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SUMMARY We consider geostatistical models that allow the locations at which data are collected to be informative about the outcomes. A Bayesian approach is proposed, which models the locations using a log Gaussian Cox process, while modelling the outcomes conditionally on the locations as Gaussian with a Gaussian process spatial random effect and adjustment(More)
A wide variety of priors have been proposed for nonparametric Bayesian estimation of conditional distributions, and there is a clear need for theorems providing conditions on the prior for large support, as well as posterior consistency. Estimation of an uncountable collection of conditional distributions across different regions of the predictor space is a(More)
We consider the problem of robust Bayesian inference on the mean regression function allowing the residual density to change flexibly with predictors. The proposed class of models is based on a Gaussian process prior for the mean regression function and mixtures of Gaussians for the collection of residual densities indexed by predictors. Initially(More)
In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor)(More)
We consider geostatistical models that allow the locations at which data are collected to be informative about the outcomes. Diggle et al. [2009] refer to this problem as preferential sampling, though we use the term informative sampling to highlight the relationship with the longitudinal data literature on informative observation times. In the longitudinal(More)
In this article, we propose new Bayesian methods for selecting and estimating a sparse coefficient vector for skewed heteroscedastic response. Our novel Bayesian procedures effectively estimate the median and other quantile functions, accommodate non-local prior for regression effects without compromising ease of implementation via sampling based tools, and(More)
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a fixed design for covariates. The only random design result we are aware of (van der Vaart and van Zanten, 2011)(More)
Unlike majority of current statistical models and methods focusing on mean response for highly skewed longitudinal data, we present a novel model for such data accommodating a partially linear median regression function, a skewed error distribution and within subject association structures. We provide theoretical justifications for our methods including(More)
Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with the university requirements. ii To my husband, Jamiu T. Williams, your love speaks and my heart listens. Thank you so very much for understanding my long working hours and my continuous(More)