Related papers: How much randomness is needed for statistics?
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a {\em stochastic maximal inequality} derived by using the formula for…
Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these…
A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary…
Replication studies estimate the replicability rate of scientific results by aggregating binary verdicts of experiments. Exact replications are rarely attainable, so most replication sequences are non-exact. Experiments differ in ways that…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
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…
A concept of randomness for infinite time register machines (ITRMs), resembling Martin-L\"of-randomness, is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies…
A cornerstone of human statistical learning is the ability to extract temporal regularities / patterns from random sequences. Here we present a method of computing pattern time statistics with generating functions for first-order Markov…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
Randomization procedures are used in legal and statistical applications, aiming to shield important decisions from spurious influences. This article gives an intuitive introduction to randomization and examines some intended consequences of…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
Since their appearance in the 1950s, computational models capable of performing probabilistic choices have received wide attention and are nowadays pervasive in almost every areas of computer science. Their development was also inextricably…
Traditional statistical inference considers relatively small data sets and the corresponding theoretical analysis focuses on the asymptotic behavior of a statistical estimator when the number of samples approaches infinity. However, many…
Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…