A statistical version of Arrow’s paradox

Unfortunately, when we deal with scientists, statisticians are often put in a setting reminiscent of Arrow’s paradox, where we are asked to provide estimates that are informative and unbiased and confidence statements that are correct conditional on the data and also on the underlying true parameter. [It’s not generally possible for an estimate to do all these things at the same time — ed.] Larry Wasserman feels that scientists are truly frequentist, and Don Rubin has told me how he feels that scientists interpret all statistical estimates Bayesianly. I have no doubt that both Larry and Don are correct. Voters want lower taxes and more services, and scientists want both Bayesian and frequency coverage; as the saying goes, everybody wants to go to heaven but nobody wants to die.

2 thoughts on “A statistical version of Arrow’s paradox

  1. Maybe just a function of not showing functions?

    How often are scientists shown nice plots of type one error rates or CI coverage as a function of true parameters and or sample features – rather than _lied_ to about these being a constants?

    Some nice (seperate?) work by Michael Fay and Scott Emmerson on how to do this.

    K?

  2. Maybe its time for some dissociative identity disorder?

    That is some pragmatic (purposeful) frequency evaluation of Bayesian methods.

    The time does seem ripe.

    Andrew had a recent post on this with a draft (re small sample size and power), Jim Berger has the Fisher, Jefferies, Neyman talks/papers, Mike Evans has the Relative Surprise Inference papers (in particular Optimal properties of some Bayesian Inferences) and Paul Gustafson and Sander Greenland have stuff on frequency evaluation of omnipitent versus wrong prior assumptions (Interval estimation for messy observational data).

    Enough reading for my next trip to the beach.

    But also someone might start organizing joint talks and journal paper sessions on this.

    The timing does seem right and my guess is the (better) scientists would welcome it.

    K?

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