Related papers: The Preferred System of Reference Reloaded
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…
Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for…
The aim of this paper is to argue that the "preferred basis problem" is not a real problem in measurement. We will show that, given an apparatus, among the infinite corrrelations that can be established in the final state by means of a…
We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing…
As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
Case-oriented physics education research - which seeks to refine and develop theory by linking that theory to cases - incorporates distinct practices for selecting data for analysis, generalizing results, and making causal claims.…
We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…
The issue of confidence factors in Knowledge Based Systems has become increasingly important and Dempster-Shafer (DS) theory has become increasingly popular as a basis for these factors. This paper discusses the need for an empirical…
Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum…
Dempster/Shafer (D/S) theory has been advocated as a way of representing incompleteness of evidence in a system's knowledge base. Methods now exist for propagating beliefs through chains of inference. This paper discusses how rules with…
This article explores the following methodological principle for theory construction in physics: if an ontological theory predicts two scenarios that are ontologically distinct but empirically indiscernible, then this theory should be…
The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
In consistent history quantum theory, a description of the time development of a quantum system requires choosing a framework or consistent family, and then calculating probabilities for the different histories which it contains. It is…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
This is a report about the use and misuse of citation data in the assessment of scientific research. The idea that research assessment must be done using ``simple and objective'' methods is increasingly prevalent today. The ``simple and…
Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation…
A very simple example demonstrates that Fisher's application of the conditionality principle to regression ("fixed-$x$ regression"), endorsed by Sprott and many other followers, makes prediction impossible in the context of statistical…