For Comte, the ultimate motivation for scientific activity is practical: "From Science Comes Prevision: From Prevision Comes Action" (1853, v. 1, 21).
Comte's education as an engineer had made him quite aware of the links between science and its applications, which he summarized in an oft-quoted slogan: 'From science comes prevision, from prevision comes action'.
This chapter focuses on the extension of coherent lower previsions from the set of bounded random variables to a larger set.
Whereas, in alcaline solutions, the oxydation rate is extremely slow; so, it is possible to reach potentials positive enough to let electrocrystallization of PbO2 take place, which is in contradiction with the thermodynamic previsions derived from Pourbaix diagrams.
Monster division, Monster Worldwide, Maynard, Mass., expanded its relationship with Deutsch, New York, part of the Interpublic Group of Companies, by shifting the direct marketing part of its account to the Direct Deutsch unit from PreVision, Lincoln, Mass.
We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior (updated) probabilities.
Call this your "lower prevision" for $f$.
That is, your lower prevision for the gamble $f$ is the largest amount you would pay to receive the gamble $f$.
In addition, prevision for a booster immunization may be considered, and clinical trials to determine its benefit must also be performed.
The chapter defines an extension of a coherent lower prevision to a linear space of previsible, not necessarily bounded random variables, and highlights that this extension still has properties similar to those of coherent lower previsions.
Putting this together, \[\max\{p(X),p(Y \} \le p(X\cup Y) \le \min\{p(X)+p(Y),1\}.\] These constraints are effectively what you get from de Finetti's Fundamental Theorem of Prevision (de Finetti 1990 [1974]: 112; Schervish, Seidenfeld, and Kadane 2008).
