Related papers: A short note on extended probability theory
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
What do binary (or probabilistic) forecasting abilities have to do with overall performance? We map the difference between (univariate) binary predictions, bets and "beliefs" (expressed as a specific "event" will happen/will not happen) and…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
The interpretation of the squared norm as probability and the apparent stochastic nature of observation in quantum mechanics are derived from the strong law of large numbers and the algebraic properties of infinite sequences of simultaneous…
This is an introduction to some of the most probabilistic aspects of free probability theory.
Conceptual problems in quantum mechanics result from the specific quantum concept of reality and require, for their solution, including the observer's consciousness into quantum theory of measurements. Most naturally this is achieved in the…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
To what extent can our limited set of observations be used to pin down the specifics of a ``Theory of Everything''? In the limit where the links are arbitrarily tenuous, a ``Theory of Everything'' might become a ``Theory of Anything''. A…
It is suggested that probabilities need not apply at all to matter in the physical world, which may be entirely described by the amplitudes given by the quantum mechanical state. Instead, probabilities may apply only to conscious…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
Two works related to the concept of probability in the framework of the many-worlds interpretation are presented. The first deals with recent controversy in classical probability theory. Elga and D. Lewis argues that Sleeping Beauty should…
On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…
Here an extended form of the reaction rate probability integral, in the case of nonresonant thermonuclear reactions with the depleted tail and the right tail cut off, is considered. The reaction rate integral then can be looked upon as the…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.