Monday, February 28, 2005

Sample Space Ignorance, and the Nature of Investigation

If you find the logic of standard probability calculus compelling -- as I do -- AND if you are always unsure of your ground -- as I am -- AND if you believe -- as I do -- that fact investigation involves uncertainty, THEN you feel compelled to explain over and over -- and I do! -- why standard probability theory does not capture, or portray, the way thought moves when the mind is engaged in investigative discovery, in relatively radical forms of discovery.

Taking my cue from the thinking or suggestions some very enlightened people (e.g., Glenn Shafer, David Schum), in the past I have said (effectively) that standard probability theory cannot get into gear before and until there are defined hypotheses; one cannot speak meaningfully of the probability of a hypothesis {H|not-H} unless and until one has a hypothesis such as H in hand a/k/a in mind.

By surfing on the web I have found another phrase that describes the situation in which the investigator is engaged in hypothesis formation rather than hypothesis assessment:

sample space ignorance
See Michael James Smithson, Human Judgment and Imprecise Probabilities at SIPTA, Documentation on Imprecise Probability

In probability theory parlance, the sample space is the canvas on which are painted the possibilities that are to be assessed.

The point of this canvas metaphor: in some forms of investigation the possibilities that ought to be in play have not yet been drawn on the canvas, on the sample space, and investigators sometimes must busy themselves with activities that may lead to the drawing of lines that form pictures that may be worth both further thought, deliberation, investigation, and assessment.

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