experimental: support for power spectrum data

[wcxve]

Summary by Sourcery

This pull request introduces support for power spectrum data analysis by implementing the Whittle likelihood function. It includes a custom exponential distribution (BetterExponential) and integrates the new likelihood into the existing inference and plotting framework. It also adds a check to ensure that the quantile residuals are finite.

New Features:

• Adds support for the Whittle likelihood function, enabling power spectrum (periodogram) analysis.

Enhancements:

• Introduces a BetterExponential distribution for improved handling of exponential distributions in the context of the Whittle likelihood.

Tests:

• Adds an assertion to check that the quantile residuals are finite.

[sourcery-ai]

Reviewer's Guide by Sourcery

This pull request introduces support for the Whittle likelihood, enabling the analysis of power spectrum data. It includes a new likelihood function, a custom exponential distribution, and updates to data handling, simulation, and plotting functions to accommodate the new statistic.

Updated class diagram for Statistic enum

classDiagram
    class Statistic {
      <<enumeration>>
      chi2
      cstat
      pstat
      pgstat
      wstat
      whittle
    }

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File-Level Changes

Change	Details	Files
Added support for the 'whittle' statistic for power spectrum data, including a new likelihood function and modifications to data handling and simulation.	Added 'whittle' to the Statistic type. Implemented the whittle likelihood function. Added a BetterExponential distribution for use with the Whittle likelihood. Modified get_counts_data to handle 'whittle' statistic. Added 'exp' as a possible distribution for data simulation. Updated simulate to include the whittle likelihood. Modified get_stat to include a check for the validity of using the whittle statistic. Modified _pearson_residuals to handle 'whittle' statistic. Modified quantile_residuals_mle to assert that the residuals are finite. Modified pit to handle 'whittle' statistic.	src/elisa/infer/likelihood.py src/elisa/infer/helper.py src/elisa/plot/data.py src/elisa/infer/fit.py

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[sourcery-ai]

Hey @wcxve - I've reviewed your changes - here's some feedback:

Overall Comments:

• Consider adding a short example demonstrating how to use the new whittle likelihood.
• The BetterExponential class could be simplified by directly calculating the log probability instead of using jnp.log.

Here's what I looked at during the review

• 🟢 General issues: all looks good
• 🟢 Security: all looks good
• 🟢 Testing: all looks good
• 🟢 Complexity: all looks good
• 🟢 Documentation: all looks good

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