Related papers: Approximate Reference Prior for Gaussian Random Fi…
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…
Prior specifications for hyperparameters of random fields in Bayesian spatial point process modelling can have a major impact on the statistical inference and the conclusions made. We consider fitting of log-Gaussian Cox processes to…
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…
We develop a novel reference prior for Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) random effects. This is particularly important in the context of objective Bayes variable selection with sample size $n$…
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…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets…
In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…
Constraints are a natural choice for prior information in Bayesian inference. In various applications, the parameters of interest lie on the boundary of the constraint set. In this paper, we use a method that implicitly defines a…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
This is a companion paper to Yarkoni and Westfall (2017), which describes the Python package Bambi for estimating Bayesian generalized linear mixed models using a simple interface. Here I give the statistical details underlying the default,…
In Bayesian theory, the role of information is central. The influence exerted by prior information on posterior outcomes often jeopardizes Bayesian studies, due to the potentially subjective nature of the prior choice. In modeling where a…
Statistical techniques used in air pollution modelling usually lack the possibility to understand which predictors affect air pollution in which functional form; and are not able to regress on exceedances over certain thresholds imposed by…
In the context of the expected-posterior prior (EPP) approach to Bayesian variable selection in linear models, we combine ideas from power-prior and unit-information-prior methodologies to simultaneously produce a minimally-informative…