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 <[email protected]> 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 <[email protected] >> > 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 >> >> _______________________________________________ >> R-SIG-Mac mailing list >> [email protected] >> https://stat.ethz.ch/mailman/listinfo/r-sig-mac > > 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 _______________________________________________ R-SIG-Mac mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-mac
