相关论文: Bayesian Fitting of Dirichlet Type I and II Distri…

Many scientific and industrial processes produce data that is best analysed as vectors of relative values, often called compositions or proportions. The Dirichlet distribution is a natural distribution to use for composition or proportion…

The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…

When modeling the distribution of a set of data by a mixture of Gaussians, there are two possibilities: i) the classical one is using a set of parameters which are the proportions, the means and the variances; ii) the second is to consider…

For an observed response that is composed by a set - or vector - of positive values that sum up to 1, the Dirichlet distribution (Bol'shev, 2018) is a helpful mathematical construction for the quantification of the data-generating mechanics…

There exist several endeavors proposing a new family of extended distributions using the beta-generating technique. This is a well-known mechanism in developing flexible distributions, by embedding the cumulative distribution function (cdf)…

Statistical inference in high-dimensional settings is challenging when standard unregularized methods are employed. In this work, we focus on the case of multiple correlated proportions for which we develop a Bayesian inference framework.…

Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., multivariate data in the form of probability vectors that contain relative proportions. In particular,…

Bayesian A/B testing investigates metric changes using the joint posterior distribution of two (or more) experimentally-derived datasets. The construction of said joint posterior is often a time-consuming process requiring specialized…

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…

Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning. DPMMs are generally used in clustering problems where the number of clusters is not known…

In the present paper new light is shed on the non-central extensions of the Dirichlet distribution. Due to several probabilistic and inferential properties and to the easiness of parameter interpretation, the Dirichlet distribution proves…

Bayesian graphical modeling provides an appealing way to obtain uncertainty estimates when inferring network structures, and much recent progress has been made for Gaussian models. These models have been used extensively in applications to…

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new…

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…

The Bayesian approach to inference stands out for naturally allowing borrowing information across heterogeneous populations, with different samples possibly sharing the same distribution. A popular Bayesian nonparametric model for…

Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…

An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…

In binary-transaction data-mining, traditional frequent itemset mining often produces results which are not straightforward to interpret. To overcome this problem, probability models are often used to produce more compact and conclusive…