Related papers: How much randomness is needed for statistics?
The meaning of randomization tests has become obscure in statistics education and practice over the last century. This article makes a fresh attempt at rectifying this core concept of statistics. A new term -- "quasi-randomization test" --…
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…
Classical countably additive real-valued probabilities come at a philosophical cost: in many infinite situations, they assign the same probability value -- namely, zero -- to cases that are impossible as well as to cases that are possible.…
Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…
The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Randomness plays a central rol in the quantum mechanical description of our interactions. We review the relationship between the violation of Bell inequalities, non signaling and randomness. We discuss the challenge in defining a random…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
The notion of Schnorr randomness refers to computable reals or computable functions. We propose a version of Schnorr randomness for subcomputable classes and characterize it in different ways: by Martin L\"of tests, martingales or measure…
Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical…
Nies and Scholz introduced the notion of a state to describe an infinite sequence of qubits and defined quantum-Martin-Lof randomness for states, analogously to the well known concept of Martin-L\"of randomness for elements of Cantor space…
Randomization is a common technique used in clinical trials to eliminate potential bias and confounders in a patient population. Equal allocation to treatment groups is the standard due to its optimal efficiency in many cases. However, in…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in…
The classic model of computable randomness considers martingales that take real or rational values. Recent work by Bienvenu et al. (2012) and Teutsch (2014) shows that fundamental features of the classic model change when the martingales…
We respond to Aronow et al. (2025)'s paper arguing that randomized controlled trials (RCTs) are "enough," while nonparametric identification in observational studies is not. We agree with their position with respect to experimental versus…