Adversarial and Amiable Inference in Medical Diagnosis, Reliability and Survival Analysis
Autor: | Hon Keung Tony Ng, Barry C. Arnold, Joseph L. Gastwirth, Nozer D. Singpurwalla, Anna S. Gordon |
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Rok vydání: | 2015 |
Předmět: |
Statistics and Probability
Computer science 05 social sciences Bayesian probability Inference Bivariate analysis Bayesian inference 01 natural sciences 010104 statistics & probability Component (UML) 0502 economics and business 0101 mathematics Statistics Probability and Uncertainty Beta distribution Mathematical economics Reliability (statistics) Survival analysis 050205 econometrics |
Zdroj: | International Statistical Review. 84:390-412 |
ISSN: | 0306-7734 |
DOI: | 10.1111/insr.12104 |
Popis: | In this paper, we develop a family of bivariate beta distributions that encapsulate both positive and negative correlations, and which can be of general interest for Bayesian inference. We then invoke a use of these bivariate distributions in two contexts. The first is diagnostic testing in medicine, threat detection, and signal processing. The second is system survivability assessment, relevant to engineering reliability, and to survival analysis in biomedicine. In diagnostic testing one encounters two parameters that characterize the efficacy of the testing mechanism, {\it test sensitivity}, and {\it test specificity}. These tend to be adversarial when their values are interpreted as utilities. In system survivability, the parameters of interest are the component reliabilities, whose values when interpreted as utilities tend to exhibit co-operative (amiable) behavior. Besides probability modeling and Bayesian inference, this paper has a foundational import. Specifically, it advocates a conceptual change in how one may think about reliability and survival analysis. The philosophical writings of de Finetti, Kolmogorov, Popper, and Savage, when brought to bear on these topics constitute the essence of this change. Its consequence is that we have at hand a defensible framework for invoking Bayesian inferential methods in diagnostics, reliability, and survival analysis. Another consequence is a deeper appreciation of the judgment of independent lifetimes. Specifically, we make the important point that independent lifetimes entail at a minimum, a two-stage hierarchical construction. |
Databáze: | OpenAIRE |
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