Statistical machine translation
Statistical machine translation (SMT) is an approach that translates by learning probabilities from parallel text and assembling output from the most likely phrase translations. It was the mainstream method through the 2000s and early 2010s, before neural machine translation replaced it. Its output was usable but often stilted, with visible seams between phrases.
How it works
SMT breaks the source into phrases, looks up likely translations for each from tables learned from data, and searches for the combination with the highest overall probability, guided by a separate model of what the target language normally looks like.
Because it works phrase by phrase rather than sentence by sentence, it struggles with word order and long-range meaning, which is exactly where neural systems later pulled ahead.
How SourceTarget uses it
SourceTarget's engines are neural, not statistical. Statistical machine translation matters here mainly as the baseline that modern engines improved on: understanding it explains why today's output is so much more fluent, and why fluency alone is not proof of accuracy.