Sentence examples for pair of hypotheses from inspiring English sources
Similarly, we consider the second pair of hypotheses, i.e., H0: P1 - P2 ≤ -0.05 and H1: P1 - P2 > -0.05.
The leading idea in expressing such ignorance is usually the principle of indifference: ignorance means that we are indifferent between any pair of hypotheses.
We present a framework for machine translation evaluation using neural networks in a pairwise setting, where the goal is to select the better translation from a pair of hypotheses, given the reference translation.
So, given a specific pair of hypotheses and a proposed sequence of experiments, we don't need a general Convergence Theorem to tell us the likelihood of obtaining refuting evidence.
Thus, the following part of the convergence theorem applies to just that part of the total stream of evidence that consists of experiments and observations that fail to be fully outcome compatible for the pair of hypotheses involved.
It turns out that in almost every case (for almost any pair of hypotheses) the actual likelihood of obtaining such evidence (i.e., evidence that has a likelihood ratio value less than ε) will be much closer to 1 than this factor indicates.[21] Thus, the theorem provides an overly cautious lower bound on the likelihood of obtaining small likelihood ratios.
No hypothesis explains perfectly all variations in the data, however and all Bayes Factors for all pairs of hypotheses are decisive.
Thus, they show that the CoA is satisfied in advance of our using the logic to test specific pairs of hypotheses against one another.
This version of Bayes's Theorem shows that in order to evaluate the posterior probability ratios for pairs of hypotheses, the prior probabilities of hypotheses need not be evaluated absolutely; only their ratios are needed.
Given some specific pair of scientific hypotheses hi and hj one may directly compute the likelihood, given (hi·b·cn), that a proposed sequence of experiments or observations cn will result in one of the sequences of outcomes that yield low likelihood ratios.
A quick glance at Table 1 immediately reveals that there are many such predictions that follow from the EES position, since each row can be recast as a pair of alternative hypotheses.
