Re: Support for complex data in stats.pearsonr

After the addition of `stats.permutation_test`, `stats.monte_carlo_test`,
and `stats.bootstrap`, the natural next step was to make them easier to use
with statistics that SciPy already defines. IMO, the main question has been
API.

I added a permutation version of `anderson_ksamp` in [3] to resolve [4],
but I wanted to decide on a more longer-term plan before adding that sort
of feature to many other functions.

Some questions to consider:

   - If we want a function like `pearsonr` to perform a permutation test,
   how should the user specify the required information?
      - Parameters `n_resamples` and `random_state` as we did in [3]?
      - A single object with both of these pieces of information (and
      possibly more configuration information) to avoid adding several new
      parameters to the function?
      - Alternatively, should the user just call `permutation_test` with
      the callable as `stats.pearsonr`, and we can automatically choose some
      appropriate settings for the test (e.g. the permutation type)?


   - In many cases, it can also make sense to perform a Monte Carlo test
   using the same statistic.
      - How does the user specify whether to perform the Monte Carlo
      version of the test or the permutation version (e.g. a `method`
parameter)?
      - There is often a natural choice of distribution(s) from which to
      draw Monte Carlo samples (e.g. for a two-sample t-test, draw samples from
      the standard normal). But if one knows something about the
distribution(s)
      from which their data is drawn, it might make sense to customize the test
      using that information but still use the t-statistic. Should there be
      options for that, or at that point, do we just direct the user to use
      `monte_carlo_test` directly?
   - We can ask the same sorts of questions about the `confidence_interval`
   method of `pearsonr` and other functions. For some tests, one can envision
   getting confidence intervals not only via the bootstrap, but also using
   permutation or Monte Carlo ideas!

I'd be happy to discuss this further. I've been interested in this for a
while; I've just put this on the back burner because there are a lot of
questions to answer ahead of time (unless we are OK with every function
re-inventing the interface).

Please feel free to open an issue!

Matt

[3] https://github.com/scipy/scipy/pull/16996
[4] https://github.com/scipy/scipy/issues/9527


On Thu, Feb 16, 2023, 2:01 PM Christopher Cowden <[email protected]>
wrote:

> Hi,
>
> A recent issue [1] brought up the idea of adding support for complex data
> in stats.pearsonr.  It seems like this would be a useful feature,
> especially for folks working in signal processing.  It wouldn't be too
> difficult to implement, see [2].  The current estimation of p-values,
> however, seems to underestimate the significance.  That is, the error rate
> tends to be lower than the p-value.  It would be possible to introduce a
> permutation test to estimate the p-value of the correlation between complex
> numbers.
>
> Is this something worth pursuing?  What do you think of introducing an
> alternative p-value estimation method?
>
> Cheers,
> Chris
>
> [1] https://github.com/scipy/scipy/issues/17518
> [2] https://en.wikipedia.org/wiki/Complex_random_variable
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