smooth_grid_table#

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The Smooth Grid Table#

Purpose#

Each row of the smooth_grid table specifies an age, time, value prior, age difference prior, and time difference prior for a single model_variable . (The difference priors represent the smoothing in a mathematical sense.) A set of rows with the same smooth_id , defines a statistical prior for a function of age and time.

smooth_grid_id#

This column has type integer and is the primary key for the smooth_grid table. Its initial value is zero, and it increments by one for each row.

smooth_id#

This column has type integer and is the primary key for the smooth_table . Each smooth_id value corresponds to a different statistical prior for a function of age and time.

null#

If smooth_id is null, the corresponding row of the smooth grid table is not used. This can be useful for deleting a row or column corresponding to a smooth_id .

age_id#

This column has type integer and is a age_id in the age table. The age_id value corresponds to a specific age.

time_id#

This column has type integer and is a time_id in the time table. Each time_id value corresponds to a specific time.

value_prior_id#

This column has type integer and is the prior_id for the function’s values at the corresponding age and time.

null#

If value_prior_id is null, const_value must not be null and is used for the value prior at the corresponding age and time.

dage_prior_id#

This column has type integer and is the prior_id for the function’s forward difference w.r.t age at the corresponding age and time; see age difference function A^s . The corresponding density_id cannot specify a censored density .

Maximum Age#

For each time grid point in the smoothing, the dage_prior_id at the maximum age is not used.

null#

If dage_prior_id is null, the corresponding prior is a uniform from minus to plus infinity.

dtime_prior_id#

This column has type integer and is the prior_id for the function’s forward difference w.r.t time at the corresponding age and time; see time difference function T^s . The corresponding density_id cannot specify a censored density .

Maximum Age#

For each age grid point in the smoothing, the dtime_prior_id at the maximum time is not used.

null#

If dtime_prior_id is null, the corresponding prior is a uniform from minus to plus infinity.

const_value#

This column has type real and specifies a specific value for a function using this smoothing at this age and time (when it is not null). This case is equivalent to lower , upper , and mean , equal to const_value and density is uniform .

null#

If const_value is null, value_prior_id must not be null. If const_value is not null, value_prior_id must be null.

Rectangular Grid#

For each fixed value of smooth_id the set of age_id , time_id pairs is rectangular. In other words, if an age_id value appears, it appears once with each time_id that appears with this smooth_id . This also means, if a time_id value appears, it appears once with each age_id that appears with this smooth_id .

Example#

The file smooth_grid_table.py contains an example smooth table.