Unexplained statistics reset? Help tracking it down.

I've been seeing some unexplained behavior whereas the statistics in a Postgres
database reset with no explanation as to why. This is concerning because it
results in terrible query plans until someone manually runs analyze, and that
it negatively impacts autovacuum.

This is Postgres 9.5.4 on Ubuntu 14 (yes, I know there's a patch I need to
apply -- it's on my TODO list, but I don't see any mention of fixing unexplained
stats resets in that version, so I'm not assuming that will fix it)

My first thought is that some random user was calling pg_reset_stats() without
realizing what they were doing. However, I have full query logging enabled on
this system, and the logs don't show this happening. (Yes, I've also checked
for someone disabling query logging for their connection before doing myseterious
things).

Before I start theorizing that this might be a bug in Postgres, does anyone have
any suggestions on what other ways the stats could be reset that I need to check
on? Has anyone else experienced this to lend credence to the possibility that it's
a bug? I have no clue how to reproduce it, as the occurrance is rare and still
seems random.

--
Bill Moran <wmoran(at)potentialtech(dot)com>