arXiv subjects

H. Dennis Tolley

Publications and source records attributed to H. Dennis Tolley.

4 recordsLinked to original sources

arXiv2025

Expanding the Standard Diffusion Process to Specified Non-Gaussian Marginal Distributions

We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation to flexibly model skewness, heavy tails, and other non-Gaussian features often observed in real data. We rigorously define the process, establish key probabilistic properties, and construct a corresponding diffusion model via stochastic calculus, including proofs of existence and uniqueness. A simplified approximation is introduced and analyzed, with error bounds derived from asymptotic expansions. Simulations demonstrate that both the full and simplified models recover target marginals with high accuracy. Examples using the Student's t, asymmetric Laplace, and Exponentialized Generalized Beta of the Second Kind (EGB2) distributions illustrate the flexibility and tractability of the framework.

math.ST↗

arXiv2005

A New Efficient Algorithm for Construction of LLS Models

We present a new efficient algortithm for construction of linear latent structure (LLS) models. This algorithm reduces a problem of estimation of model parameters to a sequence of problems of linear algebra, which assures a low computational complexity and ability to handle on desktop computers data that involve up to thousands of variables.

math.PR↗

arXiv2005

Linear Latent Structure Analysis: Mixture Distribution Models with Linear Constraints

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the local independence assumption. LLS analysis explicitly considers a family of mixed distributions as a linear space and LLS models are obtained by imposing linear constraints on the mixing distribution. LLS models are identifiable under modest conditions and are consistently estimable. A remarkable feature of LLS analysis is the existence of a high-performance numerical algorithm, which reduces parameter estimation to a sequence of linear algebra problems. Preliminary simulation experiments with a prototype of the algorithm demonstrated a good quality of restoration of model parameters.

math.PR↗

arXiv2004

Grade of Membership Analysis: One Possible Approach to Foundations

Grade of membership (GoM) analysis was introduced in 1974 as a means of analyzing multivariate categorical data. Since then, it has been successfully applied to many problems. The primary goal of GoM analysis is to derive properties of individuals based on results of multivariate measurements; such properties are given in the form of the expectations of a hidden random variable (state of an individual) conditional on the result of observations. In this article, we present a new perspective for the GoM model, based on considering distribution laws of observed random variables as realizations of another random variable. It happens that some moments of this new random variable are directly estimable from observations. Our approach allows us to establish a number of important relations between estimable moments and values of interest, which, in turn, provides a basis for a new numerical procedure.

math.ST↗