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A.P. Dempster 271As the world of statistical analysis moves more and more to “big data”and associated “complex systems,” the DS middle ground can be expected tobecome increasingly important. DS puts no restraints on making state spacestructures as large as judged essential for bias protection, while the accompanyingincreases in many probabilities of “don’t know” will often require payingserious attention to the introduction of more evidence, including futureresearch studies. Contrary to the opinion of critics who decry all dependenceon mathematical models, the need is for more inclusive and necessarily morecomplex mathematical models that will continue to come on line as associatedinformation technologies advance.24.4 The standard DS protocolDeveloping and carrying out a DS analysis follows a prescribed sequence ofactivities and operations. First comes defining the state space structure, referredto henceforth by its acronym SSS. The purpose of initializing an SSSis to render precise the implied connection between the mathematical modeland a piece of the actual real world. Shafer introduced the insightful term“frame of discernment” for what I am calling the SSS. The SSS is a mathematicalset whose elements are the possible true values of some “small world”under investigation. The SSS is typically defined by a vector or multi-wayarray of variables, each with its own known or unknown true value. Such anSSS may be very simple, such as a vector of binary variables representing theoutcomes of successive tosses of a bent coin, some observed, and some such asfuture tosses remaining unobserved. Or, an SSS may be huge, based on a setof variables representing multivariate variation across situations that repeatacross times and spatial locations, in fields such as climatology, genomics, oreconomics.The requirement of an initialized SSS follows naturally from the desirabilityof clearly and adequately specifying at the outset the extent of admissiblequeries about the true state of a small world under analysis. Each such querycorresponds mathematically to a subset of the SSS. For example, before thefirst toss of a coin in an identified sequence of tosses, I might formulate aquery about the outcome, and respond by assigning a (p, q, r) personalprobabilitytriple to the outcome “head,” and its reordered (q, p, r) tripletothe“complementary” outcome “tail.” After the outcome “head” is observed andknown to “you,” the appropriate inference concerning the outcome “head” is(1, 0, 0), because the idealized “you” is sure about the outcome. The assertion“head on the first toss” is represented by the “marginal” subset of the SSSconsisting of all possible outcomes of all the variables beyond the first toss,which has been fixed by observation. A DS inference (1, 0, 0) associated with“head” signifies observed data.