Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing

By Alan E. Gelfand, Athanasios Kottas, S. MacEachern. 2005

409 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Environmental Chemistry, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/e24622199fca470b9cf610d4f13dc6f4db993333

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Citations in the corpus

The Matrix Stick-Breaking Process (2008, methodology): “The DDP formulation of MacEachern (1999, 2000), as implemented by De Iorio et al. (2004) and Gelfand, Kottas, and MacEachern (2005), relies on assuming fixed probability weights, π = {πh,h = 1, . . . ,∞}, while allowing the atoms to vary across probability measures in the collection according to a…”
Hybrid Dirichlet mixture models for functional data (2009, methodology): “The priors for μ, σ2 and σ20 are chosen following Gelfand et al. (2005).”
On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions (2012, methodology): “2010), spatial modeling (Gelfand et al. 2005), functional data (Dunson and Herring 2006), time series (Caron et al.”
Geostatistical inference under preferential sampling (2010, methodology): “These approaches could be extended to the setting that is presented by Diggle and his colleagues by replacing the Gaussian spatial model for S with a non-Gaussian spatial model (e.g. Gelfand et al. (2005), Grifﬁn and Steel (2006) and Reich and Fuentes (2007)).”
The Nested Dirichlet Process (2008, methodology): “…this construction (where dependence is introduced only on the atoms) has been used by DeIorio, Müller, Rosner & MacEachern (2004) to create ANOVA-like models for densities, and by Gelfand, Kottas, and MacEachern (2005) to generate spatial processes that allow for nonnormality and nonstationarity.”
Bayesian dynamic density estimation (2008, background): “2007b; Griffin and Steel 2007; Dunson 2006) or by introducing dependence in the elements of the stick-breaking representation of the distribution (MacEachern 1999; DeIorio et al. 2004; Gelfand et al. 2005; Griffin and Steel 2006; Rodriguez et al. 2008).”
Bayesian density regression (2007, methodology): “De Iorio et al. (2004) used the dependent DP to produce an analysis-of-variance type of dependence structure, whereas Gelfand et al. (2005) applied the dependent DP to spatial modelling applications by using a Gaussian process for the atoms.”
Bayesian Semiparametric Modelling in Quantile Regression (2009, background): “The DDP was developed by MacEachern (1999; 2000) as a non-parametric prior for a stochastic process of random distributions; these distributions are dependent but such that, at each index value, the distribution is a DP (see also De Iorio et al., 2004; Gelfand et al., 2005).”
A Tutorial on Bayesian Nonparametric Models (2011, methodology): “One way to capture such dependencies in a BNP model is to make the base distribution G0 of the DP dependent on a location variable (Gelfand et al., 2005; Duan et al., 2007).”
Order-Based Dependent Dirichlet Processes (2006, methodology): “Of particular relevance for this article is the nonparametric approach of Gelfand, Kottas, and MacEachern (2004), where the locations θ of the stick-breaking representation of a Dirichlet process are assumed to come from a Gaussian process.”
Generalized spatial dirichlet process models (2007, methodology): “The spatial Dirichlet process introduced by Gelfand et al. (2005) produces a random spatial process which is neither Gaussian nor stationary.”