FLAT LIKELIHOODS: BINOMIAL CASE

The shape of the likelihood function is often considered as one of the underlying causes of strange or counterintuitive estimation results. However, strange likelihood shapes may be a symptom of inferential issues related with the nature of the model and experimental data. In the cases discussed here, binomial flat likelihoods are related not only to sample size, but also to an embedded Poisson model problem. It is essential to understand the shapes of the likelihood function in order for being able to legitimately criticize likelihood inferences. This is particularly important since the likelihood function is a key ingredient in many inferential methods