How does PolyBase collect statistics from external tables?
Creation and maintenance of PolyBase statistics is in the hands of the DBA.
The &quot;getting started&quot; guide provides several steps to establish PolyBase, the last of which is CREATE STATISTICS referencing the external table.
The documentation on CREATE STATISTICS states:

Statistics for external tables
When creating external table statistics, SQL Server imports the external table into a temporary SQL Server table, and then creates the statistics. For samples statistics, only the sampled rows are imported. If you have a large external table, it will be much faster to use the default sampling instead of the full scan option.

and further down

Limitations and Restrictions
Updating statistics is not supported on external tables. To update statistics on an external table, drop and re-create the statistics.

From this I conclude it is up to the system administrator to

create appropriate statistics for the intended workload
monitor for stale statistics
implement maintenance procedures for external statistics
ensuring there is sufficient space for the &quot;temporary table&quot; (TempDB?)

One imagines that, as the product matures and gains traction, more features from the current data engine (auto create &amp; auto update statistics) will be ported to PolyBase. On the flip side, do you really want to wait for results while a 5PB store is sampled?