Related papers: Systematic Errors: facts and fictions
Credit allocation in the mainstream bibliometrics is fundamentally flawed and the popular indicators have been misleading science for decades. Originally a simple technical mistake has become an integral part of our culture and is very…
Multiple testing problems arise naturally in scientific studies because of the need to capture or convey more information with more variables. The literature is enormous, but the emphasis is primarily methodological, providing numerous…
Previous research on spreadsheet risks has predominantly focussed on errors inadvertently introduced by spreadsheet writers i.e. it focussed on the end-user aspects of spreadsheet development. When analyzing a faulty spreadsheet, one might…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
Machine learning algorithms tend to create more accurate models with the availability of large datasets. In some cases, highly accurate models can hide the presence of bias in the data. There are several studies published that tackle the…
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
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…
This note presents a few observations on the nonlocal nature of quantum errors and the expected performance of the recently proposed quantum error-correction codes that are based on the assumption that the errors are either bit-flip or…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
We analyze the fate of dynamical systems that consist of two kind of processes. The first type is supposed to perform a certain function by processing information at a required high accuracy, which is, however, limited to less than 100…
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
Thanks to the enormous flexibility they provide, spreadsheets are considered a priceless blessing by many end-users. Many spreadsheets, however, contain errors which can lead to severe consequences in some cases. To manage these risks,…
After a review of linear imperfections and their causes, we discuss how to model them, the diagnostic equipment needed to monitor them, and the correction algorithms to fix the problem they cause. We first address linear systems - beam…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
Safety and assurance standards often rely on the principle that requirements errors can be minimised by expressing the requirements more formally. Although numerous case studies have shown that the act of formalising previously informal…
Instances of Artificial Intelligence (AI) systems failing to deliver consistent, satisfactory performance are legion. We investigate why AI failures occur. We address only a narrow subset of the broader field of AI Safety. We focus on AI…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
Bad statistics make research papers unreproducible and misleading. For the most part, the reasons for such misusage of numerical data have been found and addressed years ago by experts and proper practical solutions have been presented…
This article discusses a number of incorrect statements appearing in textbooks on data analysis, machine learning, or computational methods; the common theme in all these cases is the relevance and application of statistics to the study of…