstract Case-influence diagnostics are in wide use in classical linear regression and are common in Bayesian analysis. Most common Bayesian diagnostics assess influence on all parameters; influence on parameter subsets have not been formally developed, in contrast with classically based influence diagnostics. Influence on parameter subsets should be assessed when some parameters are ‘nuisance’ parameters while others are of primary inferential interest. Influence on parameter subsets can be substantially less than influence on the full parameter vector, leading to different conclusions from the influence analysis. We discuss Bayesian influence assessment in normal linear and hierarchical normal random effects models. We give formulae for case deletion influence diagnostics in normal linear regression for joint and marginal posterior distributions using several divergence measures. In more complex models, we describe a nested sampling procedure for computing marginal influence measures when closed-form computations are not available.

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