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Abstract:
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We discuss a general paradigm for combining information across diverse data sources. In broad terms, suppose $\phi$ is a parameter of interest, built up via components $\psi_1,\ldots,\psi_k$ from data sources $1,\ldots,k$. 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 $C_j(\psi_j)$ for the relevant focus parameter $\psi_j$ associated with data source $j$. Second, Confidence Conversion (CC) techniques are used to translate the confidence distributions to confidence log-likelihood functions, say $\ell_j(\psi_j)$. Finally, the Focused Fusion (FF) step uses relevant and context-driven techniques to construct a confidence distribution for the primary focus parameter $\phi=\phi(\psi_1,\ldots,\psi_k)$, acting on the combined confidence log-likelihood. In simpler setups, the II-CC-FF strategy amounts to versions of meta-analysis, but its potential lies in applications to harder problems. Illustrations are given, related to actual applications.
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