24 papers · ranked by Valyu relevance
Luai Al-Labadi, Zeynep Baskurt, Michael Evans
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a prior, checking the prior for bias, checking for prior-data conflict and…
David J. Hand
The nature of statistics has changed over time. It was originally concerned with descriptive ‘matters of state’-with summarizing population numbers, economic strength and social conditions. But during the course of the twentieth century its aim broadened to include inference-how to use data to shed light on underlying…
Oscar Sheynin
- 2. Theory of Probability, NNo. 1 214 - 2.1.Origin and Aims, NNo. 1 44 - 2.2. Main Notions, NNo. 45 99 - 2.3. Logical Difficulties and Mistaken Opinions, NNo. 100 –114 - 2.4. Moral Expectation, NNo. 115 121 - 2.5. Law of Large Numbers and Central Limit Theorem, NNo. 122 – 181 - 2.6. The Axiomatic Approach and the…
Lakshman Mahto
Till now, we have described and computed the exact probability of events based on known probability mass functions (PMFs)/probability density functions (PDFs) and the implementation of its summation/integration. Also of importance were the methods to determine the moments/statistic/parameters of these random variables.…
Roger W. Hoerl, Ronald D. Snee
Several authors, including the American Statistical Association (ASA), have noted the challenges facing statisticians when attacking large, complex and unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of selecting the one "correct" statistical method for such problems…
Paul Vos
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We show how measure-theoretic probability provides a framework for modeling…
Peter Harremoës, Raúl Alcaraz, Leandro Pardo, Luca Faes + 1 more
'Boris Ryabko'] Rate distortion theory was developed for optimizing lossy compression of data, but it also has applications in statistics. In this paper, we illustrate how rate distortion theory can be used to analyze various datasets. The analysis involves testing, identification of outliers, choice of compression…
Erkan Buzbas, Berna Devezer
Motivated by the recent putative reproducibility crisis, we discuss the relationship between replicability of scientific studies, reproducibility of results obtained in these replications, and the philosophy of statistics. Our approach focuses on challenges in specifying scientific studies for scientific inference via…
Zhiyi Zhang
During the last few decades, research activity in modeling the properties of random systems via entropies has grown noticeably across a wide spectrum of fields. From the early days of statistical thermodynamics, the concept of entropy has evolved into many practically useful tools. For example, in modern data science…
Clément Gain, Bénédicte Rhoné, Philippe Cubry, Israfel Salazar + 4 more
Genomic offset statistics predict the maladaptation of populations to rapid habitat alteration based on association of genotypes with environmental variation. Despite substantial evidence for empirical validity, genomic offset statistics have well-identified limitations, and lack a theory that would facilitate…
E. Seneta
The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob Bernoulli's Theorem: 1. As limit theorem (sample size n → ∞), and: 2. Determining…
Peter Harremoës, Sebastian Deffner
Since the seminal work of Kolmogorov, probability theory has been based on measure theory, where the central components are so-called probability measures, defined as measures with total mass equal to 1. In Kolmogorov’s theory, a probability measure is used to model an experiment with a single outcome that will belong…
Paolo Rocchi, Leonida Gianfagna
Classical statistics and Bayesian statistics refer to the frequentist and subjective theories of probability respectively. Von Mises and De Finetti, who authored those conceptualizations, provide interpretations of the probability that appear incompatible. This discrepancy raises ample debates and the foundations of…
Denes Szucs, John PA Ioannidis
Null hypothesis significance testing (NHST) has several shortcomings that are likely contributing factors behind the widely debated replication crisis of psychology, cognitive neuroscience and biomedical science in general. We review these shortcomings and suggest that, after about 60 years of negative experience, NHST…
Dirk Ostwald, Sebastian Schneider, Rasmus Bruckner, Lilla Horvath
Recent discussions on the reproducibility of task-related functional magnetic resonance imaging (fMRI) studies have emphasized the importance of power and sample size calculations in fMRI study planning. In general, statistical power and sample size calculations are dependent on the statistical inference framework that…
Christian G. Habeck, Adam M. Brickman
Our ability to draw conclusions from experiments often relies on the application of inferential statistics, such as those included within the general-linear-modeling framework. The purpose of this commentary is to direct attention a common fallacy that can be observed in paper reviews and professional exchanges in the…
Authors not listed
We developed OpenStats, a user-friendly web application that brings the power of the R language to researchers through a high-level interface and broad support for statistical methods such as t-tests and ANOVA. OpenStats was integrated into our electronic lab notebook Chemotion ELN via its third-party API, enabling…
Dínis Pestana, Rui Santos
The liberal struggles of the 19th century forced many illustrious Portuguese to exile, particularly in the United Kingdom and/or France. Some of these new estrangeirados, namely Solano Constˆancio, Alexandre Herculano, and Oliveira Marreca, were important agents for the dissemination of Statistics in Portugal. The…
John Levi Martin
There has always been a close relation between thermodynamic theory and sociological theory, although they repeatedly part company and later rejoin. I discuss some of the most important ways in which the two have been in contact, focusing on the potential passage from theories of energy to theories of information and…
Benedikt Axel Brandes
In this contribution, I derive the transition state theory through a probabilistic model embedded in statistical mechanics. This leads to a formulation equivalent to the Eyring equation proving that the transfer coefficient must always be one. This derivation proves that the transition between two systems that are…
Authors not listed
Gibbs’ paradox—the apparent discontinuity in mixing entropy for gases of varying similarity and the seeming reversibility of mixing-separation cycles—has resisted fully satisfactory resolution for 150 years. We present a solution based on categorical state theory, which posits that physical con f igurations are…
Danilo Bzdok, Denis Engemann, Olivier Grisel, Gaël Varoquaux + 1 more
In the 20^th^ century many advances in biological knowledge and evidence-based medicine were supported by p-values and accompanying methods. In the beginning 21^st^ century, ambitions towards precision medicine put a premium on detailed predictions for single individuals. The shift causes tension between traditional…
Authors not listed
Quantitative Structure-Activity Relationship (QSAR) modeling is a pillar of computational drug discovery. However, standard machine learning (ML) models are often confounded by the high-dimensional and intensely correlated nature of molecular descriptors. A model may identify a "bulk" property (e.g., molecular weight)…
Amelia Carolina Sparavigna
Previous studies (Sparavigna, 2023) have demonstrated the Tsallis q-Gaussian functions suitable for the analysis of Raman spectra. Here we consider two asymmetric forms of them, with the aim of further improving the fitting of Raman spectra. The first asymmetric form, that we are here proposing for the first time, is a…