15 all-timers [back]

Following an earlier post and poll. six of my graduate students took the Reading Classics seminar this year (plus two who dropped out). They chose

1. W.K.Hastings (1970) Monte Carlo sampling methods using Markov chains and their applications, Biometrika
2. G. Casella & W. Strawderman (1981) Estimation of a bounded mean Annals of Statistics
3. A.P. Dawid, M. Stone & J. Zidek (1973) Marginalisation paradoxes in Bayesian and structural inference J. Royal Statistical Society
4. C. Stein (1981) Estimation of the mean of a multivariate normal distribution Annals of Statistics
5. D.V. Lindley & A.F.M. Smith (1972) Bayes Estimates for the Linear Model  J. Royal Statistical Society
6. 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

“If an experiment is chosen by a random process independent of the states of nature θ, then only the experiment actually performed is relevant to inferences about θ”

seems to imply the sufficiency principle

“If T(X) is a sufficient statistic for θ, and if in two experiments with data x₁ and x₂ we have T(x₁) = T(x₂), then the evidence about θ given by the two experiments is the same”

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.