Binomial Update with Uncertain Ground Truth I have a problem in which I'm trying to maintain a binomial distribution likelihood function. The wrinkle is that I have uncertainty about the results of an individual trial.
For example, each trial's success may come as a probability value (say, 0.78) rather than as a binary value (1 or 0).
Is there a standard or recommended way to handle this kind of nondeterministic evidence for updating a likelihood? I don't require that it be exactly a binomial likelihood.

Section 5.2 in Sokal and Rohlf's Biometry 3rd edition breaks down expansion of binomial frequencies and may help to see how the binomial proportion probabilities distribute. If 0.78 is the proportion of successes out of N trials, one way to model it is with the frequencies in, for example, a glm in R. An R Companion to Applied Regression has several glm models for binomial or binary outcomes, one of which you may feel is suitable for your research goal and data.
