Related papers: Hilbert's Sixth Problem: Descriptive Statistics as…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
In the course of computer modeling of the most probable stationary macrostates of non-ergodic closed systems, a forecast was obtained about the existence of limits of applicability of the basic axiomatic postulate of statistical physics,…
After a brief flirtation with logicism in 1917-1920, David Hilbert proposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays and Wilhelm Ackermann, throughout the…
Statistical science (as opposed to mathematical statistics) involves far more than probability theory, for it requires realistic causal models of data generators - even for purely descriptive goals. Statistical decision theory requires more…
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…
This monograph is an account of the theory of fallible probability and of the dynamics of degrees of belief. It discusses the first order subjective theory in which first order degrees of belief are expressed by subjective probabilities and…
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space,…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
A number of well-known theorems, such as Cox's theorem and de Finetti's theorem. prove that any model of reasoning with uncertain information that satisfies specified conditions of "rationality" must satisfy the axioms of probability…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We shall argue in this paper that a central piece of modern physics does not really belong to physics at all but to elementary probability theory. Given a joint probability distribution J on a set of random variables containing x and y,…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…
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 purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
Why are the laws of physics formulated in terms of complex Hilbert spaces? Are there natural and consistent modifications of quantum theory that could be tested experimentally? This book chapter gives a self-contained and accessible summary…