Related papers: Natural density and probability, constructively
This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
We consider the use of the energy density for describing a localization of relativistic particles. This method is consistent with the causality requirements. The related positive operator valued measure is presented. The probability…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Measurements of a weighted energy density average taken in the vacuum state of a conformal field theory in $1+1$ dimensions are randomly distributed with vanishing expectation value. The probability distribution is computed in closed form…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
This paper is motivated by the questions of how to give the concept of probability an adequate real-world meaning, and how to explain a certain type of phenomenon that can be found, for instance, in Ellsberg's paradox. It attempts to answer…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
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…
We define a general class of models representing natural selection between two alleles. The population size and spatial structure are arbitrary, but fixed. Genetics can be haploid, diploid, or otherwise; reproduction can be asexual or…