Bayesian inference viewed as a computational approximation to classical calculations

Dave Armstrong writes:

I have a hopefully quick question about Multilevel Models . . . While being Bayesian would make the attached question [having to do with calculating confidence intervals for linear combinations of fixed and varying coefficents] moot, and I am certainly sympathetic in my own work, I am looking to understand the Frequentist perspective as I need to explain how to do this in R to people without experience in WinBUGS and who are generally uninterested in gaining such experience.

My reply:

This sort of thing happens to me all the time, which is one reason I try to do these inferences using simulations, so I don’t have to keep track of covariances. The simulation-based Bayes inferences can be interpreted as classical freq inferences; to put it another way, the Bayesian inference can be thought of as a computational trick to work with the multivariate normal and t distributions that arise in classical confidence intervals.

2 thoughts on “Bayesian inference viewed as a computational approximation to classical calculations

  1. "OneEyed" if you refrain from using a statistical technique until you are sufficently aware of it's type 1 and 2 error rates – you have been classical.

    There is a pair of papers by Scott Emerson and others that does Bayesian evaluation of sequential trials in one paper and Frequency evaluation in the other and discusses this nicely.

    Andrew has also discussed this a couple times before

    K?

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