This paper reviews algorithmic information theory, which is an attempt to apply information-
theoretic and probabilistic ideas to recursive function theory. Typical concerns in this …

In this monograph, I introduce the basic concepts of Online Learning through a modern view
of Online Convex Optimization. Here, online learning refers to the framework of regret …

The most widely used concept of statistical inference—the p-value—is too complicated for
effective communication to a wide audience. This paper introduces a simpler way of …

Ming Li Paul Vitányi Fourth Edition Page 1 An Introduction to Kolmogorov Complexity and Its
Applications Ming Li Paul Vitányi Fourth Edition Texts in Computer Science Page 2 Texts in …

E-values: Calibration, combination and applications Page 1 The Annals of Statistics 2021, Vol.
49, No. 3, 1736–1754 https://doi.org/10.1214/20-AOS2020 © Institute of Mathematical Statistics …

Vladimir Vovk Alexander Gammerman Glenn Shafer Second Edition Page 1 Vladimir Vovk
Alexander Gammerman Glenn Shafer Algorithmic Learning in a Random World Second …

CONTENTS 1. Introduction PART I. QUASI-MONTE CARLO METHODS 2. Quasi-Monte
Carlo integration 3. Quasi-random points 4. Good lattice points 5. Application of diophantine …

Abstract CONTENTS Introduction Chapter I. The main notions and facts § 1.1. The notion of
randomness depends on a given probability distribution § 1.2. Three faces of randomness …

The article further develops Kolmogorov's algorithmic complexity theory. The definition of
randomness is modified to satisfy strong invariance properties (conservation inequalities) …

We present a new theory of hypothesis testing. The main concept is the s-value, a notion of
evidence which, unlike p-values, allows for effortlessly combining evidence from several …