Bret Devereaux

Yes, but it is possible for the Pax Romana to not be terribly peaceful (by modern standards) and at the same time represent a reduction in overall levels of violence. Just going by demographic evidence, it very likely was the latter - a relative, if not absolute, peace.

Is this anecdotal or supported by statistical analysis of data? Was the Julian-Trajanic period numerically less violent than the Republican or Marian eras?

Nature of the evidence makes statistical comparisons of deaths impossible - too many battles without casualty reports, or where casualty reports are unreliable. But use militarization (% pop under arms per year) as a proxy, and yes, supported by data.

That may be a misleading indicator because another thing that progresses over time is the amount of sq. ft. of ground that can be held by a single warrior.

I mean, we're not looking at major organizational or technological changes in the first 2 centuries CE though? So if fewer soldiers are holding more ground, it is because violence is being 'pushed out' to the frontier, creating zones of peace where they didn't exist before.

Of course, you are doing that by inflicting new violence at the frontier, but the limes is a smaller zone than the imperial core and those areas were not exactly peaceful before the Romans showed up either.

Also, how much of the low level Kashmir-border style violence with Bastarnae and Dacian tribes went unreported?

Probably a lot, but then our evidence suggests that violence would be happening with or without the Romans. Rhine/Danube region looks pretty violent (inter-state/non-state anarchy) pre-Romans.