Related papers: Strictly Frequentist Imprecise Probability
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…
I show that frequentism, as an explanation of probability in classical statistical mechanics, can be extended in a natural way to a decoherent quantum history space, the analogue of a classical phase space. The result is a form of finite…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…
Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the…
We investigate determining the exact bounds of the frequencies of conjunctions based on frequent sets. Our scenario is an important special case of some general probabilistic logic problems that are known to be intractable. We show that…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
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…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
There has long been an impression that reliabilism implies externalism and that frequentist statistics, due to its reliabilist nature, is inherently externalist. I argue, however, that frequentist statistics can plausibly be understood as a…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
Possible parameter values in a random sampling model are shown by definition to have uniform base-rate prior probabilities. This allows a frequentist posterior probability distribution to be calculated for such possible parameter values…
The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection…
The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the…