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The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs.
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The binomial probability mass function (equation 6) provides the probability that x successes will occur in n trials of a binomial experiment.
A binomial experiment has four properties: (1) it consists of a sequence of n identical trials; (2) two outcomes, success or failure, are possible on each trial; (3) the probability of success on any trial, denoted p, does not change from trial to trial; and (4) the trials are independent.
Note that also "no transition" is possible outcome of the binomial experiment.
State Y(t + 1) is the result of a binomial experiment with the probabilities obtained in (ii).
This is difficult to understand because a power calculation can only be done before specifying the outcome of the binomial experiment, and not after.
Event types were generated by the binomial experiment of the two-step algorithm, substituting the CSHs by the increments of the cumulative CSHs.
To assess whether observed results were likely due to preexisting infections, we treated each replicate (i.e., paddock) as an independent binomial experiment because the conditions in one paddock had no opportunity to influence the events in another paddock.
Is it a binomial experiment?
Hamza et al [ 17, 18] compared in extensive simulation experiments the binomial and approximate normal within-study models, and showed that in general the performance of the binomial within-study model is much better.
The crow with a significant preference for the baited cup in the un-baited condition in experiment 1 kept its preference in experiment 3 (Binomial test: P = 0.004).
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