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.

3 Responses to “15 all-timers [back]”

  1. […] few days ago, one of my students, Jacopo Primavera (from La Sapienza, Roma) presented his “reading the classic” paper, namely the terrific bounded normal mean paper by my friends George Casella and Bill […]

  2. Paulo C. Marques F. Says:

    Dear Xian,

    We wrote a short review on the LP

    http://link.aip.org/link/?APCPCS/1073/96/1

    In this paper, the Sufficiency Principle is not used.

    Cheers,

    Paulo.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.