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ancillary statistic argue argument Barnard Basu Bayes Bayesian analysis Bayesian inference Berger and Wolpert betting Birnbaum censoring mechanism Censoring Principle classical conclusion conditional confidence conditionalist Conditionality Principle Confidence Principle consider Dawid defined DeGroot depend discrete error probabilities estimator Evaluation Game example experiment E experimenter finitely additive Fraser frequentist measures given Godambe hence Hill Hinkley improper prior Indeed information about e interpretation intuitive issue likelihood function likelihood principle LP does measures of evidence methods mixed experiment non-Bayesian noninformative prior nuisance parameter nuisance variable observation x performance possible posterior distribution posterior probability pre-experimental prior distribution problem procedure randomization analysis reasonable sample space Section 3.5 seems sequential significance level significance testing simple situation Sprott Statistical Inference statisticians Stein stopping rule Stopping Rule Principle sufficient statistic Suppose theorem theory theta Thus uniform prior unknown viewpoint
Page 174 - Objective evidence and certitude are doubtless very fine ideals to play with, but where on this moonlit and dream-visited planet are they found? I am, therefore, myself a complete empiricist so far as my theory of human knowledge goes. I live, to be sure, by the practical faith that we must go on experiencing and thinking over our experience, for only thus can our opinions grow more true...
Page 174 - I am, therefore, myself a complete empiricist so far as my theory of human knowledge goes. I live, to be sure, by the practical faith that we must go on experiencing and thinking over our experience, for only thus can our opinions grow more true ; but to hold any one of them — I absolutely do not care which — as if it never could be re-interpretable or corrigible, I believe to be a tremendously mistaken attitude, and I think that the whole history of philosophy will bear me out.
Page 81 - ... have precisely determined alternatives, with which you want to compare a given hypothesis, and you use another method when you do not have these alternatives. SAVAGE: May I digress to say publicly that I learned the stoppingrule principle from Professor Barnard, in conversation in the summer of 1952. Frankly, I then thought it a scandal that anyone in the profession could advance an idea so patently wrong, even as today I can scarcely believe that some people resist an idea so patently right.
Page 76 - This irrelevance of stopping rules to statistical inference restores a simplicity and freedom to experimental design that had been lost by classical emphasis on significance levels (in the sense of Neyman and Pearson) and on other concepts that are affected by stopping rules. Many experimenters would like to feel free to collect data until they have either conclusively proved their point, conclusively disproved it, or run out of time, money, or patience.
Page 65 - In the past, the need for probabilities expressing prior belief has often been thought of, not as a necessity for all scientific inference, but rather as a feature peculiar to Bayesian inference. This seems to come from the curious idea that an outright assumption does not count as a prior belief... I believe that it is impossible logically to distinguish between model assumptions and the prior distribution of the parameters.
Page 104 - What the use of P implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred.
Page 151 - Bayesian and classical influence in the analysis of variance and in the testing of models. In DL Meyer & RO Collier, Jr.
Page 10 - A cv = s/x, (4.1) where x and s are the sample mean and standard deviation, respectively.
Page 158 - Berger, JO and Delampady, M. (1987). Testing Precise Hypotheses. With Discussion. Statistical Science 2, 317-352. Berger, JO and Mortera, J.
Page 64 - ... Would you offer 19 to 1 odds that the standard deviation of the height of Meccans is less than 1-13 mm? That is the 95 per cent upper confidence limit computed from chi-squared with one degree of freedom. No, I think you would not have even enough confidence in that limit to offer odds of 1 to 1 . The only use I know for a confidence interval is to have confidence in it.