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Abstract:
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Bayesian methods provide the optimal solution for statistical inference, provided model, prior, and loss are ``correctly'' specified. However, deficiencies in any of these components can lead to suboptimal inference, even for large samples. Deficiencies in the model have traditionally been handled as part of data analysis, as analysts make many decisions to adjust the data before conducting a formal analysis. Restricted likelihood provides a formal framework within which many of these adjustments fit. The framework replaces the likelihood of the full data, x, with the likelihood of a summary of the data, T(x). Bayesian restricted likelihood then updates the prior distribution with T(x) rather than the usual x. When T(x) is insufficient, some information is lost-harming inference when all components of the problem are perfectly specified-but allowing the flexibility to choose summaries which are insensitive to plausible deficiencies in the model. This insensitivity improves inference. This talk will motivate the restricted likelihood framework, discuss implementation, and provide examples of its use.
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