Effective sample size in a dichotomous process with noise

The effect of noise in a dichotomous process is studied from the Bayesian viewpoint. Winkler's approximation to the posterior distribution in the presence of noise is shown to break down badly near the limits of its application. Information loss is measured using effective sample size. An account of the relationship between effective sample size/information loss and sampling data is given which differs sharply from that of previous work in this area.