Related papers: Non-Archimedean Probability
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…
This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…
Some drawbacks of the formalism of Bayes Theorem can be avoided by the rMPE-Method, a modification of the cMPE-Method that permits (i): Adding probabilities in spite of non-linearity. (ii): Taking into account extensional evidence and…
We develop a new semantics for defeasible inference based on extended probability measures allowed to take infinitesimal values, on the interpretation of defaults as generalized conditional probability constraints and on a preferred-model…
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…
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
We show how to provide a structure of probability space to the set of execution traces on a non-confluent abstract rewrite system, by defining a variant of a Lebesgue measure on the space of traces. Then, we show how to use this probability…
We propose in this short note a prime numbers-based method for constructing probability measures on infinite-dimensional Banach spaces annihilating all finite-dimensional subspaces, supplementing the methods of construction of Gaussian…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
Nested sampling is a simulation method for approximating marginal likelihoods proposed by Skilling (2006). We establish that nested sampling has an approximation error that vanishes at the standard Monte Carlo rate and that this error is…
This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy…
In 1991 J.F. Aarnes introduced the concept of quasi-measures in a compact topological space $\Omega$ and established the connection between quasi-states on $C (\Omega)$ and quasi-measures in $\Omega$. This work solved the linearity problem…
We extend the notion of randomness (in the version introduced by Schnorr) to computable Probability Spaces and compare it to a dynamical notion of randomness: typicality. Roughly, a point is typical for some dynamic, if it follows the…
We formulate and verify a non-Archimedean analogue of Chase's lemma. Following the framework by K.\ Eda removing restriction of cardinality from analogy on direct product between countability and non-$\omega_1$-measurability, we extend the…
We introduce a new mathematical framework for the probabilistic description of an experiment upon a system of any type in terms of initial information representing this system. Based on the notions of an information state, an information…
Incomplete preferences provide the epistemic foundation for models of imprecise subjective probabilities and utilities that are used in robust Bayesian analysis and in theories of bounded rationality. This paper presents a simple…
We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained.
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…