INFERENCES WITH AN UNKNOWN NOISE-LEVEL IN A BERNOULLI PROCESS

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.