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Bayesian nonparametric dependent model for partially replicated data: the influence of fuel spills on species diversity
Julyan Arbel
,
Kerrie A Mengersen
,
Judith Rousseau
,
Collegio Carlo Alberto
Published
2017
in
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Abstract
Semantic Scholar extracted view of "Bayesian nonparametric dependent model for partially replicated data: the influence of fuel spills on species diversity" by Julyan Arbel et al.
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10 Figures and Tables
Fig 1: Comparison of probabilities of presence in raw data at site i = 9 (left) and probabilities sampled from the Griffiths–Engen–McCloskey prior with M = 6 (right). The x-axis represents species j = 1, . . . , 32.
Fig 2: Diagram representation for the Dep-GEM model. Squares represent observed data, i.e. covariates X = (Xi)i=1,...,I and observations Y Ni i = (Y1,i, . . . , YNi,i), and circles represent parameters for the Dep-GEM model.
Fig 3: Illustration of Proposition 1. Left : E(HSimp(X)) w.r.t. M . Middle: Var(HSimp(X)) w.r.t. M . Right : three paths of Cov(HSimp(X1), HSimp(X2)) w.r.t. |X1 −X2| for M ∈ {1/2, 1, 3}.
Fig 6: Log-conditional predictive ordinates (log-CPO) for different models and prior specifications (see text). (a) Boxplots of log-CPO. (b) Summaries of log-CPO, mean and median.
Fig 7: Dependence factor µM (X1, X2) = (M + 1) 2E ( V (X1)V (X2) ) w.r.t. |X1−X2| for M ∈ {1/2, 1, 3}, where V is obtained by transforming a Gaussian process with squared exponential covariance function, with σZ = 1 and λ = 1.
Fig 1: Comparison of probabilities of presence in raw data at site i = 9 (left) and probabilities sampled from the Griffiths–Engen–McCloskey prior with M = 6 (right). The x-axis represents species j = 1, . . . , 32.
Fig 2: Diagram representation for the Dep-GEM model. Squares represent observed data, i.e. covariates X = (Xi)i=1,...,I and observations Y Ni i = (Y1,i, . . . , YNi,i), and circles represent parameters for the Dep-GEM model.
Fig 3: Illustration of Proposition 1. Left : E(HSimp(X)) w.r.t. M . Middle: Var(HSimp(X)) w.r.t. M . Right : three paths of Cov(HSimp(X1), HSimp(X2)) w.r.t. |X1 −X2| for M ∈ {1/2, 1, 3}.
Fig 6: Log-conditional predictive ordinates (log-CPO) for different models and prior specifications (see text). (a) Boxplots of log-CPO. (b) Summaries of log-CPO, mean and median.
Fig 7: Dependence factor µM (X1, X2) = (M + 1) 2E ( V (X1)V (X2) ) w.r.t. |X1−X2| for M ∈ {1/2, 1, 3}, where V is obtained by transforming a Gaussian process with squared exponential covariance function, with σZ = 1 and λ = 1.
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