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random_value#
View page sourceThe Random Effects Value Density Function#
u_j#
We use \(u_j\) to denote one component of the random effects vector.
prior_id#
We use prior_id for the prior that is attached to the j-th random effect; see Prior for a Variable .
lambda_j#
We use \(\lambda_j\) to denote the mulstd_value_prior_id multiplier for the smooth_id corresponding to \(u_j\).
mu_j#
We use \(\mu_j\) to denote the mean corresponding to prior_id .
epsilon_j#
We use \(\sigma_j\) to denote the std corresponding to prior_id .
eta_j#
We use \(\eta_j\) to denote the eta corresponding to prior_id .
d_j#
We use \(d_j\) to denote the density_id corresponding to prior_id . In an abuse of notation, we include eta and eta in d_j ; see d .
delta_j#
We use \(\delta_j\) to denote the transformed standard deviation corresponding to prior_id
V_j^u#
The value density for the j-th component of \(u\) is
where \(D\) is the log-density function .
V^u#
Let \(n\) be the number of random effects. The value density for all the random effects \(u\) is defined by