data_sim_table#

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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.