Add context to data: specify the type of experimental error


  • Alias: variance_type

  • Arguments: STRINGLIST

  • Default: none


There are four options for specifying the experimental error (e.g. the measurement error in the data you provide for calibration purposes): ‘none’ (default), ‘scalar’, ‘diagonal’, or ‘matrix.’

If the user specifies scalar, they can provide a scalar variance per calibration term. Note that for scalar calibration terms, only ‘none’ or ‘scalar’ are options for the measurement variance. However, for field calibration terms, there are two additional options. ‘diagonal’ allows the user to provide a vector of measurement variances (one for each term in the calibration field). This vector corresponds to the diagonal of the full covariance matrix of measurement errors. If the user specifies ‘matrix’, they can provide a full covariance matrix (not just the diagonal terms), where each element (i,j) of the covariance matrix represents the covariance of the measurement error between the i-th and j-th field values.

Usage Tips

Variance information is specified on a per-response group (descriptor), per-experiment basis. Off-diagonal covariance between response groups or between experiments is not supported.


The figure below shows an observation vector with 5 responses; 2 scalar + 3 field (each field of length > 1). The corresponding covariance matrix has scalar variances \(\sigma_1^2, \sigma_2^2\) for each of the scalars \(s1, s2\) , diagonal covariance \(D_3\) for field \(f3\) , scalar covariance \(\sigma_4^2\) for field \(f4\) , and full matrix covariance \(C_5\) for field \(f5\) . In total, Dakota supports block diagonal covariance \(\Sigma\) across the responses, with blocks \(\Sigma_i\) , which could be fully dense within a given field response group. Covariance across the highest-level responses (off-diagonal blocks) is not supported, nor is covariance between experiments.

image html ObsErrorCovariance.png “An example of scalar and field response data, with associated block-diagonal observation error covariance.”