A note on p-values interpreted as plausibilities

P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for most practical hypothesis testing problems, there exists an inferential model such that the corresponding plausibility function, evaluated at the null hypothesis, is exactly the p-value. The advantages of this representation are that the notion of plausibility is consistent with the way practitioners use and interpret p-values, and the plausibility calculation avoids the troublesome conditioning on the truthfulness of the null. This connection with plausibilities also reveals a shortcoming of standard p-values in problems with non-trivial parameter constraints.Comment: 13 pages, 1 figur

Some Remarks on the Model Theory of Epistemic Plausibility Models

Classical logics of knowledge and belief are usually interpreted on Kripke models, for which a mathematically well-developed model theory is available. However, such models are inadequate to capture dynamic phenomena. Therefore, epistemic plausibility models have been introduced. Because these are much richer structures than Kripke models, they do not straightforwardly inherit the model-theoretical results of modal logic. Therefore, while epistemic plausibility structures are well-suited for modeling purposes, an extensive investigation of their model theory has been lacking so far. The aim of the present paper is to fill exactly this gap, by initiating a systematic exploration of the model theory of epistemic plausibility models. Like in 'ordinary' modal logic, the focus will be on the notion of bisimulation. We define various notions of bisimulations (parametrized by a language L) and show that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type result, and also two undefinability results. However, our main point is a negative one, viz. that bisimulations cannot straightforwardly be generalized to epistemic plausibility models if conditional belief is taken into account. We present two ways of coping with this issue: (i) adding a modality to the language, and (ii) putting extra constraints on the models. Finally, we make some remarks about the interaction between bisimulation and dynamic model changes.Comment: 19 pages, 3 figure

Naturalness of the relaxion mechanism

The relaxion mechanism is a novel solution to the hierarchy problem. In this first statistical analysis of the relaxion mechanism, we quantify the relative plausibility of a QCD and a non-QCD relaxion model versus the Standard Model with Bayesian statistics, which includes an automatic penalty for fine-tuning. We find that in light of the hierarchy between the weak and Planck scales, relaxion models are favoured by colossal Bayes-factors. Constraints upon \eg the vacuum energy during relaxation, however, shrink the Bayes-factors such that relaxion models are only slightly favoured. Including the bounds on $\left|\theta_\text{QCD}\right|$ shatters the plausibility of the QCD relaxion model as it typically yields $\left|\theta_\text{QCD}\right| \gg 0$. Finally, we augment our models with scalar-field inflation and consider measurements of inflationary observables from BICEP/Planck. We find that, all told, the Standard Model is favoured by huge Bayes-factors as the relaxion models require fine-tuning such that the Hubble parameter is less than the height of the periodic barriers. Thus, whilst we confirm that relaxion models could solve the hierarchy problem, we find that their unconventional cosmology demolishes their plausibility

Evidence and plausibility in neighborhood structures

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood $N$ indicates that the agent has reason to believe that the true state of the world lies in $N$. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this evidence structure, yielding our intended models for evidence-based beliefs. In addition, we also consider a second more general flavor, where belief and plausibility are modeled using additional primitive relations, and we prove a representation theorem showing that each such general model is a $p$-morphic image of an intended one. This semantics invites a number of natural special cases, depending on how uniform we make the evidence sets, and how coherent their total structure. We give a structural study of the resulting `uniform' and `flat' models. Our main result are sound and complete axiomatizations for the logics of all four major model classes with respect to the modal language of evidence, belief and safe belief. We conclude with an outlook toward logics for the dynamics of changing evidence, and the resulting language extensions and connections with logics of plausibility change

Localist but Distributed Representations

A number of examples are given of how localist models may incorporate distributed representations, without the types of non-local interactions that often render distributed models implausible. The need to analyze the information that is encoded by these representations is also emphasized as a metatheoretical constraint on model plausibility

Light aircraft sound transmission study

The plausibility of using the two microphone sound intensity technique to study noise transmission into light aircraft was investigated. In addition, a simple model to predict the interior sound pressure level of the cabin was constructed