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@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\W}[1]{ \; #1 \; }@)@This is dismod_at-20221105 documentation: Here is a link to its current documentation .
The Sample Command

Syntax
database
Purpose
method
variables
number_sample
simulate_index
simulate
asymptotic
     Fixed Effects Distribution
     Random Effects Distribution
Extra Input Tables
     data_sim_table
     prior_sim_table
     fit_var_table
Output Tables
     sample_table
     No Sample Table
     hes_fixed_table
     hes_random_table
Bounds
Example

Syntax
dismod_at database sample method variables number_sample
 dismod_at database sample method variables number_sample simulate_index
database
Is an http://www.sqlite.org/sqlite/ database containing the dismod_at input tables which are not modified.

Purpose
This command simulates samples of the model_variables from the posterior distribution; see simulation for the posterior distribution.

method
The sample command argument method must be simulate or asymptotic; see discussion below:

variables
The sample command argument variables must be fixed or both. This corresponds to the asymptotic statistics for fit fixed and fit both respectively.

number_sample
Is the number of samples. Each sample contains a complete set of model variables. If method is simulate, number_sample must be equal to number_simulate in the previous simulate command.

simulate_index
If this argument is present, method must be asymptotic and simulate_index must be the same as in the corresponding fit command .

simulate
A complete set of model_variables , corresponding to each sample_index , is written to the sample table. They correspond to fitting the data in the data_sim table with simulate_index equal to sample_index . The fixed effects correspond to the optimal fit of both the fixed and random effects with the prior for the fixed effects replaced by the corresponding values in the prior_sim_table . This value is used for the fixed effects and the value for the random effects is obtained by optimizing just the random effects with the prior for the random effects replaced by the corresponding values in the prior_sim_table . This requires running number_sample fits of the model variables (fitting just the random effects is faster compared to fitting both). See simulation in the discussion of the posterior distribution of maximum likelihood estimates.

asymptotic
If method is asymptotic, the fit_var_table is an additional input in this case and it assumed to correspond to a fit both . If the previous fit did (did not) have a simulate_index it must (must not) be included in the sample_command. The asymptotic statistics of the model variables is used to generate number_sample samples of the model variables The samples with different values of sample_index are independent. All of the Laplace density terms are ignored by the asymptotic statistics. The constraints are also ignored, except the constraints were the lower and upper limits for a variable are equal.

Fixed Effects Distribution
The asymptotic distribution used to simulate the fixed effects is a normal with mean equal to the value of the fixed effects in the fit_var_table and covariance equal to the inverse of the Hessian of the fixed effect objective hes_fixed_table . If a fixed effect is scaled (see scaling fixed effects ) the scaled version of the fixed effect has the asymptotic distribution. If the lower and upper limits are equal, the corresponding variable is simulated as having that constant value.

Random Effects Distribution
If the lower and upper limits for a random effect are equal, the random effect is simulated as having that constant value. If the lower and upper limits are not equal and variables is fixed, the random effect is simulated with value zero. Otherwise, the asymptotic distribution used to simulate a random effect is a normal with mean equal to the value of the random effect in the fit_var_table This is the optimal value given the fixed effects; see fit_var_table below. The covariance of the random effects is equal to the inverse of the Hessian of the random effect objective hes_fixed_table .

Extra Input Tables

data_sim_table
If method is simulate, this command has the extra input data_sim_table which was created by the previous simulate_command .

prior_sim_table
If method is simulate, this command has the extra input prior_sim_table which was created by the previous simulate_command .

fit_var_table
If method is asymptotic, this command has the extra input fit_var_table which was created by a previous fit command which must have included both fixed and random effects.

Output Tables

sample_table
A new sample_table is created each time this command is run. It contains samples of the model variables. Hence the number of rows in this table is number_sample times the number of rows in the var_table . If the asymptotic command fails because the fixed effects information matrix is not positive definite, this command will terminate with an error and the sample table will not exist. The corresponding fixed effects information matrix will be in the hes_fixed_table .

No Sample Table
In the special case where method is asymptotic and the Hessian of the fixed objective is not positive definite, the sample table is not created; i.e., there is be no sample table in the database after this command. In addition, if variables is both and the Hessian of the random effects objective is not positive definite, the sample table is not created.

hes_fixed_table
A new hes_fixed_table is created each time this command is run with method equal to asymptotic. The Hessian of the fixed effects objective is written in this table. If simulate_index is present (is not present) the Hessian corresponds to the simulated measurements in the data_sim_table (measurements in the data_table ).

hes_random_table
A new hes_random_table is created each time this command is run with method equal to asymptotic and variables equal to both. The Hessian of the random effects objective is written in this table. If simulate_index is present (is not present) the Hessian corresponds to the simulated measurements in the data_sim_table (measurements in the data_table ).

Bounds
If you use the simulate method, the samples are all within the specified bounds, including the bounds on the random effects specified by bound_random . If you use the asymptotic method, the only bounds that are enforced are where the upper and lower limits are equal.

Example
The files sample_command.py , user_sample_asy.py contain examples and tests using this command.
Input File: devel/cmd/sample_command.cpp