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Hierarchical Bayesian Models (hierarchical + bayesian_models)
Selected AbstractsComparison of Hierarchical Bayesian Models for Overdispersed Count Data using DIC and Bayes' FactorsBIOMETRICS, Issue 3 2009Russell B. Millar Summary When replicate count data are overdispersed, it is common practice to incorporate this extra-Poisson variability by including latent parameters at the observation level. For example, the negative binomial and Poisson-lognormal (PLN) models are obtained by using gamma and lognormal latent parameters, respectively. Several recent publications have employed the deviance information criterion (DIC) to choose between these two models, with the deviance defined using the Poisson likelihood that is obtained from conditioning on these latent parameters. The results herein show that this use of DIC is inappropriate. Instead, DIC was seen to perform well if calculated using likelihood that was marginalized at the group level by integrating out the observation-level latent parameters. This group-level marginalization is explicit in the case of the negative binomial, but requires numerical integration for the PLN model. Similarly, DIC performed well to judge whether zero inflation was required when calculated using the group-marginalized form of the zero-inflated likelihood. In the context of comparing multilevel hierarchical models, the top-level DIC was obtained using likelihood that was further marginalized by additional integration over the group-level latent parameters, and the marginal densities of the models were calculated for the purpose of providing Bayes' factors. The computational viability and interpretability of these different measures is considered. [source] Local- to continental-scale variation in the richness and composition of an aquatic food webGLOBAL ECOLOGY, Issue 5 2010Hannah L. Buckley ABSTRACT Aim, We investigated patterns of species richness and composition of the aquatic food web found in the liquid-filled leaves of the North American purple pitcher plant, Sarracenia purpurea (Sarraceniaceae), from local to continental scales. Location, We sampled 20 pitcher-plant communities at each of 39 sites spanning the geographic range of S. purpurea, from northern Florida to Newfoundland and westward to eastern British Columbia. Methods, Environmental predictors of variation in species composition and species richness were measured at two different spatial scales: among pitchers within sites and among sites. Hierarchical Bayesian models were used to examine correlates and similarities of species richness and abundance within and among sites. Results, Ninety-two taxa of arthropods, protozoa and bacteria were identified in the 780 pitcher samples. The variation in the species composition of this multi-trophic level community across the broad geographic range of the host plant was lower than the variation among pitchers within host-plant populations. Variation among food webs in richness and composition was related to climate, pore-water chemistry, pitcher-plant morphology and leaf age. Variation in the abundance of the five most common invertebrates was also strongly related to pitcher morphology and site-specific climatic and other environmental variables. Main conclusions, The surprising result that these communities are more variable within their host-plant populations than across North America suggests that the food web in S. purpurea leaves consists of two groups of species: (1) a core group of mostly obligate pitcher-plant residents that have evolved strong requirements for the host plant and that co-occur consistently across North America, and (2) a larger set of relatively uncommon, generalist taxa that co-occur patchily. [source] Physiological responses of two contrasting desert plant species to precipitation variability are differentially regulated by soil moisture and nitrogen dynamicsGLOBAL CHANGE BIOLOGY, Issue 5 2009LISA D. PATRICK Abstract Alterations in global and regional precipitation patterns are expected to affect plant and ecosystem productivity, especially in water-limited ecosystems. This study examined the effects of natural and supplemental (25% increase) seasonal precipitation on a sotol grassland ecosystem in Big Bend National Park in the Chihuahuan Desert. Physiological responses , leaf photosynthesis at saturating light (Asat), stomatal conductance (gs), and leaf nitrogen [N] , of two species differing in their life form and physiological strategies (Dasylirion leiophyllum, a C3 shrub; Bouteloua curtipendula, a C4 grass) were measured over 3 years (2004,2006) that differed greatly in their annual and seasonal precipitation patterns (2004: wet, 2005: average, 2006: dry). Precipitation inputs are likely to affect leaf-level physiology through the direct effects of altered soil water and soil nitrogen. Thus, the effects of precipitation, watering treatment, soil moisture, and nitrogen were quantified via multivariate hierarchical Bayesian models that explicitly linked the leaf and soil responses. The two species differed in their physiological responses to precipitation and were differentially controlled by soil water vs. soil nitrogen. In the relatively deeply rooted C3 shrub, D. leiophyllum, Asat was highest in moist periods and was primarily regulated by deep (16,30 cm) soil water. In the shallow-rooted C4 grass, B. curtipendula, Asat was only coupled to leaf [N], both of which increased in dry periods when soil [N] was highest. Supplemental watering during the wet year generally decreased Asat and leaf [N] in D. leiophyllum, perhaps due to nutrient limitation, and physiological responses in this species were influenced by the cumulative effects of 5 years of supplemental watering. Both species are common in this ecosystem and responded strongly, yet differently, to soil moisture and nitrogen, suggesting that changes in the timing and magnitude of precipitation may have consequences for plant carbon gain, with the potential to alter community composition. [source] Bayesian estimation of cognitive decline in patients with alzheimer's diseaseTHE CANADIAN JOURNAL OF STATISTICS, Issue 1 2002Patrick Béalisle Abstract Recently, there has been great interest in estimating the decline in cognitive ability in patients with Alzheimer's disease. Measuring decline is not straightforward, since one must consider the choice of scale to measure cognitive ability, possible floor and ceiling effects, between-patient variability, and the unobserved age of onset. The authors demonstrate how to account for the above features by modeling decline in scores on the Mini-Mental State Exam in two different data sets. To this end, they use hierarchical Bayesian models with change points, for which posterior distributions are calculated using the Gibbs sampler. They make comparisons between several such models using both prior and posterior Bayes factors, and compare the results from the models suggested by these two model selection criteria. Estimation bayésienne du déclin cognitif de patients atteints de la maladie d'Alzheimer On s'est beaucoup intéressé ces derniers temps à l'estimation du déclin des fonctions cognitives des personnes atteintes de la maladie d'Alzheimer. Il n'est pas facile de quantifier ce déclin, qui dépend de l'échelle utilisée pour mesurer les fonctions cognitives, mais aussi de la variabilité entre les individus, de 1'incertitude entourant le moment exact du début de leur maladie et d'éventuels effets plancher et plafond. Les auteurs montrent comment il est possible de tenir compte de ces différents éléments en modélisant le déclin observé dans les résultats obtenus par deux groupes de patients au mini-examen de l'état mental. Ils utilisent pour ce faire des modèles bayésiens hiérarchiques avec points de jonction, pour lesquels ils calculent les lois a posteriori au moyen de l'échantillonneur de Gibbs. Ils comparent plusieurs modèles de ce type au moyen de facteurs de Bayes a priori et a posteriori; ils comparent ensuite les résultats des modèles suggérés par ces deux critères de sélection. [source] Hierarchical Bayesian Analysis of Correlated Zero-inflated Count DataBIOMETRICAL JOURNAL, Issue 6 2004Getachew A. Dagne Abstract This article presents two-component hierarchical Bayesian models which incorporate both overdispersion and excess zeros. The components may be resultants of some intervention (treatment) that changes the rare event generating process. The models are also expanded to take into account any heterogeneity that may exist in the data. Details of the model fitting, checking and selecting alternative models from a Bayesian perspective are also presented. The proposed methods are applied to count data on the assessment of an efficacy of pesticides in controlling the reproduction of whitefly. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||