Related papers: Response to the Letter to the Editor

Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic provability of double negation of that formula. We generalise Glivenko's theorem from double negation to an arbitrary nucleus,…

This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…

The classic "Bell's Theorem" of Clauser, Holt, Shimony and Horne tells us that we must give up at least one of: (1) objective reality (aka "hidden variables"); (2) locality; or (3) time-forwards macroscopic statistics (aka "causality"). The…

In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we…

The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…

In this paper, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing…

An influential argument for scientific realism posits that, if scientific theories were not true, their empirical success would be a coincidence. Here, I show that the false Drude's theory succeeds in explaining the Wiedemann-Franz law by…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…

Increasing integration and availability of data on large groups of persons has been accompanied by proliferation of statistical and other algorithmic prediction tools in banking, insurance, marketiNg, medicine, and other FIelds (see e.g.,…

Amato et al.[arXiv:1205.6418] maintain that certain data published in Carpinteri et al.[2] are not the result of independent measurements, and are in any case affected by uncertainties such that our conclusions are not valid. We will…

Frank Porter has recently posted a review of "Confidence intervals for the Poisson distribution" (arXiv:2509.02852). The long, diverse history of such intervals is closely related to that of confidence intervals for the parameter of the…

This purpose of this letter is to handle a gap that was found in the proof of Theorem 2 in the paper "The generalized stochastic likelihood decoder: random coding and expurgated bounds."

This paper was written, apart from one technical correction, in July and August of 2013. The, then very recent, breakthrough of Y. Zhang \cite{Z} had revived in us an intention to produce a second edition of our book "Opera de Cribro", one…

A recent paper "Single-world interpretations of quantum theory cannot be self-consistent" [arXiv:1604.07422] by D. Frauchiger and R. Renner has attracted a considerable interest of a broader physics audience and shortly elicited a number of…

A 1992 conjecture of Alon and Spencer says, roughly, that the ordinary random graph $G_{n,1/2}$ typically admits a covering of a constant fraction of its edges by edge-disjoint, nearly maximum cliques. We show that this is not the case. The…

In the Bayesian paradigm for presenting forensic evidence to court, it is recommended that the weight of the evidence be summarized as a likelihood ratio (LR) between two opposing hypotheses of how the evidence could have been produced.…

Here we argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the…

Work in Counterfactual Explanations tends to focus on the principle of "the closest possible world" that identifies small changes leading to the desired outcome. In this paper we argue that while this approach might initially seem…

Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…

Vaidman's analysis of the photon's past is based on incorrect interpretation of quantum probability amplitudes. The confusion stems from his original work [{\it Phys. Rev. Lett.} \textbf{60}, 1351 (1988)], which missed the connection…