"probability density" refers to how likely or probable it is for an event or outcome to occur within a given range. It measures the concentration of probabilities over a specific interval. Full definition
There is no way of obtaining just a limited segment of the flat interval in a CI for the self - evident reason that the posterior CDF is flat; there is zero change of probability density across this interval. (climateaudit.org)
A number of subsequent publications qualitatively describe parameter values that allow models to reproduce features of observed changes, but without directly estimating a climate sensitivity probability density function (PDF). (ipcc.ch)
I don't know about compartmentalization but I can't see why anything matters in investment except the payoff probability density function, or more simply, the expected value. (basehitinvesting.com)