/pdf/reference-posterior-distributions-for-bayesian-inference-3y0fopskn8.pdf

Reference Posterior Distributions for Bayesian Inference

Likelihood Inference and Time Series

/pdf/the-relationship-between-sufficiency-and-invariance-with-36b7oazgg4.pdf

The Relationship Between Sufficiency and Invariance with Applications in Sequential Analysis

SUMMARY Sequential and group sequential procedures are proposed for monitoring repeated t, X2or F statistics. These can be used to construct sequential hypothesis tests or repeated confidence intervals when the parameter of interest is a normal mean with unknown variance or a multivariate normal mean with variance matrix known or known up to a scale factor. Exact methods for calculating error probabilities and sample size distributions are described and tables of critical values needed to implement the procedures are provided.

/pdf/exact-calculations-for-sequential-t-x2-and-f-tests-1vm05r77lp.pdf

Exact calculations for sequential t, X2 and F tests

In a logical probability approach to inference, distributions on a parameter space are interpretable as representing states of knowledge, and any prevailing state of knowledge may be taken to have been arrived at from a previous state of ignorance (indifference) followed by an accumulation of prior data. In this paper an indifference procedure is introduced that requires postulating what size and what kind of samples will and will not (in a special sense) permit statistical inference and prediction—e.g., one observation from a two-parameter normal model is not (in our special sense) sufficient to permit inference about the variance but two observations are. In essence, the procedure stipulates that prior indifference distributions be improper but become proper after an appropriate minimal sample. With some limitation on the family of priors considered, this procedure permits unique specification of indifference for the more commonly encountered statistical models. Furthermore, these specification...

/pdf/a-bayesian-indifference-procedure-4h6c8c69rx.pdf

G. A. Barnard

Papers

The frequency justification of certain sequential tests