[Rd] Extreme bunching of random values from runif with Mersenne-Twister seed

[Serguei Sokol]

Le 05/11/2017 à 15:17, Duncan Murdoch a écrit :
> On 04/11/2017 10:20 PM, Daniel Nordlund wrote:
>> Tirthankar,
>>
>> "random number generators" do not produce random numbers.  Any given
>> generator produces a fixed sequence of numbers that appear to meet
>> various tests of randomness.  By picking a seed you enter that sequence
>> in a particular place and subsequent numbers in the sequence appear to
>> be unrelated.  There are no guarantees that if YOU pick a SET of seeds
>> they won't produce a set of values that are of a similar magnitude.
>>
>> You can likely solve your problem by following Radford Neal's advice of
>> not using the the first number from each seed.  However, you don't need
>> to use anything more than the second number.  So, you can modify your
>> function as follows:
>>
>> function(x) {
>>         set.seed(x, kind = "default")
>>         y = runif(2, 17, 26)
>>         return(y[2])
>>       }
>>
>> Hope this is helpful,
>
> That's assuming that the chosen seeds are unrelated to the function output, which seems unlikely on the face of it.  You can certainly choose a set of seeds 
> that give high values on the second draw just as easily as you can choose seeds that give high draws on the first draw.
To confirm this statement, I did

s2_25=s[sapply(s, function(i) {set.seed(i); runif(2, 17, 26)[2] > 25})]
length(s2_25) # 48990

For memory, we had
length(s25) # 48631 out of 439166

which is much similar length.
So if we take the second or even the 10-th pseudo-random value we can
fall as easily (or as hard) at a seed sequence giving some narrow set.

Serguei.

>
> The interesting thing about this problem is that Tirthankar doesn't believe that the seed selection process is aware of the function output.  I would say that 
> it must be, and he should be investigating how that happens if he is worried about the output, he shouldn't be worrying about R's RNG.
>
> Duncan Murdoch
>
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