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Comparing Ambiguous Inferences When Probabilities are Imprecise

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Abstract

Suppose you are interested in the level of a state variable (e.g. a disease is present or absent or of a pre-specified level of severity, or a failure is recorded or not, etc.) and have a potentially useful but imperfect diagnostic test method, (e.g. a blood test result for this disease, or a quality control check for manufacturing defects, is either definitely positive or not). How do you interpret the result of the diagnostic test for the level of the state variable when some or all of the information underlying the inference is ambiguous (imprecise)? This publication for the Wolfram Demonstration project is designed to facilitate the "what-if" exploration of the effects of ambiguities (imprecision) in sensitivity, specificity, and base rate information, alone or in combination, on posterior inferences through a linked tabular natural frequency and graphical probability format representation of underlying uncertainties. The textual description explains the underlying theory of boundedly rational inference. An appendix contains the full Mathematica code used to implement the interactive software that implements and explains the underlying theory.

Suggested Citation

  • John Fountain & Philip Gunby, 2010. "Comparing Ambiguous Inferences When Probabilities are Imprecise," Working Papers in Economics 10/08, University of Canterbury, Department of Economics and Finance.
  • Handle: RePEc:cbt:econwp:10/08
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    File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1008.pdf
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    Keywords

    Ambiguity; Bayesian decision making; inverse probabilities; choice under uncertainty; natural frequencies; Mathematica;

    JEL classification:

    • A20 - General Economics and Teaching - - Economic Education and Teaching of Economics - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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