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Abstract:
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The Bayesian restricted likelihood framework combines Bayesian methods with summarization. A formal model is written for the entirety of the data, implying a distribution on summary statistics. When the summary is insufficient, some information is lost. A formal Bayesian update is performed based on the summary statistic alone. This takes one from the prior distribution to the restricted-posterior distribution. We apply the method to the quantile regression problem, using the traditional quantile regression estimator and using more accurate quantile regression estimators for the summaries.
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