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Similarly, xtmixed and gllamm can be used in Stata and the lme4 package in R. In the Stata program gllamm, a full pseudo-maximum-likelihood estimation which allows for specification of probability weights, is implemented via adaptive quadrature [ 27].
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The design process requires identifying the structure of the network, followed by specification of the probability parameters that operationalize these dependencies for the purpose of inference.
Quantification of the impacts of epistemic uncertainty is naturally difficult, because most of the existing stochastic tools rely on the specification of the probability distributions and thus do not readily apply to epistemic uncertainty.
Alternatively, the beta distribution allows specification of a probability model for continuous random variables with support over the interval (0,1).
We applied a Bayesian methodology detailed in [ 24] which entails the specification of prior probability distributions for model parameters and these are listed in Table 1.
Bayesian inversion requires the specification of prior probability distributions for model inputs and the calculation of the likelihood function that quantifies the ability of the model to reproduce the observed data (Mosegaard and Tarantola 1995; Kennedy and O'Hagan 2001).
The estimating equations rely entirely on the expectation and variance of the biomarker measurements in terms of the unknown exposure parameters, bypassing the need for an explicit likelihood equation or even specification of exact probability distributions.
When using a Bayesian approach, the specification of prior probability distributions for model parameters is required, and in this instance we selected priors that were vague to induce little bias in parameter estimation.
More sophisticated models resort to hierarchical specification of link probabilities, or to grouping of nodes within blocks of varying probability.
This comes at the cost of additional modeling assumptions; namely, specification of prior probabilities for each hypothesis and prior distributions over model parameters conditional on the hypotheses.
First, it allows the specification of prior probabilities on model parameters.
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