describes modeling various statisticy
things this way, like tree growth and the monty hall problem, I think it's
likely this is applicable to monte carlo processes as well.
thomas.
Paul Johnson <paul@cogito.org.uk> Sent by: haskell-cafe-bounces@haskell.org
08/15/2007 02:38 PM
To
Chad Scherrer <chad.scherrer@gmail.com>
cc
haskell-cafe@haskell.org
Subject
Re: [Haskell-cafe] monte carlo trouble
Chad Scherrer wrote:
> There's a problem I've been struggling with for a long time...
>
> I need to build a function
> buildSample :: [A] -> State StdGen [(A,B,C)]
>
> given lookup functions
> f :: A -> [B]
> g :: A -> [C]
>
> The idea is to first draw randomly form the [A], then apply each
> lookup function and draw randomly from the result of each.
>
I don't understand why this returns a list of triples instead of a
single triple. Your description below seems to imply the latter.
You should probably look at the "Gen" monad in Test.QuickCheck,
which is
basically a nice implementation of what you are doing with "State
StdGen" below. Its "elements" function gets a single
random element,
and you can combine it with replicateM to get a list of defined length.
(BTW, are you sure want multiple random samples rather than a shuffle?
A shuffle has each element exactly once whereas multiple random samples
can pick any element an arbitrary number of times. I ask because
shuffles are a more common requirement. For the code below I'll assume
you meant what you said.)
Using Test.QuickCheck I think you want something like this (which I have
not tested):
buildSample :: [A] -> Gen (A,B,C)
buildSample xs = do
x <- elements xs
f1 <- elements $ f x
g1 <- elements $ g x
return
If you want n such samples then I would suggest
samples <- replicateM n $ buildSample xs
> It's actually slightly more complicated than this, since for the real
> problem I start with type [[A]], and want to map buildSample over
> these, and sample from the results.
>
> There seem to be so many ways to deal with random numbers in Haskell.
>
Indeed.
> After some false starts, I ended up doing something like
>
> sample :: [a] -> State StdGen [a]
> sample [] = return []
> sample xs = do
> g <- get
> let (g', g'') = split g
> bds = (1, length xs)
> xArr = listArray bds xs
> put g''
> return . map (xArr !) $ randomRs bds g'
>
Not bad, although you could instead have a sample function that returns
a single element and then use replicateM to get a list.
> buildSample xs = sample $ do
> x <- xs
> y <- f x
> z <- g x
> return (x,y,z)
>
> This is really bad, since it builds a huge array of all the
> possibilities and then draws from that. Memory is way leaky right
now.
> I'd like to be able to just have it apply the lookup functions as
> needed.
>
> Also, I'm still using GHC 6.6, so I don't have
> Control.Monad.State.Strict. Not sure how much difference this makes,
> but I guess I could just copy the source for that module if I need
to.
>
Strictness won't help. In fact you would be better with laziness
if
that were possible (which it isn't here). The entire array has to
be
constructed before you can look up any elements in it. That forces
the
entire computation. But compare your implementation of buildSample
to
mine.
Paul.
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