Log-likelihood Density
Introduction
User Interface since version 11.0
The Log-Likelihood Density tool enables us to understand how the Log-Likelihood varies and we can test how anomalous a particular evidence/scenario is.
This tool is invaluable, because log-likelihood values, whilst comparable, do not lie in an easily interpretable range. This tool allows us to convert a log-likelihood into a probability, which makes for easier anomaly detection and diagnostics.
Background
Log-Likelihood enables us to determine how unusual/rare a scenario (evidence) is. However it does not have useful range (e.g. 0 to 100).
By sampling a network, we cam determine what the likely range of the log-likelihood is and build an empirical density which we can then use to determine whether our evidence is unusual or not.
Once we have an empirical density function for the log-likelihood, we can understand how likely our evidence is in percentage terms (Cdf) or the value the log-likelihood would take for a given percentage (inverse Cdf).
Cdf
Tells us how likely our evidence is in percentage terms.
Inverse Cdf
Tells us the value the log-likelihood would take for a given percentage.