Related papers: Measures and integrals in conditional set theory
In clinical trials, inferences on clinical outcomes are often made conditional on specific selective processes. For instance, only when a treatment demonstrates a significant effect on the primary outcome, further analysis is conducted to…
Positive semi-definite kernels are used to induce pseudo-metrics, or ``distances'', between measures. We write these as an expected quadratic variation of, or expected inner product between, a random field and the difference of measures.…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
Measurement models (MMs) stand at the highest structural level of quantum measurement theory. MMs can be employed to construct instruments which stand at the next level. An instrument is thought of as an apparatus that is used to measure…
Quantization of a probability measure means representing it with a finite set of Dirac masses that approximates the input distribution well enough (in some metric space of probability measures). Various methods exists to do so, but the…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
In the absence of a satisfactory interpretation of quantum theory, physical law lacks physical basis. This paper reviews the orthodox, or Dirac-von Neumann interpretation, and makes explicit that Hilbert space describes propositions about…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
In this thesis, we consider the properties of measurements in quantum theory and other operational theories. After having introduced the framework of operational theories, we consider a communication scheme based on an experimental…
In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference…
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of…
It is often of interest to condition on a singular event given by a random variable, e.g. $\{Y=y\}$ for a continuous random variable $Y$. Conditional measures with respect to this event are usually derived as a special case of the…
We propose a realistic, spacetime interpretation of quantum theory in which reality constitutes a *single* history obeying a "law of motion" that makes definite, but incomplete, predictions about its behavior. We associate a "quantum…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…
In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…