Related papers: The Foundation of Big Data: Experiments, Formulati…
Bigdata is a dataset of which size is beyond the ability of handling a valuable raw material that can be refined and distilled into valuable specific insights. Compact data is a method that optimizes the big dataset that gives best assets…
Perhaps one of the mostly hotly debated topics in recent years has been the question of "GIS and Big Data". Much of the discussion has been about the data: huge volumes of 2D and 3D spatial data and spatio-temporal data are now being…
One can argue that one of the main roles of the subject of statistics is to characterize what the evidence in collected data says about questions of scientific interest. There are two broad questions that we will refer to as the estimation…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical…
With the growing attention and investment in recent AI approaches such as large language models, the narrative that the larger the AI system the more valuable, powerful and interesting it is is increasingly seen as common sense. But what is…
The term Big Data has been coined to refer to the gargantuan bulk of data that cannot be dealt with by traditional data-handling techniques. Big Data is still a novel concept, and in the following literature, we intend to elaborate on it in…
The aim of this paper is to study the historical evolution of mathematical thinking and its spatial spreading. To do so, we have collected and integrated data from different online academic datasets. In its final stage, the database…
Big Data can mean different things to different people. The scale and challenges of Big Data are often described using three attributes, namely Volume, Velocity and Variety (3Vs), which only reflect some of the aspects of data. In this…
The "large p, small n" paradigm arises in microarray studies, where expression levels of thousands of genes are monitored for a small number of subjects. There has been an increasing demand for study of asymptotics for the various…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
Background: Big Data is a relatively new field of research and technology, and literature reports a wide variety of concepts labeled with Big Data. The maturity of a research field can be measured in the number of publications containing…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…
Big data research has attracted great attention in science, technology, industry and society. It is developing with the evolving scientific paradigm, the fourth industrial revolution, and the transformational innovation of technologies.…
For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
This article provides the role of big idea statisticians in future of Big Data Science. We describe the `United Statistical Algorithms' framework for comprehensive unification of traditional and novel statistical methods for modeling Small…
The community lacks theory-informed guidelines for building good data sets. We analyse theoretical directions relating to what aspects of the data matter and conclude that the intuitions derived from the existing literature are incorrect…