Great post, thanks for the learning. I am a bit puzzled however as to why you go out of your way to say "In addition, we expect Θsens>1-Θspec," (which expectation BTW makes sense to me), only to follow this up by assuming priors for Θsens and Θspec which (assuming independence) violate this expectation with significant probability (perhaps 25% of the time, based on a crude eyeballing of the curves).

Can you help me better understand your thinking here (or clear up any misconception on my part)?