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This paper investigates Gaussian copula mixture models (GCMM), which are an extension of Gaussian mixture models (GMM) that incorporate copula concepts. The paper presents the mathematical definition of GCMM and explores the properties of…

Nonstationary and non-Gaussian spatial data are common in various fields, including ecology (e.g., counts of animal species), epidemiology (e.g., disease incidence counts in susceptible regions), and environmental science (e.g.,…

Meta-analysis methods are used to combine evidence from multiple studies. Meta-regression as well as model-based meta-analysis are extensions of standard pairwise meta-analysis in which information about study-level covariates and…

The generalized partially linear additive model (GPLAM) is a flexible and interpretable approach to building predictive models. It combines features in an additive manner, allowing each to have either a linear or nonlinear effect on the…

Variable selection remains a difficult problem, especially for generalized linear mixed models (GLMMs). While some frequentist approaches to simultaneously select joint fixed and random effects exist, primarily through the use of…

The Linear Model of Co-regionalization (LMC) is a very general multitask gaussian process model for regression or classification. While its expressiveness and conceptual simplicity are appealing, naive implementations have cubic complexity…

Multiplicative mixed models can be applied in a wide range of scientific disciplines, since they are relevant in every situation where an interaction between a fixed effect and a random effect is present. Until now, no R package has been…

While graphical models for continuous data (Gaussian graphical models) and discrete data (Ising models) have been extensively studied, there is little work on graphical models linking both continuous and discrete variables (mixed data),…

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of…

We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…

Large language models (LLMs) are powerful tools that, in a number of settings, overlap with the results of human pattern recognition and reasoning. Retrieval-augmented generation (RAG) further allows LLMs to produce tailored output…

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of $K$ Gaussians with generic means…

General log-linear models specified by non-negative integer design matrices have a potentially wide range of applications, although using models without the genuine overall effect, that is, ones which cannot be reparameterized to include a…

Both linear mixed models (LMMs) and sparse regression models are widely used in genetics applications, including, recently, polygenic modeling in genome-wide association studies. These two approaches make very different assumptions, so are…

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension…

Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…

With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a…

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be…

Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…

We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…