Related papers: Discussion of "Analysis of variance--why it is mor…
A brief introduction into Idempotent Mathematics and an idempotent version of Interval Analysis are presented. Some applications are discussed.
Some connections between operator theory and wavelet analysis: Since the mid eighties, it has become clear that key tools in wavelet analysis rely crucially on operator theory. While isolated variations of wavelets, and wavelet…
This special volume of Statistical Sciences presents some innovative, if not provocative, ideas in the area of reliability, or perhaps more appropriately named, integrated system assessment. In this age of exponential growth in science,…
Discussion of "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet [arXiv:1208.3378].
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
This chapter argues for more informed target metrics for the statistical processing of stylistic variation in text collections. Much as operationalised relevance proved a useful goal to strive for in information retrieval, research in…
Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…
Multivariate Analysis is an increasingly common tool in experimental high energy physics; however, many of the common approaches were borrowed from other fields. We clarify what the goal of a multivariate algorithm should be for the search…
The recent paper by Byrd & Lipton (2019), based on empirical observations, raises a major concern on the impact of importance weighting for the over-parameterized deep learning models. They observe that as long as the model can separate the…
Fundamental physical constants play important role in modern physics. Studies of their variation can open an interface to new physics. An overview of different approaches to a search for such variations is presented as well as possible…
A large deviation function mathematically characterizes the statistical property of atypical events. Recently, in non-equilibrium statistical mechanics, large deviation functions have been used to describe universal laws such as the…
This is a survey paper on several aspects of differential geometry for the last 30 years, especially in those areas related to non-linear analysis. It grew from a talk I gave on the occasion of seventieth anniversary of Chinese Mathematical…
Graphic statics is undergoing a renaissance, with computerized visual representation becoming both easier and more spectacular as time passes. While methods of the past are revived and tweaked, little emphasis has been placed on studying…
We generalize the random graph evolution process of Bohman, Frieze, and Wormald [T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms, 25, 432 (2004)]. Potential edges, sampled uniformly at random from the complete graph, are…
Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
This article discusses von Neumann's "proof" that hidden variable theories are impossible.
This article, produced as a result of the Symposium on Statistical Inference, is an introduction to the literature on the function of expertise, judgment, and choice in the practice of statistics and scientific research. In particular,…
In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be…