Intuitive Probability on Finite Sets

Posterior Probability on Finite Set1

In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior ...

A structural model of intuitive probability

Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This paper proposes a new model of rarity and randomness assessment, designed to be cognitively plausible. Intuitive randomness is defined as a function of structur...

Notes on counting finite sets

Semigroup Kernels on Finite Sets

Complex objects can often be conveniently represented by finite sets of simpler components, such as images by sets of patches or texts by bags of words. We study the class of positive definite (p.d.) kernels for two such objects that can be expressed as a function of the merger of their respective sets of components. We prove a general integral representation of such kernels and present two par...

Infinite games on finite sets

We study a family of infinite games with imperfect information introduced by B. Model for two players that alternately remove and add points to a finite set. We investigate the existence of imperfect information strategies for the remover for different ambient cardinalities. We also study a variant of a game of D. Gale introduced by Scheepers and Weiss.