On Tue, 4 Aug 2009, Jack Schmidt wrote:
> In real-world statistical analysis one often has many random variables
> whose probability distributions can only be defined piecewise...
> This type of problem occurs... virtually never, I would guess, in
> academia or science.
You'd be surprised.
As a grad student, I needed to introduce a piecewise probability
distribution, which I used to represent various uncertainties in
instrument calibration, to get a particular Markov Chain Monte Carlo
method to work efficiently. The section of my thesis where it's
introduced is at
<http://www.bib.hatton.btinternet.co.uk/dan/Natural_Sciences/PER_CoCu/node61.html>;.
Also, several of the surface topographies used in standard theroetical
analyses of friction between elastic materials (cf. Archard, 1957,
_Proc. R. Soc. Lond. A_, 243(1233):190-205; Greenwood and Williamson,
1966, _Proc. R. Soc. Lond. A_, 295(1442):300-319) can be interpreted
as piecewise-defined probability distributions over the heights of
peaks (i.e. local height maxima) on the surface.
--
Regards,
Dan