An ANOVA Model for Dependent Random Measures

By Maria De Iorio, Peter Müller, Gary Rosner, S. MacEachern. 2004

378 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/21d3394e220715696bfbccce446aa693a88bfc1e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

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).”
Comparing distributions by using dependent normalized random‐measure mixtures (2013, methodology): “The ANOVA dependent Dirichlet process model of De Iorio et al. (2004) assumes that wg,i =wi and the density k is a normal distribution with mean zTg βi, where βi is a vector of parameters, and variance σ 2.”
Stick-breaking autoregressive processes (2011, background): “…y, the infinite mixture model can be extended by allowing the kernel k to depend on x (Leslie et al., 2007; Chib and Greenberg, 2009), the mixing measure G to depend on x (De Iorio et al., 2004; Müller et al., 2004; Griffin and Steel, 2006; Dunson et al., 2007) or both (Geweke and Keane, 2007).”
Order-Based Dependent Dirichlet Processes (2006, methodology): “The same method to induce dependence is used in De Iorio et al. (2004) to achieve an analysis of variance (ANOVA)-type structure.”
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 s”
A Bayesian Nonparametric Approach to Inference for Quantile Regression (2010, methodology): “work of Chib (1992) developed Bayesian inference for linear Tobit regression with normal errors”
Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing (2005, methodology): “, De Iorio et al. (2004) for an illustration in the ANOVA setting. In our setting, G induces a random distribution G(Y (s)) for each s, hence the set GD ≡ {G(Y (s)) : s ∈ D}. MacEachern (2000, Theorem 3.1) provides sufficient conditions such that GD will be a DDP. In fact, we can envision the possib”
The Dependent Dirichlet Process and Related Models (2020, methodology): “To accommodate a continous response, De Iorio et al. (2004) extended the above construction through a convolution with a continuous kernel, e.g., a normal kernel, leading to yi | Gxi ind.∼ ∫ N (yi | µ, φ) dGxi(µ) = ∫ N ( yi | λ′dxi , φ ) dG(λ).”
On the Support of MacEachern’s Dependent Dirichlet Processes and Extensions (2012, methodology): “Versions of the single weights DDP have been applied to ANOVA (De Iorio et al. 2004), survival (De Iorio et al. 2009; Jara et al. 2010), spatial modeling (Gelfand et al. 2005), functional data (Dunson and Herring 2006), time series (Caron et al. 2008), discriminant analysis (De la Cruz et al.…”
On the stick-breaking representation of normalized inverse Gaussian priors (2012, background): “Important contributions to this area include, among others, [3, 4, 5, 6, 10, 11, 27].”
Smoothly mixing regressions (2007, methodology): “DeIorio et al. (2004) uses this strategy for categorical covariates, and Griffin and Steel (2005) for continuous covariates.”
Regression Density Estimation With Variational Methods and Stochastic Approximation (2012, methodology): “We do not discuss these methods any further, but refer readers to MacEachern (1999), De Iorio et al. (2004), Griffin and Steel (2006), and Dunson, Pillai,”
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): “One of the primary reasons for the great success and rapidly expanding use of DP mixtures is the development of simple and efficient MCMC algorithms for posterior computation (MacEachern (1994), Escobar and West (1998), MacEachern and Müller (1998) and Ishwaran and James (2001), among others).”
Bayesian Selection and Clustering of Polymorphisms in Functionally Related Genes (2008, background): “Hence, when the number of loci is moderate to large or ∑ c,l,h 1(gicl = h) is small for some c, l, h (as is typically the case), maximum likelihood estimation of model (1) runs into difficulties.”
Hierarchical Dirichlet Processes (2006, background): “…dependencies among multiple DPs through links among the parameters G0j and/or α0j (Cifarelli and Regazzini 1978; MacEachern 1999; Tomlinson 1998; Müller, Quintana, and Rosner 2004; De Iorio, Müller, and Rosner 2004; Kleinman and Ibrahim 1998; Mallick and Walker 1997; Ishwaran and James 2004).”