I dig into where the statistics against a Polybase table actually live:
Today, we learned that Polybase statistics are stored in the same way as other statistics; as far as SQL Server is concerned, they’re just more statistics built from a table (remembering that the way stats get created involves loading data into a temp table and building stats off of that temp table). We can do most of what you’d expect with these stats, but beware calling sys.dm_db_stats_properties() on Polybase stats, as they may not show up.
Also, remember that you cannot maintain, auto-create, auto-update, or otherwise modify these stats. The only way to modify Polybase stats is to drop and re-create them, and if you’re dealing with a large enough table, you might want to take a sample.
The result isn’t very surprising in retrospect, and it’s good that “stats are stats are stats” is the correct answer.