Random Numbers ...

[Herman Rubin]

In article <709 at cresswell.quintus.UUCP>, ok at quintus.UUCP (Richard A. O'Keefe) writes:
> In article <690 at l.cc.purdue.edu>, cik at l.cc.purdue.edu (Herman Rubin) writes:
> > Second, get some physical random bits.
> > And make sure that all bits are random.
> Um, how *do* you "make sure that all bits are random"?
> Physical random numbers aren't all that simple, either.

I meant that the physical random number should be on a storage device.
I did point out that they might have to be reused.

> Journals like JASA and Applied Statistics seem to be happy with the
> use of pseudo-random numbers in Monte Carlo studies.

I would not trust them.  They may take this attitude because they do not
know that there is a cheap alternative.  About 15 years ago, one of my
colleagues came to me about a simulation problem--his 5% significance
values (known theoretically) were coming out 7%.  Changing the random
numbers to XOR with the a binary version of the RAND numbers solved the
problem.

Many Monte Carlo studies suffer from this and other defects.  One should
always put in checks with directly calculable quantities--are you that
sure that you have not made a programming error?  There are several sets
of physical random numbers available.  Also note that I recommended that
physical and pseudo random numbers be XORed; we only need assume that the
physical random numbers do not have their quirks matching the quirks of 
the pseudo random numbers.  That is a much smaller assumption than saying
the pseudo random numbers' quirks will not affect the simulation.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907
Phone: (317)494-6054
hrubin at l.cc.purdue.edu (ARPA or UUCP) or hrubin at purccvm.bitnet