come in many shapes and forms, but the most relevant for our discussion here are those which hold that (subjectively or objectively) expected consequences matter.
might assume that when you know nothing, the rational starting point is fifty percent.
For example, eighteenth-century "moral scientists" studied the behavior of rational individuals and probabilists
coined the term "moral expectation" (utility) to evaluate risk.
skip is the linkage between propositions derived from observations of phenomena, and the implications of these propositions allowing us to draw conclusions about legal liability.
of all stripes will appreciate Lindley's description of the palpable angst experienced by many of the principals as they contended with the realization that the scientific method was abandoning them only to be superseded by a disquieting uncertainty.
283), opposing probabilism of the sort widely endorsed by philosophers who embrace Bayesianism, supportive of the importance of forming testable conjectures, but in opposition to both probabilists
and Popperians in favoring ampliative induction.
And, of course, what economist wouldn't relish this revelation of the great debt owed to this early financial economist by the mathematical physicists and probabilists
to be added to the well-known debt owed to Malthus by the Darwinian biologists?
The Kohonen algorithm has also attracted the attention of probabilists
concerned with establishing rigorous proofs of some of its properties.
Third, it is worth noting that the difficulty probabilists
assign to defining an appropriate reference class inheres even in the example of the coin toss.
, by comparison, instead maintain that:
legal theories of evidence supplied probabilists
with a model for
Many if not most statisticians and mathematical probabilists
, including Kolmogorov, Neyman, Doob, Cramer, and Feller, among others, regard the relation between probability and long-run frequency as less determinate, and defined by the limit theorems of the mathematical theory, like the weak and strong laws of large numbers and the central limit theorem.
Second, even if analysis shows that some historical figures did not accept all of the central premises of the standard modern theory of probability, a comparison of the principles favored by such historical figures and those embraced by conventional modern probabilists
could throw historical conceptions of evidence and proof into sharper relief and thus make them more transparent and more intelligible to a modern observer.
might assume that when you know nothing, the rational starting point is 50% (thus, many a Bayesian would make 50% the initial prior probability).
In order to include the thirty-one propositions that are used in the ECHO model, a probabilist
would need 2(31) (2,147,483,648) probabilities for a full joint distribution, more than two billion probabilities.