I / The Probability Framework.- II Classical Statistical Theory.- III R. A. Fisher: Likelihood and Fiducial Inference.- IV Decision V Subjective Logical Approaches.- VI Comparison of VII Language: Syntax.- VIII Rational Corpora.- IX Randomness.- X Probability.- XI Conditional XII Interpretations XIII Bayesian XIV Argument.- XV Confidence Methods.- XVI Epistemological Considerations.- Appendix Mathematical Background.

Suppose that a probability measure $P$ is known to lie in set of measures $M$. Upper and lower bounds on the any event may then be computed. Sometimes, an $A$ conditional $B$ strictly contain unconditional $A$. Surprisingly, this might happen for every partition $\mathscr{B}$. If so, we say dilation has occurred. In addition being interesting statistical curiosity, counterintuitive phenomenon important implications robust Bayesian inference theory upper probabilities. We investigate...

This essay considers decision-theoretic foundations for robust Bayesian statistics. We modify the approach of Ramsey, de Finetti, Savage and Anscombe Aumann in giving axioms a theory preferences. establish that preferences which satisfy can be represented by set expected utilities. In presence two relating to state-independent utility, are probability/utility pairs, where utilities almost (in sense we make precise). Our goal is focus on preference alone extract whatever probability and/or...

This essay is, primarily, a discussion of four results about the principle maximizing entropy (MAXENT) and its connections with Bayesian theory. Result 1 provides restricted equivalence between two: where model for MAXENT inference uses an “a priori“ probability that is uniform, all constraints are limited to 0–1 expectations simple indicator-variables. The other three report on inability extend beyond these specialized constraints. 2 established sensitivity choice algebra possibilities even...

Can there be good reasons for judging one set of probabilistic assertions more reliable than a second? There are many candidates measuring “goodness“ forecasts. Here, I focus on such aspirant: calibration. Calibration requires an alignment announced probabilities and observed relative frequency, e.g., 50 percent forecasts made with the probability .5 occur, 70 .7 etc. To summarize conclusions: (i) Surveys designed to display calibration curves, from which recalibration is calculated, useless...

It is a familiar argument that advocates accommodating the so-called paradoxes of decision theory by abandoning “independence” postulate. After all, if we grant choice reveals preference, anomalous patterns Allais and Ellsberg problems (reviewed in Section 3) violate postulate P2 (“sure thing”) Savage's (1954) system. The strategy making room for new preference relaxing independence adopted each following works: Samuelson (1950), Kahneman Tversky's “Prospect Theory” (1979), Hagen Fishburn...

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence normative theory preference. (De achieves reduction belief to desire with his generalized Dutch-Book argument previsions. ) Both and rebel against legislating countable additivity probability. They require merely that be finitely additive. Simultaneously, they insist their theories preference are weak, accommodating all but self-defeating desires. In this paper we dispute these...

Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect “dilation”. In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. we further investigate dilation on several models. particular, consider conditions under which persists marginalization quantify the degree of also show that manifests itself asymptotically in certain robust Bayesian models characterize rate at occurs.

Abstract When can a Bayesian select an hypothesis H and design experiment (or sequence of experiments) to make certain that, given the experimental outcome(s), posterior probability will be greater than its prior probability? We discuss elementary result that establishes sufficient conditions under which this reasoning foregone conclusion cannot occur. illustrate how when fail, because is finitely but not countably additive, it may lead his/her into conclusion. The problem has decision...

Abstract Several axiom systems for preference among acts lead to a unique probability and state-independent utility such that are ranked according their expected utilities. These axioms have been used as foundation Bayesian decision theory subjective calculus. In this article we note the uniqueness of is relative choice what counts constant outcome. Although it sometimes clear should be considered constant, in many cases there several possible choices. Each can different "unique" utility. By...

I am a logician and philosopher; have not studied statistics for very long, so still quickly get out of my depth in discussion the technicalities statistical inference. But think it is important, none less, people whose interests lie area inference as such to do best they can reacting having an action upon -current work that particular kind called statistical. That this interaction difficult both parties more reason attempting it. (p. 938)