Related papers: A Modern Retrospective on Probabilistic Numerics
Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Conventional statistics begins with a model, and assigns a likelihood of obtaining any particular set of data. The opposite approach, beginning with the data and assigning a likelihood to any particular model, is explored here for the case…
Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy…
On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain concept descriptions involving, e.g., "usually true" concept properties, generalized quantifiers, or exceptions. On the other…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on…
We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Tasks such as social network analysis, human behavior recognition, or modeling biochemical reactions, can be solved elegantly by using the probabilistic inference framework. However, standard probabilistic inference algorithms work at a…
Quantification is well known to be a major obstacle in the construction of a probabilistic network, especially when relying on human experts for this purpose. The construction of a qualitative probabilistic network has been proposed as an…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…
Quantum technology is seeing a remarkable explosion in interest due to a wave of successful commercial technology. As a wider array of engineers and scientists are needed, it is time we rethink quantum educational paradigms. Current…