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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 .
Simulated Measurements and Adjusted Standard Deviations

Discussion
data_sim_id
simulate_index
data_subset_id
data_sim_value
Method
     data_id
     y
     Capital Delta
     d
     eta
     A
     Capital E
     sigma
     delta
     e
     z
Example

Discussion
The data_sim table is created during a simulate_command . It contains number_simulate sets of measurements where each set has one value for each entry in the data_subset_table .

data_sim_id
This column has type integer and is the primary key for this table. Its initial value is zero, and it increments by one for each row. Given the model_variables as specified by truth_var_table , the measurement uncertainty is independent for each row and has standard deviation meas_std .

simulate_index
The column has type integer. It specifies the index for this simulated measurement set. This index starts at zero, repeats as the same for the entire subset of data_id values, and then increments by one between measurement sets. The final (maximum) value for simulate_index is number_simulate minus one.

data_subset_id
This column has type integer and is the primary key for the data_subset_table . This identifies which data_id each row of the data_sim table corresponds to. If n_subset is the number of rows in the data_subset table,
   data_sim_id = simulate_index * n_subset + data_subset_id
 for simulate_index equal zero to number_simulate-1 and data_subset_id equal zero to n_subset-1 .

data_sim_value
This column has type real and is the simulated measurement value that for the specified row of the data table; see z in the method below. If the density for this data_id is censored (not censored) data_sim_value has value max(z, 0) , ( z ).

Method

data_id
We use data_id to denote the data_id corresponding to the data_subset_id corresponding to this data_sim_id .

y
We use @(@ y @)@ to denote the data table meas_value corresponding to this data_id .

Capital Delta
We use @(@ \Delta @)@ to denote the minimum cv standard deviation corresponding to the data table and this data_id .

d
We use @(@ d @)@ to denote the density_id corresponding to the data table and this data_id .

eta
We use @(@ \eta @)@ to denote the eta corresponding to the data table and this data_id .

A
We use @(@ A @)@ denote the average integrand corresponding to the truth_var table value for the model variables, the values in the data table, and this data_id .

Capital E
We use @(@ E @)@ for the average noise effect corresponding to the truth_var table value for the model variables, the values in the data table, and this data_id .

sigma
We use @(@ \sigma @)@ to denote the transformed standard deviation corresponding to the data table and this data_id ; i.e., @[@ \sigma = \left\{ \begin{array}{ll} \log( y + \eta + \Delta ) - \log(y + \eta) & \R{if \; log \; density} \\ \Delta & \R{otherwise} \end{array} \right. @]@ Note that @(@ \sigma @)@ does not depend on simulated noise @(@ e @)@ defined below (because it is defined using @(@ y @)@ instead of @(@ z @)@).

delta
We use @(@ \delta @)@ to denote the adjusted standard deviation corresponding to the truth_var table value for the model variables, the values in the data table, and this data_id . Note that @(@ \sigma @)@ does not depend on simulated noise @(@ e @)@ defined below.

e
We use @(@ e @)@ to denote the noise simulated with mean zero, standard deviation @(@ \delta @)@, and density corresponding to this data_id without log qualification. For example, if the data density for this data_id is log_gaussian, the @(@ e @)@ is simulate using a Gaussian distribution.

z
We use @(@ z @)@ to denote the simulated data value data_sim_value corresponding to this data_sim_id . It the density is linear , @[@ z = A + e @]@ It the density is log scaled , @[@ \begin{array}{rcl} e & = & \log( z + \eta ) - \log( A + \eta ) \\ \exp (e) & = & ( z + \eta ) / ( A + \eta ) \\ z & = & \exp(e) ( A + \eta ) - \eta \end{array} @]@

Example
See the user_data_sim.py and simulate_command.py examples / tests.
Input File: omh/table/data_sim_table.omh