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from Part II - Stochastic models
Published online by Cambridge University Press: 05 November 2014
Introduction
Statistical experiments are conducted in order to infer information about various processes and thus to guide decision making. The effectiveness of a certain drug on a particular disease, surgical procedures, therapy techniques, or demographic effects on disease are a few examples of statistical inference based on a statistical experiment.
A statistical experiment may be described in terms of a population, a phenomenon to be investigated, and a scaling procedure to quantify the spread of the phenomena in a population. Traditionally, a statistical experiment E is described in terms of a trilogy:
the sample space Ω, which is the set of all possible elementary outcomes (the ‘alphabet’ of the experiment);
the field σF, which is the set of all measurable events;
probability measure P, which is a positive scalar function measuring the occurrence of the events; i.e. it assigns probabilities to events on σF.
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