Internal and External Reliability

We are now introducing a new and exciting statistical feature to GeoLab - Internal and External reliability testing!

This tool can be used in a network Adjustment or Simulation mode, and provides deeper insight into the statistical reliability of a network, including each of its observations (Internal) and coordinates (External).

Further described below, Internal and External reliability are ultimately used to determine the strength at which a network can be validated. Internal reliability describes a hypothetical bias, the Marginally Detectable Error (MDE), which can influence the estimated parameters of a network by a degree expressed by the External reliability.

Together, these measures demonstrate the maximum positional errors in estimated parameters caused by undetectable measurement outliers.

The MDE is given as the size of an error which might remain undetected within each measurement (Internal reliability / Observational MDE) and within each estimated coordinate (External reliability / Positional MDE), based on corresponding probabilities specified through statistical measures.

Thus, each observation in a network is assigned an Internal reliability and a resulting External reliability. The maximum External reliability measure in the network can then be used in infer the weakest network point and observation, and the overall reliability statistics can be used to determine which points are the weakest and strongest as a result of which observations, based on statistically undetectable errors.

You can access this tool through GeoLab’s Project Options dialog.

Look down to the bottom right of this tab to find the options for this feature:

Calculate Internal Reliability: This option enables the internal/external reliability features. If no external reliability type is selected, only internal reliability will be calculated.

External Reliability Type: This option selects the type of external reliability (None (no external reliability), 1D (1-dimensional), 2D (2-dimensional), 3D (3-dimensional), Aux (Auxiliary parameters))

Significance Level: This allows the user to select the probability of rejecting a valid observation.

Power of Test: This option allows for the selection of the probability of rejecting an invalid observation.

Non-Centrality: This is a measure of the non-centrality of the distribution curve of the statistical test, and is set automatically based on the above two settings.

Internal Reliability is expressed in terms of the Observational MDE for each observation as horizontal Euclidian distance, listed beside each residual in GeoLab’s .LST adjustment summary file. This describes the size of an error that may remain undetected in the measurements of a network.

External Reliability is expressed in terms of the resultant Positional MDE at each observation, as horizontal Euclidian distance, listed beside each Internal Reliability result in the .LST adjustment summary. This describes the influence of a bias equivalent to the Observational MDE (Internal Reliability) on the estimated positional parameters of a network.

The maximum Positional MDE for an adjustment is given at the end of the residual listing in the .LST file, showing its value and the observation which caused it.