The statistical analysis of compositional data
The statistical analysis of compositional data
Benefits of embedding structural constraints in coherent diagnostic processes
International Journal of Approximate Reasoning
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This paper displays the productive role of the judgment of exchangeability and even conditional exchangeability that should replace the misleading assertion of independence of various experts' opinions regarding uncertain situations. The application is technically rather complicated, and a basic understanding of exchangeability in its simple applications is presumed. One component of the analysis is novel. It suggests how we might specify a likelihood function that allows us to learn about one exchangeable sequence of events from the outcomes of another exchangeable sequence. The substantive content of the the paper concerns the use of personal probabilities by two experts in assessing the sex of human skulls found in anthropological investigations. Although we initially value the two experts' assertions exchangeably, we learn to value one of the expert's assertions more than the other's. Moreover we identify precisely how much to value the elicitation from a second expert after we have already learned the assertion of the first. Valuation is based on a decision theoretic procedure assessing reduction in risk.