Sorry, what I should have said was Halton numbers are quasi-random,
and not pseudo-random. Quasi-random is the technically appropriate
terminology.
Halton sequences are low discrepancy: the subsequence looks/smells
random. Hence, they are often used in quasi monte carlo simulations.
To be precise, there is only 1 Halton sequence for a particular
prime.
Repeated calls to Halton should return the same numbers. The first
column is the Halton sequence for 2. the second for 3, the third
for 5
and so on using the first M primes (for M columns). (You can also
scramble the sequence to avoid this.)
I am using them to integrate over a multivariate normal space. If you
take 1000 random draws, then sum f() over the draws is the
expectation
of f(). If f() is very non-linear (and/or multi-variate) then even
with large N, its often hard to get a good integral. With quasi-
random
draws, the integration is better for the same N. (One uses the
inverse
distribution function.) For an example, you can look at Train's paper
(page 4 and 5 have a good explanation) at:
http://elsa.berkeley.edu/wp/train0899.pdf
In the context of simulated maximum likelihood estimation, such
integrals are very common. Of course true randomness has its own
place/importance: its just that quasi-random numbers can be very
useful in certain contexts.
Regards,
Anirban
PS: qnorm(halton()) gets around the problem of the random deviates
not working.
On Tue, Sep 15, 2009 at 11:37 AM, David Winsemius
<dwinsem...@comcast.net> wrote:
On Sep 15, 2009, at 11:10 AM, Anirban Mukherjee wrote:
Thanks everyone for your replies. Particularly David.
The numbers are pseudo-random. Repeated calls should/would give the
same output.
As I said, this package is not one with which I have experience. It
has _not_ however the case that repeated calls to (typical?) random
number functions give the same output when called repeatedly:
> rnorm(10)
[1] -0.8740195 2.1827411 -0.1473012 -1.4406262 0.1820631
-1.3151244 -0.4813703 0.8177692
[9] 0.2076117 1.8697418
> rnorm(10)
[1] -0.7725731 0.8696742 -0.4907099 0.1561859 0.5913528
-0.8441891 0.2285653 -0.1231755
[9] 0.5190459 -0.7803617
> rnorm(10)
[1] -0.9585881 -0.0458582 1.1967342 0.6421980 -0.5290280
-1.0735112 0.6346301 0.2685760
[9] 1.5767800 1.0864515
> rnorm(10)
[1] -0.60400852 -0.06611533 1.00787048 1.48289305 0.54658888
-0.67630052 0.52664127 -0.36449997
[9] 0.88039397 0.56929333
I cannot imagine a situation where one would _want_ the output to be
the same on repeated calls unless one reset a seed. Unless perhaps I
am not understanding the meaning of "random" in the financial
domain?
--
David
Currently, Halton works fine when used to just get the
Halton sequence, but the random deviates call is not working in
64 bit
R. For now, I will generate the numbers in 32 bit R, save them and
then load them back in when using 64 bit R. The package maintainers
can look at it if/when they get a chance and/or access to 64 bit R.
Thanks!
Best,
Anirban
On Tue, Sep 15, 2009 at 9:01 AM, David Winsemius <dwinsem...@comcast.net
wrote:
I get very different output from the two versions of Mac OSX R as
well. The 32 bit version puts out a histogram that has an
expected,
almost symmetric unimodal distribution. The 64 bit version
created a
bimodal distribution with one large mode near 0 and another
smaller
mode near 10E+37. Postcript output attached.
--
Anirban Mukherjee | Assistant Professor, Marketing | LKCSB, SMU
5062 School of Business, 50 Stamford Road, Singapore 178899 |
+65-6828-1932
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David Winsemius, MD
Heritage Laboratories
West Hartford, CT
--
Anirban Mukherjee | Assistant Professor, Marketing | LKCSB, SMU
5062 School of Business, 50 Stamford Road, Singapore 178899 |
+65-6828-1932
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