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How do you interpret the result of the diagnostic test for the level of a state variable when some or all of the information underlying the inference is ambiguous (imprecise)? Let ... be the logical truth value (1 or 0) of a proposition about the state variable (e.g. a disease is present or absent, or a failure is recorded or not) and let ... be the logical truth value of a proposition about the outcome of an imperfect diagnostic test being a positive indicator for the state (e.g. a blood test result for this disease, a quality control check for a manufacturing failure). From a statistical perspective there are three precise numerical inputs that feed into a coherent posterior inference about binary-valued ... after having observed the result of the binary-valued diagnostic signal ... : a sensitivity number, a specificity number, and a base rate number (as explained in the Details section). The sliders on the left control these three numbers, and the table and graphical representation update dynamically. To facilitate the "what-if" exploration of the effects on posterior inferences of ambiguities (imprecision) in sensitivity, specificity, and base rate information, there are two sets of sliders: the lower set, a benchmark, remains slightly faded out in the picture as the upper set of slider values varies.
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