How do you allow inertia in bones for animating in pose mode? Suppose you want bones to move more realistically where energy is not instantaneously dispersed throughout a character, like a person standing on a surfboard on the ocean. When the board moves upwards due to the wave, the entire person doesn't completely move up right away, their legs move up first, then their hips/chest, then their shoulders and neck. Or, suppose someone gets hit in the chest by something like a punch. Their chest moves backwards first while their arms, legs and head remain still due to inertia in the first moments, then as their chest moves back move it pulls on those arms and legs more and more until they speed up to the same speed as the rest of the person. 

How can this cascading motion be efficiently animated for when animating keyframes in pose mode in variable circumstances? Or in other words, how can bones themselves in pose mode be made to simulate collisions as opposed to making an entire mesh a rigid or soft body? 

The closest thing I've come up with is keyframing a delay in the influence of a child-of or inverse-kinematic relationship, but it seems like there should be a more automated way of accomplishing this and its very hard to manually animate this proportional to velocity.
What you want is currently not (simply) available as far as i know.
When animating on the right there is options, there you could enable AutoIk.
Together width that i would use helper empties. So you can set Bone constrains so that for example the feed take 100 height influence of the surfboard, and the hip takes 30%... but it might not realy look 'elastic movement' that way. This is currently still mostly the art of animating.

Perhaps if your handy with python script you could automate the movement or the influence of the helper empties a bit.

Tough yet alone using empty constrains on bones to set their position can reduce work time (if the autoIK bones wont bend wrongly (fix width more constrains)..). Animating by such empties usually does give a better result.