By Daniel Dugue, E. Lukacs, V. K. Rohatgi
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Additional info for Analytical Methods in Probability Theory. Proc. conf. Oberwolfach, 1980
As I will later show, it is not always necessary to satisfy entirely the stringent low-level independence condition. A small amount of dependence on microlevel information about initial conditions may be allowed in the ﬁrst stage of epa, provided that it is eliminated in the second or third stages. 6. 2 Enion Probability Analysis 19 A terminological aside: There are two ways to articulate the requirement that enion probabilities not depend on low-level information. First, one can say, as I do, that they must be functions only of macrolevel information.
05 probability, conjoined with the assumption of stochastic independence, somehow picks out just those properties of the ecosystem that determine the system’s simple population ﬂow, and no more. It is for this reason that I see epa as a powerful framework for understanding the macrolevel simplicity of complex systems. Although this example gives a speciﬁc value for the probability of rabbit death and derives a speciﬁc form for the population law, these speciﬁcs are not what interests me in this study.
Let me begin the inquiry with the following question about epa: under what circumstances, exactly, can epa be successfully applied? 23. 11. The greater part of this book—chapters two, three, and four—is an attempt to show that there are, and more importantly, to explain why there are. The ﬁve principal properties that enion probabilities must have in order to serve as a basis for epa are: 1. Enion probabilities must have the mathematical properties assumed in the calculations that underlie epa, which is to say that they must satisfy the axioms of the probability calculus.
Analytical Methods in Probability Theory. Proc. conf. Oberwolfach, 1980 by Daniel Dugue, E. Lukacs, V. K. Rohatgi