Related papers: On minimum correlation in construction of multivar…
We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Random samples of quantum states are an important resource for various tasks in quantum information science, and samples in accordance with a problem-specific distribution can be indispensable ingredients. Some algorithms generate random…
We introduce a novel, fast, and efficient generative model built upon scattering covariances, the most recent iteration of the scattering transforms statistics. This model is designed to augment by several orders of magnitude the number of…
A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of…
We show an analytic method to construct a bivariate distribution function (DF) with given marginal distributions and correlation coefficient. We introduce a convenient mathematical tool, called a copula, to connect two DFs with any…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
Modern multivariate machine learning and statistical methodologies estimate parameters of interest while leveraging prior knowledge of the association between outcome variables. The methods that do allow for estimation of relationships do…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Growing dimensionality of data calls for beyond-pairwise interactions quantification. Measures of multidimensional interactions quantification are hindered, among others, by two issues: 1. Interpretation difficulties, 2. the curse of…
In this work we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a…
This paper introduces a novel theoretically sound approach for the celebrated CMA-ES algorithm. Assuming the parameters of the multi variate normal distribution for the minimum follow a conjugate prior distribution, we derive their optimal…
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…
Several bivariate beta distributions have been proposed in the literature. In particular, Olkin and Liu (2003) proposed a 3 parameter bivariate beta model, which Arnold and Ng (2011) extend to 5 and 8 parameter models. The 3 parameter model…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
Many types of bounded data defined on the unit interval arise naturally as ratios of the form $X/(X + Y)$. In the existing literature, the main statistical models proposed for this type of bounded data typically based on the assumption that…
We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
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)…
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…