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Abstract:
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We introduce the concept of confidence distribution (CD) and teach how to use its development to solve a wide range of problems in fusion learning and meta-analysis. CD is a sample-dependent distribution function on the parameter space that can represent confidence intervals (regions) of all levels for a parameter of interest. It provides "simple and interpretable summaries of what can reasonably be learned from data (and an assumed model)" (Cox 2013) and meaningful answers to all questions related to statistical inference. In this short course, we review the development of CD and introduce new and powerful inference tools derived from it. The main focus is on combining information from different sources. Specifically, we present several new and effective meta-analysis and fusion learning approaches from real data applications, including 1) unified framework for meta-analysis and R-package 'gmeta'; 2) meta-analysis of heterogeneous studies; 3) incorporating external information in meta-analyses; 4) exact meta-analysis approach for discrete data; 5) robust meta-analysis; 6) efficient network meta-analysis; 7) meta-analysis with no model assumptions; and 8) nonparametric combining inferences. Altogether, they show that CD can yield useful statistical inference tools for many statistical problems where methods with desirable properties have been lacking or not easily available.
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