Related papers: Non-Archimedean Probability
Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum…
Given the complexity of modern cosmological parameter inference where we are faced with non-Gaussian data and noise, correlated systematics and multi-probe correlated data sets, the Approximate Bayesian Computation (ABC) method is a…
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of {\em Colombeau type} in the sense that it contains a copy of the space of Schwartz…
An attempt of a new kind of complexity anthropology is considered.
Qualitative and infinitesimal probability schemes are consistent with the axioms of probability theory, but avoid the need for precise numerical probabilities. Using qualitative probabilities could substantially reduce the effort for…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption…
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that…
This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
We present a categorical viewpoint of probability measures by showing that a probability measure can be viewed as a weakly averaging affine measurable functional taking values in the unit interval which preserves limits. The probability…
We formulate and explore two basic axiomatic systems of typefree subjective probability. One of them explicates a notion of finitely additive probability. The other explicates a concept of infinitely additive probability. It is argued that…
Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can…
This is a chapter for the forthcoming New Handbook of Mathematical Psychology, to be published by Cambridge University Press. A systematic theory of random variables and joint distributions under varying conditions is presented. This is a…
Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…
Currently, there is a gap between the tools used by probability theorists and those used in formal reasoning about probabilistic programs. On the one hand, a probability theorist decomposes probabilistic state along the simple and natural…
Integrating non-probability samples into finite-population inference typically requires modeling unknown selection probabilities under a missing-at-random (MAR) assumption that is difficult to verify. We propose a design-based alternative…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…