Related papers: Skew-Gaussian Random Fields
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
Although there is ample work in the literature dealing with skewness in the multivariate setting, there is a relative paucity of work in the matrix variate paradigm. Such work is, for example, useful for modelling three-way data. A matrix…
We consider distributed optimization methods for problems where forming the Hessian is computationally challenging and communication is a significant bottleneck. We leverage randomized sketches for reducing the problem dimensions as well as…
This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on…
The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation.…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…
Skew-Gaussian processes (SkewGPs) extend the multivariate Unified Skew-Normal distributions over finite dimensional vectors to distribution over functions. SkewGPs are more general and flexible than Gaussian processes, as SkewGPs may also…
The ability to generate samples of the random effects from their conditional distributions is fundamental for inference in mixed effects models. Random walk Metropolis is widely used to conduct such sampling, but such a method can converge…
We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
The contribution of this work is the introduction of a multivariate circular-linear (or poly- cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its property of…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact…
We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
Gaussian random field is a ubiquitous model for spatial phenomena in diverse scientific disciplines. Its approximation is often crucial for computational feasibility in simulation, inference, and uncertainty quantification. The…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…