ANALYZE_STATISTICS and ANALYZE_STATISTICS_PARTITION

Huge tables does not change statistics quickly. Analysing once a week over weekend should be more than enough.
Vertica had problem - if you have right-handed insert into some column, for example each new record has current timestamp, value will go above column max value recorded during statistics collection. If user issue a query that selects recent data, optimiser will throw warning "value out of range" and will disable a bunch of internal optimisations.
That was the only reason to run analyse partition for recent data often, like hourly.
Still it does not help if user is selecting last minute data.
Addressing this problem is not straightforward. I have python code that export statistics, tweak it to extend max value in some columns, and import back. You can find code on github.
Vertica v 25.1 (if I remember correctly version no), finally announced that "optimiser value out of range" problem has been addressed, though there is no mention how it is done.
Easiest way to address problem is to upgrade to v 25.1 and collect stats weekly, and forget about hourly statistics collection on recent partition.
You will be able to verify how it works, by checking optimiser events.

interesting insights, thanks, Sergey, I appreciate your help!