Smooth Grid Priors

For the Rate tab, Random Effect tab, Study tab and Country Covariate tab, the interface sets priors. This describes how those settings are interpreted. Most of this work happens in the function cascade.executor.construct_model.smooth_grid_from_smoothing_form(), and you can check its source there.

The default value, dage, and dtime priors are used to initialize those parts of the smooth grid. For smooth grids with only one age, the dage priors aren’t meaningful, and the same is true for dtime priors when there is only one year.

After that, the detailed priors are applied in the order they appear in the settings, and note that the order may or may not reflect the order in the user interface. There are three ways to specify which age and time points each detailed prior applies to:

• age_lower and age_upper - A missing value here (one that’s not filled-in in the UI) is treated as -infinity or infinity, respectively.

• time_lower and time_upper - Missing values similarly set to include all points on that side.

• born_lower and born_upper - Each line for the born limit corresponds to \(a \le t - b\) or \(a \ge t - b\), respectively.

For each prior, all three of these sieves are applied to the grid of ages and times defined by the age values and time values for that smooth grid. If a detailed prior doesn’t match any of the age and time points in this grid, there will be a statement in the log that says “No ages and times match prior with extents <lower and upper extents>.”