Related papers: Linear Transformations & the Multivariate Generati…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is…
Multivariate data occurs in a wide range of fields, with ever more flexible model specifications being proposed, often within a multivariate generalised linear mixed effects (MGLME) framework. In this article, we describe an extended…
In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution…
We propose a method for inference in generalised linear mixed models (GLMMs) and several extensions of these models. First, we extend the GLMM by allowing the distribution of the random components to be non-Gaussian, that is, assuming an…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As special cases of the multilinear generating…
Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…
The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…
We discuss a method for computing the generating function for the multiplicity distribution in field theories with strong time dependent external sources. At leading order, the computation of the generating function reduces to finding a…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
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…
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
In this work we consider time series with a finite number of discrete point changes. We assume that the data in each segment follows a different probability density functions (pdf). We focus on the case where the data in all segments are…
We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial…
By using the matrix formulation of the two-step approach to the distributions of runs, a recursive relation and an explicit expression are derived for the generating function of the joint distribution of rises and falls for multivariate…
Let $\{a_\rr : \rr \in (\Z^+)^d \}$ be a $d$-dimensional array of numbers, for which the generating function $F(\zz) := \sum_\rr a_\rr \zz^\rr$ is meromorphic in a neighborhood of the origin. For example, $F$ may be a rational multivariate…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
When linear regression generates a relationship between a (dependent) scalar response and one or multiple independent variables, various datasets providing distinct graphical trends can develop resembling relationships based on the same…