The Likelihood Principle, the MVUE, Ghosts, Cakes and Elves

In my prior blog post, I wrote of a clever elf that could predict the outcome of a mathematically fair process roughly ninety percent of the time. Actually, it is ninety-three percent of the time and why it is ninety-three percent instead of ninety percent is also important. The purpose of the prior blog post was to illustrate the weakness of using the minimum variance unbiased estimator (MVUE) in applied finance. Nonetheless, that begs a more general question of when and why it should be used, or a Bayesian or Likelihood-based method should be applied. Fortunately, the prior blog post provides a way of looking at the problem. Fisher's Likelihood-based, Pearson and Neyman's Frequency-based and Laplace's method of inverse probability really are at odds with one another. Indeed, much of the literature of the mid-twentieth century had a polemical ring to it.