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Sampling-Based Approaches to Calculating Marginal Densities
Abstract Stochastic substitution, the Gibbs sampler, and the sampling-importance-resampling algorithm can be viewed as three alternative sampling- (or Monte Carlo-) based approaches to the…
Hierarchical Modeling and Analysis for Spatial Data
OVERVIEW OF SPATIAL DATA PROBLEMS Introduction to Spatial Data and Models Fundamentals of Cartography Exercises BASICS OF POINT-REFERENCED DATA MODELS Elements of Point-Referenced Modeling Spatial…
Bayesian Model Choice: Asymptotics and Exact Calculations
A general predictive density is presented which includes all proposed Bayesian approaches the authors are aware of and using Laplace approximations they can conveniently assess and compare asymptotic behavior of these approaches.
Gaussian predictive process models for large spatial data sets
- Sudipto Banerjee, A. Gelfand, A. Finley, H. Sang
- Computer ScienceJournal of The Royal Statistical Society Series B…
- 1 September 2008
This work achieves the flexibility to accommodate non‐stationary, non‐Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets in the form of a computational template encompassing these diverse settings.
Model choice: A minimum posterior predictive loss approach
A predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values is proposed, which is obtained by minimising posterior loss for a given model.
Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling
Abstract The use of the Gibbs sampler as a method for calculating Bayesian marginal posterior and predictive densities is reviewed and illustrated with a range of normal data models, including…
Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets
- A. Datta, Sudipto Banerjee, A. Finley, A. Gelfand
- Computer ScienceJournal of the American Statistical Association
- 28 June 2014
A class of highly scalable nearest-neighbor Gaussian process (NNGP) models to provide fully model-based inference for large geostatistical datasets are developed and it is established that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices.
Model Determination using sampling-based methods
- A. Gelfand
- Computer Science
Model Determination Using Predictive Distributions with Implementation via Sampling-Based Methods
Model determination is divided into the issues of model adequacy and model selection and it is proposed to validate conditional predictive distributions arising from single point deletion against observed responses.
Hierarchical Bayesian Analysis of Changepoint Problems
A general approach to hierarchical Bayes changepoint models is presented, including an application to changing regressions, changing Poisson processes and changing Markov chains, which avoids sophisticated analytic and numerical high dimensional integration procedures.