Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize

The Relationship Between Belief and Credence

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the debate thus far

A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Logical inference for inverse problems

Estimating a deterministic single value for model parameters when reconstructing the system response has a limited meaning if one considers that the model used to predict its behaviour is just an idealization of reality, and furthermore, the existence of measurements errors. To provide a reliable answer, probabilistic instead of deterministic values should be provided, which carry information about the degree of uncertainty or plausibility of those model parameters providing one or more observations of the system response. This is widely-known as the Bayesian inverse problem, which has been covered in the literature from different perspectives, depending on the interpretation or the meaning assigned to the probability. In this paper, we revise two main approaches: the one that uses probability as logic, and an alternative one that interprets it as information content. The contribution of this paper is to provide an unifying formulation from which both approaches stem as interpretations, and which is more general in the sense of requiring fewer axioms, at the time the formulation and computation is simplified by dropping some constants. An extension to the problem of model class selection is derived, which is particularly simple under the proposed framework. A numerical example is finally given to illustrate the utility and effectiveness of the method

Conceptualizing Quality in Software Industry

This paper investigates the different software quality perceptions from the different stakeholders’ perspectives and presents a critique to previously developed quality models and measurement theory frameworks associated. It emphasizes the rationale beyond the selection of the Goal Question Metric (GQM) as an evaluation method for the development of the software project with the desired quality needs satisfying the software system. Then it ends up with several concluding remarks that pinpoint the main discussion points and offers guidance for further research

Evidentialism and Moral Encroachment

Moral encroachment holds that the epistemic justification of a belief can be affected by moral factors. If the belief might wrong a person or group more evidence is required to justify the belief. Moral encroachment thereby opposes evidentialism, and kindred views, which holds that epistemic justification is determined solely by factors pertaining to evidence and truth. In this essay I explain how beliefs such as ‘that woman is probably an administrative assistant’—based on the evidence that most women employees at the firm are administrative assistants—motivate moral encroachment. I then describe weaknesses of moral encroachment. Finally I explain how we can countenance the moral properties of such beliefs without endorsing moral encroachment, and I argue that the moral status of such beliefs cannot be evaluated independently from the understanding in which they are embedded