Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.                                                                    .

Download full-text PDF

Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6012604PMC
http://dx.doi.org/10.1093/bjps/axw013DOI Listing

Publication Analysis

Top Keywords

infinitesimal probabilities
8
non-archimedean probability
8
probabilities non-archimedean
4
probability functions
4
functions allow
4
allow combine
4
combine regularity
4
regularity perfect
4
perfect additivity
4
additivity discuss
4

Similar Publications

Statistical counting is the holographic observable to a statistical dynamics with finite states under independent and identically distributed sampling. Entropy provides the infinitesimal probability for an observed empirical frequency ν^ with respect to a probability prior p, when ν^≠p as N→∞. Following Callen's postulate and through Legendre-Fenchel transform, without help from mechanics, we show that an internal energy u emerges; it provides a linear representation of real-valued observables with full or partial information.

View Article and Find Full Text PDF

There are gaps in our understanding of sturgeon's response to anthropogenic sounds and the spatial scales at which they occur. We measured spatial displacement of Atlantic sturgeon in the St. Lawrence River at various distances of approaching merchant ships.

View Article and Find Full Text PDF

Finding patient zero in susceptible-infectious-susceptible epidemic processes.

Phys Rev E

October 2024

Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Article Synopsis
  • * The study examines backward equations in a specific SIS model to trace epidemics back to their origins in large networks, supporting sizes up to 1500.
  • * However, in a more complex Markovian SIS model, determining the epidemic source is challenging even with complete information, as accurately calculating the initial conditions involves significant numerical difficulties due to the nature of matrix exponential calculations.
View Article and Find Full Text PDF

Inference of a Susceptible-Infectious stochastic model.

Math Biosci Eng

September 2024

Departamento de Estadística e I.O., Universidad de Granada, Avenida de Fuente Nueva s/n, 18071, Granada, Spain.

We considered a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious (SI) epidemic model in which the transmission intensity function was time-dependent. Such a model was well suited to describe some classes of micro-parasitic infections in which individuals never acquired lasting immunity and over the course of the epidemic everyone eventually became infected. The stochastic process related to the deterministic model was transformable into a nonhomogeneous Wiener process so the probability distribution could be obtained.

View Article and Find Full Text PDF

Population differences in risk of disease are common, but the potential genetic basis for these differences is not well understood. A standard approach is to compare genetic risk across populations by testing for mean differences in polygenic scores, but existing studies that use this approach do not account for statistical noise in effect estimates (i.e.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!