Related papers: Projected P\'olya Tree
The Yule-Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule-Simon…
Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and…
Modeling the diameter distribution of trees in forest stands is a common forestry task that supports key biologically and economically relevant management decisions. The choice of model used to represent the diameter distribution and how to…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
It is often of interest to combine available estimates of a similar quantity from multiple data sources. When the corresponding variances of each estimate are also available, a model should take into account the uncertainty of the estimates…
A flexible model is developed for multivariate generalized spherical distributions, i.e. ones with level sets that are star shaped. To work in dimension above 2 requires tools from computational geometry and multivariate numerical…
Optional P\'{o}lya Tree (OPT) is a flexible non-parametric Bayesian model for density estimation. Despite its merits, the computation for OPT inference is challenging. In this paper we present time complexity analysis for OPT inference and…
Objective prior distributions represent an important tool that allows one to have the advantages of using the Bayesian framework even when information about the parameters of a model is not available. The usual objective approaches work off…
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial…
We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
The need for statistical models of orientations arises in many applications in engineering and computer science. Orientational data appear as sets of angles, unit vectors, rotation matrices or quaternions. In the field of directional…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
This paper proposes new linear regression models to deal with overdispersed binomial datasets. These new models, called tilted beta binomial regression models, are defined from the tilted beta binomial distribution, proposed assuming that…
We introduce the bivariate unit-log-symmetric model based on the bivariate log-symmetric distribution (BLS) defined in [Vila et al., 2022, Bivariate Log-symmetric Models: Theoretical Properties and Parameter Estimation. Avaliable at…
Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…
Exploratory data analysis is crucial for developing and understanding classification models from high-dimensional datasets. We explore the utility of a new unsupervised tree ensemble called uncharted forest for visualizing class…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…
A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…