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The "paradox" arises in the Two Envelopes Paradox from the incorrect formulation of the argument. The infomation given is misused and therefore the results are incorrect for the question asked. The key is to be clear on what question we are…
Categories with families (CwFs) have been used to define the semantics of type theory in type theory. In the setting of Homotopy Type Theory (HoTT), one of the limitations of the traditional notion of CwFs is the requirement to set-truncate…
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…
Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For…
This paper describes a framework for a systematic classification of spreadsheet errors. This classification or taxonomy of errors is aimed at facilitating analysis and comprehension of the different types of spreadsheet errors. The taxonomy…
This paper has been withdrawn by the authors, due a crucial error in the proof of the main theorem.
Identifying and disentangling sources of predictive uncertainty is essential for trustworthy supervised learning. We argue that widely used second-order methods that disentangle aleatoric and epistemic uncertainty are fundamentally…
This paper provides an algebraic reconstruction of Einstein's own argument for the incompleteness of quantum mechanics -- the one that he thought did not make it into the EPR paper -- in order to clarify the assumptions that underlie an…
This paper presents a theory of error in cross-validation testing of algorithms for predicting real-valued attributes. The theory justifies the claim that predicting real-valued attributes requires balancing the conflicting demands of…
This note corrects Example 3.2 in Two-Variable Wiman-Valiron Theory and PDEs by the authors which appeared in Ann. Acad. Sci. Fenn Math. (35) (2010), 571-580.
Event extraction (EE) is a crucial task aiming at extracting events from texts, which includes two subtasks: event detection (ED) and event argument extraction (EAE). In this paper, we check the reliability of EE evaluations and identify…
Einstein's unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found…
In randomised trials, continuous endpoints are often measured with some degree of error. This study explores the impact of ignoring measurement error, and proposes methods to improve statistical inference in the presence of measurement…
An interesting test of Einstein's equivalence principle (EEP) relies on the observed lag in arrival times of photons emitted from extragalactic transient sources. Attributing the lag between photons of different energies to the…
Thousands of papers have reported two-way cluster-robust (TWCR) standard errors. However, the recent econometrics literature points out the potential non-gaussianity of two-way cluster sample means, and thus invalidity of the inference…
To be considered reliable, a model must be calibrated so that its confidence in each decision closely reflects its true outcome. In this blogpost we'll take a look at the most commonly used definition for calibration and then dive into a…
Normalization fails in type theory with an impredicative universe of propositions and a proof-irrelevant propositional equality. The counterexample to normalization is adapted from Girard's counterexample against normalization of System F…
Although Einstein's name is closely linked with the celebrated relation E = mc2 between mass and energy, a critical examination of the more than half dozen "proofs" of this relation that Einstein produced over a span of forty years reveals…
The conventional Minimum Error Entropy criterion (MEE) has its limitations, showing reduced sensitivity to error mean values and uncertainty regarding error probability density function locations. To overcome this, a MEE with fiducial…
A recent paper [1] (El Aroudi, 2012) misapplied a critical condition (Fang and Abed, 2001) to a well-known example. Even if the mistake is corrected, the results in [1] are applicable only to buck converters and period-doubling bifurcation.…