Related papers: Sets and Probability
Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
In many situations, the decision maker observes items in sequence and needs to determine whether or not to retain a particular item immediately after it is observed. Any decision rule creates a set of items that are selected. We consider…
A new method is developed to represent probabilistic relations on multiple random events. Where previously knowledge bases containing probabilistic rules were used for this purpose, here a probability distribution over the relations is…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a…
We introduce the notion of a random mean generated by a random variable and give a construction of its expected value. We derive some sufficient conditions under which strong laws of large numbers and some limit theorems hold for random…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…
In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
We shall show in this paper that there are experiments which are Bernoulli trials with success probability p > 0.5, and which have the curious feature that it is possible to correctly predict the outcome with probability > p.
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
Let $R$ be a finite ring and $r \in R$. The aim of this paper is to study the probability that the commutator of a randomly chosen pair of elements of $R$ equals $r$.
The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying probability space. We study various notions…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…