Related papers: Open Problems in Algebraic Statistics
The use of historical estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use the uncertainty associated with historical estimates is rarely properly accounted for in the…
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have…
The problem of statistical inference for open chaotic systems measured with error is complicated by the interaction of the uncertainty introduced by chaos, and the various sources of random or external variation. Here a method of…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software…
We are pleased to present a Special Section on Statistics and Astronomy in this issue of the The Annals of Applied Statistics. Astronomy is an observational rather than experimental science; as a result, astronomical data sets both small…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex,…
Several authors, including the American Statistician (ASA), have noted the challenges facing statisticians when attacking large, complex, unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of…
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…
This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…
Given a statistical model, the maximum likelihood degree is the number of complex solutions to the likelihood equations for generic data. We consider discrete algebraic statistical models and study the solutions to the likelihood equations…
Flame graphs are a popular way of representing profiling data. In this paper we propose a possible mathematical definition of flame graphs. In doing so, we gain some interesting algebraic properties almost for free, which in turn allow us…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
The topics of Convexity and Concavity and Envelopes are central in Complex Analysis and extensively investigated. The aim of this paper is to find a possible counterpart in Algebraic Geometry. The article presents preliminary results on…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
Big data are data on a massive scale in terms of volume, intensity, and complexity that exceed the capacity of standard software tools. They present opportunities as well as challenges to statisticians. The role of computational…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…