Thomas Hartman thomas.hartman at db.com
Wed Aug 15 14:52:51 EDT 2007

```have you looked at pfp, the haskell "probabilistic functional programming
library "?

http://web.engr.oregonstate.edu/~erwig/pfp/

the paper

http://web.engr.oregonstate.edu/~erwig/papers/abstracts.html#JFP06a

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 at cogito.org.uk>
08/15/2007 02:38 PM

To
cc
Subject

> 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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