Related papers: Statistical methods: Basic concepts, interpretatio…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex,…
We provide an analytical argument for understanding the likely nature of parameter shifts between those coming from an analysis of a dataset and from a subset of that dataset, assuming differences are down to noise and any intrinsic…
In contrast to its common definition and calculation, interpretation of p-values diverges among statisticians. Since p-value is the basis of various methodologies, this divergence has led to a variety of test methodologies and evaluations…
Inferring causal effects of treatments is a central goal in many disciplines. The potential outcomes framework is a main statistical approach to causal inference, in which a causal effect is defined as a comparison of the potential outcomes…
Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because…
Statistical samples, in order to be representative, have to be drawn from a population in a random and unbiased way. Nevertheless, it is common practice in the field of model-based diagnosis to make estimations from (biased) best-first…
Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined…
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
The use of statistical software in academia and enterprises has been evolving over the last years. More often than not, students, professors, workers, and users, in general, have all had, at some point, exposure to statistical software.…
At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using…
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract…
We provide a conceptual map to navigate causal analysis problems. Focusing on the case of discrete random variables, we consider the case of causal effect estimation from observational data. The presented approaches apply also to continuous…
Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor…
Categorical data are common in educational and social science research; however, methods for its analysis are generally not covered in introductory statistics courses. This chapter overviews fundamental concepts and methods in categorical…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to…