(This article was originally published at No Hesitations, and syndicated at StatsBlogs.)

But there are also other Bayesian approaches to combining density forecasts, such as prediction pools formed to optimize a predictive score. (See, e.g. Amisano and Geweke, 2017, and the references therein. Ungated final draft, and code, here.)

Another relevant strand of new work, less familiar to econometricians, is "Bayesian predictive synthesis" (BPS), which builds on the expert opinions analysis literature. The framework, which traces to Lindley et al. (1979), concerns a Bayesian faced with multiple priors coming from multiple experts, and explores how to get a posterior distribution utilizing all of the information available. Earlier work by Genest and Schervish (1985) and West and Crosse (1992) develops the basic theory, and new work (McAlinn and West, 2017), extends it to density forecast combination.

Thanks to Ken McAlinn for reminding me about BPS. Mike West gave a nice presentation at the FRBSL forecasting meeting. [Parts of this post are adapted from private correspondence with Ken.]

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