Combining information across diverse sources: The II‐CC‐FF paradigm

Céline Cunen and Nils Lid Hjort

Scandinavian Journal of Statistics, 2022, vol. 49, issue 2, 625-656

Abstract: We introduce and develop a general paradigm for combining information across diverse data sources. In broad terms, suppose φ is a parameter of interest, built up via components ψ1,…,ψk from data sources 1, … , k. The proposed scheme has three steps. First, the independent inspection (II) step amounts to investigating each separate data source, translating statistical information to a confidence distribution (CD) Cj(ψj) for the relevant focus parameter ψj associated with data source j. Second, confidence conversion (CC) techniques are used to translate the CDs to confidence log‐likelihood functions. Finally, the focused fusion (FF) step uses relevant and context‐driven techniques to construct a confidence distribution for the primary focus parameter φ=φ(ψ1,…,ψk), acting on the combined confidence log‐likelihood. In traditional setups, the II‐CC‐FF strategy amounts to versions of meta‐analysis, and turns out to be competitive against state‐of‐the‐art methods. Its potential lies in applications to harder problems, however. Illustrations are presented, related to actual applications.

Date: 2022
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