Parameterization and Bayesian Modeling

By Andrew Gelman. 2004

293 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/564c555c05bd344227ff9bd6d673e20f7c627238

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Citations in the corpus

blavaan: Bayesian structural equation models via parameter expansion (2015, methodology): “General parameter expansion approaches to Bayesian inference are described by Gelman (2004, 2006), with applications to factor analysis models detailed by Ghosh and Dunson (2009). Our approach here is related to that of Palomo et al.”
MICE: Multivariate Imputation by Chained Equations in R (2011, methodology): “…sequential regressions (Raghunathan et al. 2001), ordered pseudo-Gibbs sampler (Heckerman et al. 2001), partially incompatible MCMC (Rubin 2003), iterated univariate imputation (Gelman 2004), MICE (van Buuren and Oudshoorn 2000; van Buuren and Groothuis-Oudshoorn 2011) and FCS (van Buuren 2007).”
Stacking for Non-mixing Bayesian Computations: The Curse and Blessing of Multimodal Posteriors (2020, background): “But for multiple chains sampled from the same parameter space, averaging over chains can be viewed a form of model expansion (Gelman, 2004) and is more desired than selecting a single chain.”
Bayesian Semiparametric Structural Equation Models with Latent Variables (2010, background): “…symptom data, we used a continuation ratio measurement model: P (yij = c|yij ≥ c, τ, λ, η) = Φ(τjc − λjηi), c = 1, . . . , Cj, (12) where Cj is the number of categories for symptom type j, Φ(.) is the CDF of the standard normal function, λ1, · · · , λ7 are the loading factors for symptoms Y1 − Y7.”
Bayesian Workflow (2020, background): “This leads to wanting them on natural scales and modeling them as independent, if possible, or with an interpretable dependence structure, as this facilitates the use of informative priors (Gelman, 2004).”
Using Stacking to Average Bayesian Predictive Distributions (with Discussion) (2017, methodology): “Ideally, we would avoid the Bayesian model combination problem by extending the model to include the separate models Mk as special cases (Gelman, 2004).”
Flexible Imputation of Missing Data (2012, methodology): “Option 3 provides finite estimates, but has been criticized as not being well interpretable in a regression context (Gelman et al., 2008) and computationally inefficient (White et al., 2010). Option 4 corrects method 1, and is simple to implement. Options 5 and 6 have been recommended by White et al”
Theoretical Analysis of Bayesian Matrix Factorization (2011, methodology): “MF can be used for learning linear relation between vectors such as reduced rank regression (Baldi and Hornik, 1995; Reinsel and Velu, 1998), canonical correlation analysis (Hotelling, 1936; Anderson, 1984), partial least-squares (Wold, 1966; Worsley et al., 1997; Rosipal and Krämer, 2006), and…”
Small Sample Size Solutions (2020, methodology): “Some statistical options can be sought in terms of the reparameterization of the model (Gelman, 2004); that is, the reformulation of the same model in an alternative form, for instance by using non-centered parametrizations in hierarchical models, see Betancourt and Girolami (2015).”
Analysis of Multinomial Models With Unknown Index Using Data Augmentation (2007, methodology): “Our use of data augmentation is consistent in form and function with classical motivations and methods of data augmentation (Tanner and Wong 1987; Gelman 2004).”
Discussion of "Analysis of variance--why it is more important than ever" by A. Gelman (2005, methodology): “…, α and τ , which are deﬁned as follows: The model can be then expressed as The auxiliary parameters α are given a uniform prior distribution, and then this reduces to the original model [see Boscardin (1996), Meng and van Dyk ( 1997), Liu, Rubin and Wu (1998), Liu and Wu (1999) and Gelman (2004)].”
The BUGS project: Evolution, critique and future directions (2009, background): “Numerous applications of the software can be found in the literature, in a wide array of application areas, including disease mapping [4], pharmacometrics [5], ecology [6], health-economics [7], genetics [8], archaeology [9], psychometrics [10], coastal engineering [11], educational performance [12]”