Related papers: The Integer-valued Moving-Average Random Field
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
The thinning-based integer-valued autoregressive moving-average (INARMA) models are popular for count time series. Recently, types of INARMA models have also been developed for count random fields, i.e., for spatial count data located on a…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…
INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…
Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference).…
We study the autocovariance functions of moving average random fields over the integer lattice $\mathbb{Z}^d$ from an algebraic perspective. These autocovariances are parametrized polynomially by the moving average coefficients, hence…
Variational inference has had great success in scaling approximate Bayesian inference to big data by exploiting mini-batch training. To date, however, this strategy has been most applicable to models of independent data. We propose an…
In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
This paper proposes the beta binomial autoregressive moving average model (BBARMA) for modeling quantized amplitude data and bounded count data. The BBARMA model estimates the conditional mean of a beta binomial distributed variable…
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…
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…
A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…
A principled method to obtain approximate solutions of general constrained integer optimization problems is introduced. The approach is based on the calculation of a mean field probability distribution for the decision variables which is…
A common theme underlying many problems in statistics and economics involves the determination of a systematic method of selecting a joint distribution consistent with a specified list of categorical marginals, some of which have an ordinal…
Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This…
The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…