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smooth_dage#
View page sourcePrior Density Function for Smoothing Age Difference#
S#
We are given a smoothing, \(s\).
I#
We use \(I\) to denote n_age the number of age points in the smoothing.
J#
We use \(J\) to denote n_time the number of time points in the smoothing.
lambda#
We use \(\lambda\) to denote the mulstd_dage_prior_id multiplier for the smoothing.
prior_ij#
For \(i = 0, \ldots , I-2\), \(j = 0, \ldots , J-1\) we use prior_ij to denote the dage_prior corresponding to age index \(i\) and time index \(j\) in the smoothing.
d_ij#
We use \(d_{i,j}\) to denote the density in prior_ij . In an abuse of notation, we include the value of eta and nu and in \(d_{i,j}\); see d .
sigma_ij#
We use \(\sigma_{i,j}\) to denote the std in prior_ij .
mu_ij#
We use \(\mu_{i,j}\) to denote the mean in prior_ij .
v_ij#
We use \(v_{i,j}\) for the value of the model variable corresponding to the i-th age point and j-th time point in the smoothing. We include the index \(I-1\) in this notation, but not the other notation above.
A^s#
The age difference density \(A^s (s, v)\) is defined by
where \(D\) is the log-density function . Note that we include \(\theta\) as an argument because \(\lambda\) is a component of \(\theta\).