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www.samsi.info On Bayesian Analysis of Generalized Linear Models: A New Perspective
, 2007
"... No. DMS0112069. Any opinions, findings, and conclusions or recommendations expressed in this ..."
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No. DMS0112069. Any opinions, findings, and conclusions or recommendations expressed in this
Identifying influential model choices in Bayesian hierarchical models
, 2008
"... Realworld phenomena are frequently modelled by Bayesian hierarchical models. The buildingblocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be well ..."
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Realworld phenomena are frequently modelled by Bayesian hierarchical models. The buildingblocks in such models are the distribution of each variable conditional on parent and/or neighbour variables in the graph. The specifications of centre and spread of these conditional distributions may be wellmotivated, while the tail specifications are often left to convenience. However, the posterior distribution of a parameter may depend strongly on such arbitrary tail specifications. This is not easily detected in complex models. In this paper we propose a graphical diagnostic which identifies such influential statistical modelling choices at the node level in any chain graph model. Our diagnostic, the local critique plot, examines local conflict between the information coming from the parents and neighbours (local prior) and from the children and coparents (lifted likelihood). It identifies properties of the local prior and the lifted likelihood that are influential on the posterior density. We illustrate the use of the local critique plot with applications involving models of different levels of complexity. The local critique plot can be derived for all parameters in a chain graph model, and is easy to implement using the output of posterior sampling. 1
Contributed Discussion on Article by Finegold and
"... This is a very interesting paper providing both theoretical and computational results for robust structure estimation in decomposable graphical models. Finegold & Drton (F&D hereafter) do a splendid job in motivating and illustrating the various ramifications of this attractive research path ..."
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This is a very interesting paper providing both theoretical and computational results for robust structure estimation in decomposable graphical models. Finegold & Drton (F&D hereafter) do a splendid job in motivating and illustrating the various ramifications of this attractive research path. We will comment on prior specification, hoping to add further insights to a paper already rich in content. Notice that model choice results strongly depend on prior specification; see, e.g., O’Hagan and Forster (2004, ch. 7). Priors on graphs Formula (3) of F&D specifies a product of Bernoulli priors with fixed edge inclusion probability d. As F&D mention in their Discussion, one could place a prior on d. We suggest exploring this avenue in real terms, because recent results suggest that substantial improvements can be obtained by placing, say, a beta prior on d; see for instance Scott and Berger (2010) and Castillo and van der Vaart (2012). Priors on matrices The Hyper Inverse Wishart (HIW) prior on Ψ, or Σ in the Gaussian case, requires the hyperparameters δ and Φ. F&D choose δ = 1 and Φ = cIp, referring to Armstrong et al. (2009) for alternative choices of Φ. A related option would be using the Fractional Bayes Factor (FBF) to implement model choice based on objective
www.mdpi.com/journal/ijerph Estimating Prevalence of Coronary Heart Disease for Small Areas Using Collateral Indicators of Morbidity
"... Abstract: Different indicators of morbidity for chronic disease may not necessarily be available at a disaggregated spatial scale (e.g., for small areas with populations under 10 thousand). Instead certain indicators may only be available at a more highly aggregated spatial scale; for example, death ..."
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Abstract: Different indicators of morbidity for chronic disease may not necessarily be available at a disaggregated spatial scale (e.g., for small areas with populations under 10 thousand). Instead certain indicators may only be available at a more highly aggregated spatial scale; for example, deaths may be recorded for small areas, but disease prevalence only at a considerably higher spatial scale. Nevertheless prevalence estimates at small area level are important for assessing health need. An instance is provided by England where deaths and hospital admissions for coronary heart disease are available for small areas known as wards, but prevalence is only available for relatively large health authority areas. To estimate CHD prevalence at small area level in such a situation, a shared random effect method is proposed that pools information regarding spatial morbidity contrasts over different indicators (deaths, hospitalizations, prevalence). The shared random effect approach also incorporates differences between small areas in known risk factors (e.g., income, ethnic structure). A Poissonmultinomial equivalence may be used to ensure small area prevalence estimates sum to the known higher area total. An illustration is provided by data for London using hospital admissions and CHD deaths at ward level, together with CHD prevalence totals for considerably larger local health authority areas. The shared random effect involved a spatially correlated common factor, that accounts for clustering in latent risk factors, and also provides a summary measure of small area CHD morbidity.