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Mathematical theory of Bayesian statistics for unknown information source [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 In statistical inference, uncertainty is unknown and all models are wrong. That is to say, a person who makes a statistical model and a prior distribution is simultaneously aware that both are fictional candidates. To study such cases, statistical measures have been constructed, such as cross validation, information criteria and marginal likelihood ...
Sumio Watanabe
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Probability Theory and Mathematical Statistics [PDF]
, 1988 Masanao Ozawa, Prokhorov, Jurii
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Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect [PDF]
Mathematics, 2022 The theory of the beam splitter (BS) in quantum optics is well developed and based on fairly simple mathematical and physical foundations. This theory has been developed for any type of BS and is based on the constancy of the reflection coefficients R ...
D. Makarov
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Diagnostics, 2022 The practice of medical decision making is changing rapidly with the development of innovative computing technologies. The growing interest of data analysis with improvements in big data computer processing methods raises the question of whether machine ...
S. K. Dhillon +4 more
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Mathematics for Machine Learning
Journal of Mathematical Sciences & Computational Mathematics, 2020 Machine learning is a way to study the algorithm and statistical model that is used by computer to perform a specific task through pattern and deduction [1].
Gaurav Kumar +4 more
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Theory of cold atoms: Bose–Einstein statistics [PDF]
, 2016 This tutorial is the continuation of the previous tutorial part, published in (2013 Laser Phys. 23 062001), where the basic mathematical techniques required for an accurate description of cold atoms for both types of quantum statistics are expounded.
V. Yukalov
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The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line [PDF]
Annals of Probability, 2016 We prove that if $\omega$ is uniformly distributed on $[0,1]$, then as $T\to\infty$, $t\mapsto \zeta(i\omega T+it+1/2)$ converges to a non-trivial random generalized function, which in turn is identified as a product of a very well behaved random smooth ...
E. Saksman, Christian Webb
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An introduction to statistical learning with applications in R
Statistical Theory and Related Fields, 2021 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics.
Fariha Sohil +2 more
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Mathematical Statistics with Applications in R, 2018 . The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics.
Robert André
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The mathematics of Benford’s law: a primer [PDF]
Statistical Methods & Applications, 2019 This article provides a concise overview of the main mathematical theory of Benford’s law in a form accessible to scientists and students who have had first courses in calculus and probability.
A. Berger, T. Hill
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