[Rd] portable parallel seeds project: request for critiques

[Thomas Lumley]

On Sat, Feb 18, 2012 at 4:33 PM, Paul Johnson <pauljohn32 at gmail.com> wrote:
> On Fri, Feb 17, 2012 at 5:06 PM, Petr Savicky <savicky at cs.cas.cz> wrote:
>> On Fri, Feb 17, 2012 at 02:57:26PM -0600, Paul Johnson wrote:
>> Hi.
>>
>> Some of the random number generators allow as a seed a vector,
>> not only a single number. This can simplify generating the seeds.
>> There can be one seed for each of the 1000 runs and then,
>> the rows of the seed matrix can be
>>
>>  c(seed1, 1), c(seed1, 2), ...
>>  c(seed2, 1), c(seed2, 2), ...
>>  c(seed3, 1), c(seed3, 2), ...
>>  ...
>>
> Yes, I understand.
>
> The seed things I'm using are the 6 integer values from the L'Ecuyer.
> If you run the example script, the verbose option causes some to print
> out.  The first 3 seeds in a saved project seeds file looks like:
>
>> projSeeds[[1]]
> [[1]]
> [1]         407   376488316  1939487821  1433925148 -1040698333   579503880
> [7] -624878918
>
> [[2]]
> [1]         407 -1107332181   854177397  1773099324  1774170776  -266687360
> [7] 816955059
>
> [[3]]
> [1]         407   936506900 -1924631332 -1380363206  2109234517  1585239833
> [7] -1559304513
>
> The 407 in the first position is an integer R uses to note the type of
> stream for which the seed is intended, in this case R'Lecuyer.
>
>
>
>
>
>> There could be even only one seed and the matrix can be generated as
>>
>>  c(seed, 1, 1), c(seed, 1, 2), ...
>>  c(seed, 2, 1), c(seed, 2, 2), ...
>>  c(seed, 3, 1), c(seed, 3, 2), ...
>>
>> If the initialization using the vector c(seed, i, j) is done
>> with a good quality hash function, the runs will be independent.
>>
> I don't have any formal proof that a "good quality hash function"
> would truly create seeds from which independent streams will be drawn.

That is essentially the *definition* of a good quality hash function,
at least in the cryptographic sense.  It maps the inputs into numbers
that are indistinguishable from uniform random except that the same
input always gives the same output.

What's harder is to prove that you *have* a good quality hash
function, but for these (non-adversarial) purposes even something like
MD4 would be fine, and certainly the SHA family.

    -thomas

-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland