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Abstract:
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Bayesian inference relies heavily on its probabilistic model assumptions, namely the class of distributions the data belongs to. However, a small deviation of these model assumptions can lead to inconsistent and misleading inferences. We develop the tilted posterior, a coherent Bayesian modeling framework robust to model mismatch: we systematically down-weight samples that are incompatible with our model assumptions. We employ the localization idea and the nonparametric tilting technique to infer weights on all samples and perform posterior inference based on this tilted data set. The inferred weights also hint at the later model criticism and revision step, which, along with the preceding model formulation and inference steps, constitutes a complete Box's loop. We illustrate our approach with real and simulated data using variational inference and demonstrate its superiority over the classical posterior inference.
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