Related papers: Mr. Bayes and the classics: a suggested interpreta…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical…
In the last months, due to the emergency of Covid-19, questions related to the fact of belonging or not to a particular class of individuals (`infected or not infected'), after being tagged as `positive' or `negative' by a test, have never…
Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…
This paper attributes the sudden emergence of mathematical probability and statistics in the second half of the seventeenth century to Calvin's Reformed theology. Calvin accommodated Epicurean chance with Stoic determinism and synthesised…
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…
This is a translation from Latin to Portuguese of Euler's 'Attempt at a theory of the friction of fluids'. According to the records, a treatise by Euler with the title 'Tentamen theoriae de frictione fluidorum' was presented to the St.…
Employing a generalized definition of Pratt (1964) and Arrow's (1965, 1971) probability premium, we introduce a new concept of attitude towards probability. We illustrate in a problem of risk sharing that whether attitude towards…
There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong…
A review of Jaynes' posthumous book "Probability Theory--The Logic of Science." I use scientific and personality elements gathered from other papers by Jaynes to help throw light on the origins of Jaynes' life quest.
Everett suggested that there is no such thing as wavefunction collapse. He hypothesized that for an idealized spin measurement the apparatus evolves into a superposition on the pointer basis of two apparatuses, each displaying one of the…
Deborah Mayo claims to have refuted Birnbaum's argument that the Likelihood Principle is a logical consequence of the Sufficiency and Conditionality Principles. However, this claim fails because her interpretation of the Conditionality…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
The probability axioms by R. T. Cox can be regarded as the modern foundations of Bayesian inference, the idea of assigning degrees of belief to logical propositions in a manner consistent with Boolean logic. In this work it is shown that…
This paper is written in honour of the centenary of Emmy Amalie Noether's famous article entitled Invariante Variationsprobleme. It firstly aims to give an exposition of what we believe to be the most significant and elegant issues…
The main object of this paper is to present some general concepts of Bayesian inference and more specifically the estimation of the hyperparameters in inverse problems. We consider a general linear situation where we are given some data…
Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…
In Jurek 1985 and 1988 the random integral representations conjecture was stated. It claims that (some) limit laws can be written as probability distributions of random integrals of the form $\int_{(a,b]}h(t)dY_{\nu}(r(t))$, for some…
During the MaxEnt 2002 workshop in Moscow, Idaho, Tony Vignaux asked again a few simple questions about using Maximum Entropy or Bayesian approaches for the famous Dice problems which have been analyzed many times through this workshop and…
Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe…