Combining Information Across Diverse Sources: The II-CC-FF Paradigm

We introduce and develop a general paradigm for combining information across diverse data sources. In broad terms, suppose $\phi$ is a parameter of interest, built up via components ${\psi }_1,\dots ,{\psi }_k$ from data sources $1,\dots ,k$. 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 ${\mathrm{\ell }}_{\mathrm{c}\mathrm{o}\mathrm{n},j}({\psi }_j)$. Finally, the Focused Fusion (FF) step uses relevant and context-driven techniques to construct a confidence distribution for the primary focus parameter $\phi =\phi ({\psi }_1,\dots ,{\psi }_k)$, 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.