Related papers: Basic univariate and bivariate statistics for symb…
A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we…
Prompted by modern technologies in data acquisition, the statistical analysis of spatially distributed function-valued quantities has attracted a lot of attention in recent years. In particular, combinations of functional variables and…
The method of surrogate data provides a framework for testing observed data against a hierarchy of alternative hypotheses. The aim of applying this method is to exclude the possibility that the data are consistent with simple linear…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
We present a symbolic representation for the poly-Bernoulli numbers. This allows us to prove several new iterated integral representations for the poly-Bernoulli numbers, including an integral transform of the Bernoulli-Barnes numbers. We…
A new symbol theory for pseudodifferential operators in the complex analytic category is given. This theory provides a cohomological foundation of symbolic calculus.
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
Some new aspects of axially symmetric spacetimes are discussed. These results open the door for future interplay between analytical and numerical studies. The new developments are based on the role of the total mass in axial symmetry.…
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
Many learning algorithms require categorical data to be transformed into real vectors before it can be used as input. Often, categorical variables are encoded as one-hot (or dummy) vectors. However, this mode of representation can be…
Explainability is an essential reason limiting the application of neural networks in many vital fields. Although neuro-symbolic AI hopes to enhance the overall explainability by leveraging the transparency of symbolic learning, the results…
We introduce a few of the key ideas of statistical analysis using two real-world examples to illustrate how these ideas are used in practice.
Motivated by a recent series of diametrically opposed articles on the relative value of statistical methods for the analysis of path diagrams in the social sciences, we discuss from a primarily theoretical perspective selected fundamental…
Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while…
It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
We point out that the traditional notion of test statistic is too narrow, and we propose a natural generalization that is arguably maximal. The study is restricted to simple statistical hypotheses.
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.