Related papers: Modeling Random Directions in 2D Simplex Data
We propose models and algorithms for learning about random directions in simplex-valued data. The models are applied to the study of income level proportions and their changes over time in a geostatistical area. There are several notable…
In many applications, the dataset under investigation exhibits heterogeneous regimes that are more appropriately modeled using piece-wise linear models for each of the data segments separated by change-points. Although there have been much…
Survey data are widely used to study how income inequality, poverty, and welfare evolve over time. A common practice is to estimate the income distribution separately for each year, treating annual observations as independent…
This article proposes a bivariate Simplex distribution for modeling continuous outcomes constrained to the interval $(0,1)$, which can represent proportions, rates, or indices. We derive analytical expressions to calculate the dependence…
We propose a method for learning and sampling from probability distributions supported on the simplex. Our approach maps the open simplex to Euclidean space via smooth bijections, leveraging the Aitchison geometry to define the mappings,…
Circular data are data measured in angles and occur in a variety of scientific disciplines. Bayesian methods promise to allow for flexible analysis of circular data. Three existing MCMC methods (Gibbs, Metropolis-Hastings, and Rejection)…
Models for distributions of shapes contained within images can be widely used in biomedical applications ranging from tumor tracking for targeted radiation therapy to classifying cells in a blood sample. Our focus is on hierarchical…
An income distribution describes how an entity's total wealth is distributed amongst its population. A problem of interest to regional economics researchers is to understand the spatial homogeneity of income distributions among different…
Understanding and predicting human migration patterns is a central challenge in population dynamics research. Traditional physics-inspired gravity and radiation models represent migration flows as functions of attractiveness using…
This paper addresses challenges in flexibly modeling multimodal data that lie on constrained spaces. Such data are commonly found in spatial applications, such as climatology and criminology, where measurements are restricted to a…
We consider monotonic, multiple regression for a set of contiguous regions (lattice data). The regression functions permissibly vary between regions and exhibit geographical structure. We develop new Bayesian non-parametric methodology…
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
Recent research has led to the development of MCMC algorithms with likelihood-informed proposals when targeting posterior distributions supported on discrete state spaces. Our work is placed within this field and puts forward a new MCMC…
The need for regression models to predict circular values arises in many scientific fields. In this work we explore a family of expressive and interpretable distributions over circle-valued random functions related to Gaussian processes…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Cities are characterized by the coexistence of general aggregate patterns, along with many local variations. This poses challenges for analyses of urban phenomena, which tend to be either too aggregated or too local, depending on the…
Discrete data are abundant and often arise as counts or rounded data. These data commonly exhibit complex distributional features such as zero-inflation, over-/under-dispersion, boundedness, and heaping, which render many parametric models…
Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous,…