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If P makes S more coherent than does P′ according to C, we fix the probability of reliability in such a way that S comes out as more probable on P′ than on P. If, on the other hand, P′ makes S more coherent, then we choose a value for the probability of reliability so that P makes S more probable.
Here, the threshold λ(D) is selected to fix the probability of detection at PD = 0.8.
As a by-product, the knowledge of the Gibbs measure provided by this analysis allows a posteriori to fix the probability distribution of V k ( s ).
To definitively establish statistical significance, we will fix the probability of Type-I error at 1%.
Fix the probability distribution (D.4).
Fix the probability distribution as (A.1).
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(The principle C1 of section 3.1 fixes the probability of inconsistent sentences at zero).
K-sequences (state descriptions in Carnap's terminology) are the most specific sentences in a language L k): every consistent sentence is logically equivalent to a disjunction of these pairwise incompatible conjunctions, so fixing the probabilities of all state descriptions, which must always sum to one, fixes the probability of every consistent sentence in the language.
Thirdly, since (gamma =frac {n}{k}) and k is fixed, the probability Pr(n) is equal to the probability of γ for all cases.
Now suppose that we have two events A and B. If we hold fixed the probability of each event individually, a probability distribution over the partition A&B, A&~B, ~A&B, ~A&~B will have more information, in the sense of Shannon (1948), when A and B are correlated.
This approach is motivated by that fact that fixing the edge density implies fixing the probability for the existence of an edge in the case of Erdös-Rényi random networks.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com