相关论文: Careful prior specification avoids incautious infe…

High-dimensional spatially correlated covariates are common in regression models encountered in environmental sciences and other fields. In such models, the regression coefficients often exhibit a sparse structure with spatial dependence.…

Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…

In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…

We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…

Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…

Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…

Gaussian process priors are a popular choice for Bayesian analysis of regression problems. However, the implementation of these models can be complex, and ensuring that the implementation is correct can be challenging. In this paper we…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

Tree-based priors for probability distributions are usually specified using a predetermined, data-independent collection of candidate recursive partitions of the sample space. To characterize an unknown target density in detail over the…

Many common correlation structures assumed for data can be described through latent Gaussian models. When Bayesian inference is carried out, it is required to set the prior distribution for scale parameters that rules the model components,…

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs.…

Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Ultrametric matrices are a class of covariance matrices that arise in latent tree models. As a parameter space in a statistical model, the set of ultrametric matrices is neither convex nor a smooth manifold. Focus in the literature has…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…