Related papers: Response to the Letter to the Editor
The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the…
In physics, there is the prevailing intuition that we are part of a unique external world, and that the goal of physics is to understand and describe this world. This assumption of the fundamentality of objective reality is often seen as a…
Bayesian evidence ratios give a very attractive way of comparing models, and being able to quote the odds on a particular model seems a very clear motivation for making a choice. Jeffreys' scale of evidence is often used in the…
An author (arXiv:1709.09262 [quant-ph] (2017), Nanoscale Research Letters (2017) 12:552) has recently questioned the security of two-way quantum key distribution schemes by referring to attack strategies which leave no errors in the (raw)…
In 1988, in cooperation with a team of experimental physicists, a Condensed Matter theorist, X, published in Physical Review Letters a crucial experimental result dealing with a revolutionary new theory. The conclusions of the paper were…
The title of the article is identical to the title of Chapter 21 in Gardner (2001): because we are going to analyze the probability calculations and the ambiguity of the problem statements. We will analyze 3 out of 4 problems from Gardner…
In a recent paper [1], it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is 1-random. We also defend the correctness of this claim and assert that the outcomes of quantum…
Much of science is (rightly or wrongly) driven by hypothesis testing. Even in situations where the hypothesis testing paradigm is correct, the common practice of basing inferences solely on p-values has been under intense criticism for over…
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…
Can we really falsify truth by dictat? A critical note on J. R. Lucas' 1996 remarks concerning non-standard models of first-order Peano Arithmetic.
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
Feynman famously recommended accepting the basic principles of quantum mechanics without trying to guess the machinery behind the law. One of the corollaries of the Uncertainty Principle is that the knowledge of probability amplitudes does…
We are grateful to all discussants of our re-visitation for their strong support in our enterprise and for their overall agreement with our perspective. Further discussions with them and other leading statisticians showed that the legacy of…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…
Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such…
The experimental setup of the self-referential quantum measurement, jovially known as the "quantum suicide" or the "quantum Russian roulette" is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the…
There have been a number of prior attempts to theoretically justify the effectiveness of the inverse document frequency (IDF). Those that take as their starting point Robertson and Sparck Jones's probabilistic model are based on strong or…
The purpose of this communication is twofold. First, it clarifies the origin of the power law obtained in the computer simulations presented in A.-L. Barabasi, Nature 435 207-211 (2005) as well as presenting a statistically more sound…