Bernoulli Pairs with Invariant Reversals: An Example of Partial Likelihood

Abstract

Bernoulli pairs with invariant reversals provide an inference situation with two parameters,θ and λ ; λ is a nuisance parameter andθ the parameter of interest. The likelihood factorizes and the partial likelihood depends onθ alone. This paper examines the problem of making inferences aboutθ in detail and concludes that although the partial likelihood method is asymptotically sound the approach to the limit is slow, so that the method can lose a lot of information even with quite large samples. Computations of posterior distributions for 100 pairs illustrate the argument.