Related papers: The probability distribution as a computational re…
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness…
Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…
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 develop a framework for certifying randomness from Bell-test trials based on directly estimating the probability of the measurement outcomes with adaptive test supermartingales. The number of trials need not be predetermined, and one can…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous…
The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…
Composite likelihood inference has gained much popularity thanks to its computational manageability and its theoretical properties. Unfortunately, performing composite likelihood ratio tests is inconvenient because of their awkward…
The classical theory for the meta-analysis of $p$-values is based on the assumption that if the overall null hypothesis is true, then all $p$-values used in a chosen combined test statistic are genuine, i.e., are observations from…
As animals interact with their environments, they must infer properties of their surroundings. Some animals, including humans, can represent uncertainty about those properties. But when, if ever, do they use probability distributions to…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…
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…
We propose a nonparametric sequential test that aims to address two practical problems pertinent to online randomized experiments: (i) how to do a hypothesis test for complex metrics; (ii) how to prevent type $1$ error inflation under…
This paper develops an empirical likelihood approach to testing for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by…
Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…
Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…
When the parameter of a map is chosen, at each iteration step, following a certain rule, is called Parametric Perturbation. If the parameters are drawn from a distribution, then this perturbation is called Random Parametric Perturbation.…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
When testing a statistical hypothesis, is it legitimate to deliberate on the basis of initial data about whether and how to collect further data? Game-theoretic probability's fundamental principle for testing by betting says yes, provided…