[Numpy-discussion] Question about numpy.random.choice with probabilties

[Robert Kern]

On Mon, Jan 23, 2017 at 9:41 AM, Nadav Har'El <nyh at scylladb.com> wrote:
>
> On Mon, Jan 23, 2017 at 4:52 PM, alebarde at gmail.com <alebarde at gmail.com>
wrote:
>>
>> 2017-01-23 15:33 GMT+01:00 Robert Kern <robert.kern at gmail.com>:
>>>
>>> I don't object to some Notes, but I would probably phrase it more like
we are providing the standard definition of the jargon term "sampling
without replacement" in the case of non-uniform probabilities. To my mind
(or more accurately, with my background), "replace=False" obviously picks
out the implemented procedure, and I would have been incredibly surprised
if it did anything else. If the option were named "unique=True", then I
would have needed some more documentation to let me know exactly how it was
implemented.
>>>
>> FWIW, I totally agree with Robert
>
> With my own background (MSc. in Mathematics), I agree that this algorithm
is indeed the most natural one. And as I said, when I wanted to implement
something myself when I wanted to choose random combinations (k out of n
items), I wrote exactly the same one. But when it didn't produce the
desired probabilities (even in cases where I knew that doing this was
possible), I wrongly assumed numpy would do things differently - only to
realize it uses exactly the same algorithm. So clearly, the documentation
didn't quite explain what it does or doesn't do.

In my experience, I have seen "without replacement" mean only one thing. If
the docstring had said "returns unique items", I'd agree that it doesn't
explain what it does or doesn't do. The only issue is that "without
replacement" is jargon, and it is good to recapitulate the definitions of
such terms for those who aren't familiar with them.

> Also, Robert, I'm curious: beyond explaining why the existing algorithm
is reasonable (which I agree), could you give me an example of where it is
actually  *useful* for sampling?

The references I previously quoted list a few. One is called "multistage
sampling proportional to size". The idea being that you draw (without
replacement) from a larger units (say, congressional districts) before
sampling within them. It is similar to the situation you outline, but it is
probably more useful at a different scale, like lots of larger units (where
your algorithm is likely to provide no solution) rather than a handful.

It is probably less useful in terms of survey design, where you are trying
to *design* a process to get a result, than it is in queueing theory and
related fields, where you are trying to *describe* and simulate a process
that is pre-defined.

--
Robert Kern
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