By Peter D. Congdon
The use of Markov chain Monte Carlo (MCMC) tools for estimating hierarchical versions contains complicated facts buildings and is frequently defined as a progressive improvement. An intermediate-level remedy of Bayesian hierarchical types and their purposes, Applied Bayesian Hierarchical Methods demonstrates the benefits of a Bayesian method of info units regarding inferences for collections of similar devices or variables and in tools the place parameters will be taken care of as random collections.
Emphasizing computational matters, the publication offers examples of the next program settings: meta-analysis, information dependent in house or time, multilevel and longitudinal facts, multivariate facts, nonlinear regression, and survival time facts. For the labored examples, the textual content often employs the WinBUGS package deal, permitting readers to discover replacement probability assumptions, regression buildings, and assumptions on earlier densities. It additionally accommodates BayesX code, that's fairly priceless in nonlinear regression. to illustrate MCMC sampling from first rules, the writer contains labored examples utilizing the R package.
Through illustrative info research and a spotlight to statistical computing, this publication makes a speciality of the sensible implementation of Bayesian hierarchical tools. It additionally discusses numerous concerns that come up whilst utilizing Bayesian suggestions in hierarchical and random results models.
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Additional info for Applied Bayesian Hierarchical Methods
K, assists in diagnosing lack of model identiﬁability. , 1995). Another example is factor and structural equation models where the loadings are not speciﬁed so as to anchor the factor scores in a consistent direction, so that the “name” of the common factor may switch during MCMC updating T&F Cat # C7206 Chapter: 1 Page: 24 8-4-2010 Bayesian Methods for Complex Data: Estimation and Inference 25 (Congdon, 2003). Single runs may still be adequate for straightforward problems, and single chain convergence diagnostics (Geweke, 1992) may be applied in this case.
Inverse gamma or uniform) as well as the degree of prior informativeness. As priors become more diﬀuse, the formal approach tends to select the simplest least parameterized models, in line with the so-called Lindley or Bartlett paradox (Bartlett, 1957). Finally, the formal approach to model averaging requires both posterior densities, p(θk |y, m = k), and posterior model probabilities, p(m = k|y). Estimates of posterior densities, p(θk |y, m = k), may be diﬃcult to obtain in complex random eﬀects models with large numbers of parameters.
5dk log(n), where ˆθk is the maximum likelihood estimator. , 2001; Mitchell and Beauchamp, 1988) for choosing predictors in regression. , Cai and Dunson, 2006; Chen and Dunson, 2003; Fruhwirth-Schnatter and Tuchler, 2008; Kinney and Dunson, 2008) and avoids the sometimes complex issues involved in estimating marginal likelihoods of diﬀerent models. 4 considers variance selection in hierarchical models. However, in more complex random eﬀect applications with discrete responses or hierarchically structured data, there remain issues that impede straightforward application of the formal approach (Han and Carlin, 2001).
Applied Bayesian Hierarchical Methods by Peter D. Congdon