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Partial orderings and measures of information for continuous univariate random variables with special roles of Gaussian and uniform distributions are discussed. The information measures and measures of non-Gaussianity including third and…

We explore a macroscopic, algebraic approach to rate independent hysteresis using semigroup theory. A macroscopic description of metastable states relevant to rate independent hysteresis is introduced using field history. The semigroup…

Racialized economic segregation, a key metric that simultaneously accounts for spatial, social and income polarization, has been linked to adverse health outcomes, including morbidity and mortality; however, statistical methods for…

In the literature on stochastic frontier models until the early 2000s, the joint consideration of spatial and temporal dimensions was often inadequately addressed, if not completely neglected. However, from an evolutionary economics…

A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…

This study introduces a general semiparametric clusterwise index distribution model to analyze how latent clusters affect the covariate-response relationships. By employing sufficient dimension reduction to account for the effects of…

We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…

We study the well-known sociological phenomenon of gang aggregation and territory formation through an interacting agent system defined on a lattice. We introduce a two-gang Hamiltonian model where agents have red or blue affiliation but…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…

The present communication addresses a set of observations, obeying both deterministic as well as statistical formal requirements, and serving to operate within the framework of the dynamical systems theory, with a certain emphasis placed on…

We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with,…

We apply stochastic process theory to the analysis of immigrant integration. Using a unique and detailed data set from Spain, we study the relationship between local immigrant density and two social and two economic immigration quantifiers…

Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations…

We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…

Scholars from diverse fields increasingly rely on high-frequency spatio-temporal data. Yet, causal inference with these data remains challenging due to spatial spillover and temporal carryover effects. We develop methods to estimate…

Transportation infrastructure, such as road or railroad networks, represent a fundamental component of our civilization. For sustainable planning and informed decision making, a thorough understanding of the long-term evolution of…

This paper presents a novel quantitative approach for comparative economic studies, addressing limitations in current classification methods. Conventional approaches in comparative economics often rely on ad hoc and categorical…

The statistical modeling of multivariate count data observed on a space-time lattice has generally focused on using a hierarchical modeling approach where space-time correlation structure is placed on a continuous, latent, process. The…

In this paper we bring to bear some new tools from statistical learning on the analysis of roll call data. We present a new data-driven model for roll call voting that is geometric in nature. We construct the model by adapting the…