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What is the relationship between plausibility logic and the principle of maximum entropy? When does the principle give unreasonable or wrong results? When is it appropriate to use the rule `expectation = average'? Can plausibility logic…
In this paper we introduce the three main notions of probability used by physicists and discuss how these are to be used when invoking spacelike separated observers in a relativistic format. We discuss a standard EPRB experiment and…
In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using…
From scientific experiments to online A/B testing, the previously observed data often affects how future experiments are performed, which in turn affects which data will be collected. Such adaptivity introduces complex correlations between…
In order to build reliable and trustworthy NLP applications, models need to be both fair across different demographics and explainable. Usually these two objectives, fairness and explainability, are optimized and/or examined independently…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
When mathematical biology models are used to make quantitative predictions for clinical or industrial use, it is important that these predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models…
I show that Quantum Electrodynamics (QED) predicts a sort of uncertainty principle on the number of the "soft photons" that can be produced in coincidence with the particles that are observed in any EPR experiment. This result is argued to…
Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…
Categorization is necessary for many decision making tasks. However, the categorization process may interfere the decision making result and the law of total probability can be violated in some situations. To predict the interference effect…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
In recent years, the shortcomings of Bayesian posteriors as inferential devices have received increased attention. A popular strategy for fixing them has been to instead target a Gibbs measure based on losses that connect a parameter of…
Contrary to counterfactual definiteness quantum theory teaches us that measuring instruments are not passively reading predetermined values of physical observables. Counterfactual definiteness allows proving Bell inequalities. If the…
This paper aims to determine the fault tolerant quantum filter and fault detection equation for a class of open quantum systems coupled to a laser field that is subject to stochastic faults. In order to analyze this class of open quantum…
In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring…
Although many fairness criteria have been proposed to ensure that machine learning algorithms do not exhibit or amplify our existing social biases, these algorithms are trained on datasets that can themselves be statistically biased. In…
Bootstrap inference is a powerful tool for obtaining robust inference for quantiles and difference-in-quantiles estimators. The computationally intensive nature of bootstrap inference has made it infeasible in large-scale experiments. In…
Recent arguments, involving entangled systems shared by sets of Wigner's friend arrangements, allegedly show that the assumption that the experiments performed by the friends yield definite outcomes, is incompatible with quantum…