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We study the degree distribution of a randomly chosen vertex in a duplication--divergence graph, under a variety of different generalizations of the basic model of Bhan, Galas and Dewey (2002) and V\'azquez, Flammini, Maritan and Vespignani…
We introduce a novel prior distribution for modelling the weights in mixture models based on a generalisation of the Dirichlet distribution, the Selberg Dirichlet distribution. This distribution contains a repulsive term, which naturally…
The broad class of multivariate unified skew-normal (SUN) distributions has been recently shown to possess important conjugacy properties. When used as priors for the coefficients vector in probit, tobit, and multinomial probit models,…
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…
Researchers frequently wish to assess the equality or inequality of groups, but this poses the challenge of adequately adjusting for multiple comparisons. Statistically, all possible configurations of equality and inequality constraints can…
This paper shows how the variational Bayes method provides a computational efficient technique in the context of hierarchical modelling using Dirichlet process priors, in particular without requiring conjugate prior assumption. It shows,…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate…
We provide novel probabilistic portrayals of two multivariate models designed to handle zero-inflation in count-compositional data. We develop a new unifying framework that represents both as finite mixture distributions. One of these…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…
For log-linear analysis, the hyper Dirichlet conjugate prior is available to work in the Bayesian paradigm. With this prior, the MC3 algorithm allows for exploration of the space of models to try to find those with the highest posterior…
When analyzing data from multiple sources, it is often convenient to strike a careful balance between two goals: capturing the heterogeneity of the samples and sharing information across them. We introduce a novel framework to model a…
Probability distribution theory helps in studying the impact of various dimensions in life while the Mittag-Leffler function and bicomplex are used in electromagnetism, quantum mechanics, and signal theory. Considering the importance of…
Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…
We present the discrete infinite logistic normal distribution (DILN), a Bayesian nonparametric prior for mixed membership models. DILN is a generalization of the hierarchical Dirichlet process (HDP) that models correlation structure between…
We propose a Bayesian inference approach for a class of latent Markov models. These models are widely used for the analysis of longitudinal categorical data, when the interest is in studying the evolution of an individual unobservable…
Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…