15 all-timers [back]
- W.K.Hastings (1970) Monte Carlo sampling methods using Markov chains and their applications, Biometrika
- G. Casella & W. Strawderman (1981) Estimation of a bounded mean Annals of Statistics
- A.P. Dawid, M. Stone & J. Zidek (1973) Marginalisation paradoxes in Bayesian and structural inference J. Royal Statistical Society
- C. Stein (1981) Estimation of the mean of a multivariate normal distribution Annals of Statistics
- D.V. Lindley & A.F.M. Smith (1972) Bayes Estimates for the Linear Model J. Royal Statistical Society
- A. Birnbaum (1962) On the Foundations of Statistical Inference J. American Statistical Assoc.
in this order and mostly managed to grasp the quintessentials of the papers and to give decent (Beamer) presentations. The hardest one was the exposition of the likelihood principle and the student who chose this paper struggled to go past a mere repetition of the proofs. I enjoyed it nonetheless because the presentation raised questions about this principle,
“Two likelihood functions are equivalent if one is a scalar multiple of the other. The likelihood principle states that all information from the data relevant to inferences about the value of θ is found in the equivalence class”
First, the conditionality principle
seems to imply the sufficiency principle
at least in cases when the data X separates into a sufficient statistics T(X) and an ancillary statistics A(X), since the latter works as an experiment indicator. This makes me wonder why we do need the sufficiency principle! Maybe because the choice of the sufficient statistics somehow involves the axiom of choice… A second questioning came from the formulation of the likelihood principle as reproduced from Birnbaum‘s paper: the inclusion of the equivalence principle sounds artificial in that the scalar multiple is not based on “first principles” (because, by its construction, the likelihood is not missing a normalising constant) but rather on the necessity to account for ancillaries in the derivation from the sufficiency principle.