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To study the frequentist properties of our proposed procedures, we have performed a Monte Carlo study that shows that our proposed Bayesian reference approaches compare favorably to a posterior analysis based on a competing prior in terms of coverage of credible intervals, relative mean squared error, and mean length of credible intervals.
However, as we have no logical or theoretical basis for considering any variable to be prior in terms of a hypothetical causal structure of the data (Cohen et al. 2013), and assigning priority to forest age would marginalise the year effect, and vice versa (Brown et al. 2011; Chen et al. 2016), we reported the results from simultaneously modelling effects of forest age and year.
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As Fig. 8 shows the HRCT-based prior moderately outperformed the non-anatomy-based priors in terms of contrast recovery of the ventricles and volume delineation, provided that the anatomical information was well aligned to the corresponding PET image.
For convenience, the prior of μ d was assumed to depend on the variance: μ d | σ d 2 ∼ N (η, σ d 2 / ϕ ), where η is our prior belief about μ d and ϕ is the "prior sample size", which expresses the strength of the prior belief in terms of σ d 2. Here, ϕ was set to 10, a small number relative to 100 QTL, to allow the data to "dominate" the posterior distribution of μ d.
Werhli and Husmeier (2007) and Husmeier and Werhli (2007) build on that work and express the available prior knowledge in terms of an energy function, from which a prior distribution over network structures is obtained.
Bayesian inference would put those prior probabilities in terms of belief – the "epistemological interpretation".
Milburn has been a strong advocate of universities looking not just at an applicant's prior attainment, in terms of raw exam results, but also the context in which the pupil achieved that result, including the average grade at the school.
Benefits of such adaptation schemes are shown in some prior works in terms of energy efficiency [1 8].
How do prior beliefs in terms of expected gains and risks from migration affect migrants' remittance-saving portfolio?
The effect of prior damage in terms of residual and absorbed energies became more pronounced as the number of impacts increased.
Although adequate performance of this seismic force resisting system was observed in prior earthquakes in terms of protecting buildings from collapse, the formation of plastic hinges in the beams and columns causes irreparable damage to the beam-column connections.
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