Related papers: Experiments with the Census
Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
The density ratio of two probability distributions is one of the fundamental tools in mathematical and computational statistics and machine learning, and it has a variety of known applications. Therefore, density ratio estimation from…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…
In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the…
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
We present a new paradigm for creating random features to approximate bi-variate functions (in particular, kernels) defined on general manifolds. This new mechanism of Manifold Random Features (MRFs) leverages discretization of the manifold…
In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
A new approach to estimate population size based on a stratified link-tracing sampling design is presented. The method extends on the Frank and Snijders (1994) approach by allowing for heterogeneity in the initial sample selection…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Parametric inference posits a statistical model that is a specified family of probability distributions. Restricted inference, e.g., restricted likelihood ratio testing, attempts to exploit the structure of a statistical submodel that is a…
We define a new stochastic process on general simplicial complexes which allows to study their spectral and homological properties. Some results for random walks on graphs are shown to hold in this general setting. As an application, the…
Population behaviours, such as voting and vaccination, depend on social networks. Social networks can differ depending on behaviour type and are typically hidden. However, we do often have large-scale behavioural data, albeit only snapshots…
There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…
This paper provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is…
We study the multifaceted question of how to sample approval elections in a meaningful way. Our analysis aims to discern the properties of various statistical cultures (both established and new ones). Based on the map-of-elections framework…