Inferences about a proportion p are often based on data generated from
dichotomous processes, which are generally modeled as processes that
are Bernoulli in p. In reality, the assumption that a data-generating
process is Bernoulli in p is often violated due to the presence of noi
se. The level of noise is usually unknown and, furthermore, dependent
on the unknown proportion in which one is interested. A specific model
which takes into account the existence of noise is developed. Any arg
uments about p based exclusively on a likelihood analysis can lead to
difficulties. A Bayesian approach is used, which also helps us to form
alize a priori dependence between the proportion and the noise level.
Empirical data are used to illustrate the model and provide some flavo
r of the implications of our uncertainty about the noise for inference
s about a proportion.