Related papers: Projected P\'olya Tree
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
We develop a non-parametric Bayesian prior for a family of random probability measures by extending the Polya tree ($PT$) prior to a joint prior for a set of probability measures $G_1,\dots,G_n$, suitable for meta-analysis with event time…
The dynamics in a primary Spectral Submanifold (SSM) constructed over the slowest modes of a dynamical system provide an ideal reduced-order model for nearby trajectories. Modeling the dynamics of trajectories further away from the primary…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
In the density estimation model, the question of adaptive inference using P\'olya tree-type prior distributions is considered. A class of prior densities having a tree structure, called spike-and-slab P\'olya trees, is introduced. For this…
Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…
Ultrametric matrices are a class of covariance matrices that arise in latent tree models. As a parameter space in a statistical model, the set of ultrametric matrices is neither convex nor a smooth manifold. Focus in the literature has…
An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We proposed two new parsimonious…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
We are interested in comparing probability distributions defined on Riemannian manifold. The traditional approach to study a distribution relies on locating its mean point and finding the dispersion about that point. On a general manifold…
Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions.…
Two-molecule theory refers to a class of microscopic, self-consistent field theories for the radial distribution function in classical molecular liquids. The version examined here can be considered as one of the very few formally derived…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
The problem of comparing probability distributions is at the heart of many tasks in statistics and machine learning. Established comparison methods treat the standard setting that the distributions are supported in the same space. Recently,…
In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…
We introduce a family of multiscale stick-breaking mixture models for Bayesian nonparametric density estimation. The Bayesian nonparametric literature is dominated by single scale methods, exception made for P\`olya trees and allied…
The aim of this paper is to show a possibility to identify multivariate distribution by means of specially constructed one-dimensional random variable. We give some inequalities which may appear to helpful for a construction of multivariate…