Mathematical Sciences: Conditional and Unconditional Confidence

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The research investigates reconciliation of unconditional (pre-data) inference and conditional (post-data) inference using an objective means of assessing conditional validity of frequentist confidence. General methods of assigning post-data confidence are considered which are based on posterior distributions. The resulting properties and frequentist validity of the post-data confidence estimator are examined. Post-data inference for volume-reducing confidence sets for normal means and variances is to be studied where it is possible to achieve lower volume and coherent post-data confidence in a frequency- valid way. The conditional properties of admissible nonrandomized confidence sets from discrete distributions will be investigated with the goal of obtaining coherent frequency-valid post-data inference.