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Abstract:
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The Bayesian framework offers the opportunity to combine diverse information sources in modeling and prediction, while managing uncertainties associated with those sources. I suggest that in complex settings, the use of substantial prior information contained in mechanistic models and theories is needed to form a sound basis for prediction. However, such models and theories are imperfect typically. The Bayesian approach is suggested to seek quantifications of and adjustments for such imperfections. In this talk I review and exemplify the incorporation of physical models in hierarchical Bayesian models. Further, numerical models are often used as input or as providing covariates, in statistical parlance, for other models leading to challenging issues in quantifying uncertainty propagation. Several illustrations indicating the wide range of possible analyses are presented including the novel approaches to causal inference in climate change and prediction of local sea levels in response to rising large-scale rising sea level.
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