Related papers: Discussion: On Arguments Concerning Statistical Pr…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
The probability that a number in many naturally occurring tables of numerical data has first significant digit $d$ is predicted by Benford's Law ${\rm Prob} (d) = \log_{10} (1 + {\displaystyle{1\over d}}), d = 1, 2 >..., 9$. Illustrations…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Discussion on "Brownian distance covariance" by G\'{a}bor J. Sz\'{e}kely and Maria L. Rizzo [arXiv:1010.0297]
Several authors have explained that the likelihood ratio measures the strength of the evidence represented by observations in statistical problems. This idea works fine when the goal is to evaluate the strength of the available evidence for…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
The Inner Model Hypothesis (IMH) and the Strong Inner Model Hypothesis (SIMH) were introduced by the first author in ``Internal consistency and the inner model hypothesis'', Bulletin of Symbolic Logic, December 2006. In this article we…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Cs\"{o}rg\H{o} and R\'{e}v\'{e}sz applied recently by Balan to…
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…
This note is a discussion of the article "Bayesian model selection based on proper scoring rules" by A.P. Dawid and M. Musio, to appear in Bayesian Analysis. While appreciating the concepts behind the use of proper scoring rules, including…
We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
Discussion of "Harold Jeffreys's Theory of Probability revisited," by Christian Robert, Nicolas Chopin, and Judith Rousseau, for Statistical Science [arXiv:0804.3173]
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We consider first the mixed discrete-continuous scheme of observation in multistate models; this is a classical pattern in epidemiology because very often clinical status is assessed at discrete visit times while times of death or other…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…