Related papers: Probability and Measurement Uncertainty in Physics…
In classical physics, probabilistic or statistical knowledge has been always related to ignorance or inaccurate subjective knowledge about an actual state of affairs. This idea has been extended to quantum mechanics through a completely…
Bayes [Philos. Trans. R. Soc. Lond. 53 (1763) 370--418; 54 296--325] introduced the observed likelihood function to statistical inference and provided a weight function to calibrate the parameter; he also introduced a confidence…
In the Bayesian approach to quantum mechanics, probabilities--and thus quantum states--represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept…
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
The forensic science community has increasingly sought quantitative methods for conveying the weight of evidence. Experts from many forensic laboratories summarize their findings in terms of a likelihood ratio. Several proponents of this…
In recent times, neural networks have become a powerful tool for the analysis of complex and abstract data models. However, their introduction intrinsically increases our uncertainty about which features of the analysis are model-related…
Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…
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…
These three lectures provide an introduction to the main concepts of statistical data analysis useful for precision measurements and searches for new signals in High Energy Physics. The frequentist and Bayesian approaches to probability…
Probabilities in eternal inflation are traditionally defined as limiting frequency distributions, but a unique and unambiguous probability measure remains elusive. In this paper, we present a different approach, based on Bayesian reasoning.…
After making some general remarks, I consider two examples that illustrate the use of Bayesian Probability Theory. The first is a simple one, the physicist's favorite "toy," that provides a forum for a discussion of the key conceptual issue…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
Starting with the neo-Bayesian revival of the 1950s, many statisticians argued that it was inappropriate to use Bayesian methods, and in particular subjective Bayesian methods in governmental and public policy settings because of their…
This is a writeup of lectures on "statistics" that have evolved from the initial version for the 2009 Hadron Collider Physics Summer School at CERN to versions for other venues and, most recently, for the African School of Fundamental…
In the quantum Bayesian (or QBist) conception of quantum theory, "quantum measurement" is understood not as a comparison of something pre-existent with a standard, but instead indicative of the creation of something new in the universe:…
Modern statistical software and machine learning libraries are enabling semi-automated statistical inference. Within this context, it appears easier and easier to try and fit many models to the data at hand, reversing thereby the Fisherian…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
In this paper, we introduce for the first time the notions of neutrosophic measure and neutrosophic integral, and we develop the 1995 notion of neutrosophic probability. We present many practical examples. It is possible to define the…
The problem of assigning probabilities when little is known is analized in the case where the quanities of interest are physical observables, i.e. can be measured and their values expressed by numbers. It is pointed out that the assignment…