Related papers: Determinantal Probability: Basic Properties and Co…
For a broad class of point processes, including determinantal point processes, we construct associated marked and conditional ensembles, which allow to study a random configuration in the point process, based on information about a randomly…
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.
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
This paper deals with the problem of estimating the probability that one event was a cause of another in a given scenario. Using structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show…
These lectures introduce key concepts in probability and statistical inference at a level suitable for graduate students in particle physics. Our goal is to paint as vivid a picture as possible of the concepts covered.
This article is a discussion of some characteristic properties in connection with global models, particularly for the application of prediction, such as the approximation property, the interpolation property and the transmission property.
The study of associations and their causal explanations is a central research activity whose methodology varies tremendously across fields. Even within specialized subfields, comparisons across textbooks and journals reveals that the basics…
The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
In this chapter, we review a principled way of defining and measuring contextuality in systems with deterministic inputs and random outputs, recently proposed and developed in \citep{KujalaDzhafarovLarsson2015,DKL2015FooP}.
The main result presented in this article is that probability can fundamentally be characterized as a subset of conditional expectation induced by a plausible preorder on random quantities. This is justified by the fact that probability is…
The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…
We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
We discuss the use of the determinantal point process (DPP) as a prior for latent structure in biomedical applications, where inference often centers on the interpretation of latent features as biologically or clinically meaningful…