The ‘Summation Hack’ as an Outlier Model

The ‘summation hack’ is the ad-hoc replacement of a product by a sum in a probabilistic expression. This hack is usually explained as a device to cope with outliers, with no formal derivation. This note shows that the hack does make sense probabilistically, and can be best thought of as replacing an outlier-sensitive likelihood with an outlier-tolerant one. This interpretation exposes the hack as an assumption about the outliers, allowing us to determine when it makes sense to use the hack.