data_sim_table¶

Simulated Measurements and Adjusted Standard Deviations¶

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 adjusted standard deviation sigma corresponding to the data table and this data_id . 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 transformed standard deviation delta corresponding to the truth_var table value for the model variables, the values in the data table, and this data_id . Note that \(\delta\) 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{eqnarray} e & = & \log( z + \eta ) - \log( A + \eta ) \\ \exp (e) & = & ( z + \eta ) / ( A + \eta ) \\ z & = & \exp(e) ( A + \eta ) - \eta \end{eqnarray}

Example¶

See the user_data_sim.py and simulate_command.py examples / tests.