For the latter, which is fully determined by the likelihoods of the hypotheses, we write the probability of the sample conditional on the hypothesis, $P(s \mid h_{\theta})$.
The result is conditional on the hypothesis that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis.
This comes at the cost of additional modeling assumptions; namely, specification of prior probabilities for each hypothesis and prior distributions over model parameters conditional on the hypotheses.
Any use of Bayes's theorem to reconstruct scientific reasoning plainly depends on the idea that scientists can assign the pertinent probabilities, both the prior probabilities and the probabilities of the evidence conditional on various hypotheses.
Further assume the likelihoods $P(s \mid h_{\theta})$, i.e., the probability assigned to the data $s$ conditional on the hypotheses $h_{\theta}$.
Our hypothesis is conditional on one X-linked gene mutation functioning as the causal event for developing SS.
This suggestion is sensitive to the well-recognized fact that we are not always able to assign a prior to every hypothesis of interest, or to say how probable a given piece of evidence is conditional on a given hypothesis.
This type of analysis generates an unconditional probability rather than a conditional one based on the null hypothesis being accepted or rejected [18].
Every 'vertical' hypothesis about testing an isotonic cutpoint x i is conditional on the rejection of the hypothesis above (vertical conditioning) and testing every hypothesis on the right hand side is conditional on the retention of the hypothesis on its left (horizontal conditioning). 1.
The first case includes studies that result, for instance, in a family of risk curves representing percentiles of the probability distribution of the future frequency of exceeding specified consequence levels conditional on a set of hypotheses.
Therefore, the expected utilities of acceptance and rejection are undefined, and we ought to use the methods of traditional statistics, which rely on comparing the probabilities of our evidence conditional on each of the hypotheses.
