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, a failure is recorded or not, an employee will quit within five years, 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 a manufacturing failure, or some demographic indicator like a high school diploma , which is either definitely positive or not) . How do you interpret the result of the diagnostic test for the level of the state variable – posterior inferences – when the some or all of the information underlying the inference is ambiguous (imprecise)?
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