Make linear regression the quickstart notebook

[paul-buerkner]

This PR addresses #309 by making the linear regression notebook the quickstart notebook and removing the current WIP quickstart notebook.

If few things we need to do before this can be merged:

• Improve diagnostics plot interfaces as discussed in Rethinking names "targets" and "references" #307 and Diagnostics that can filter keys and configure pretty names #308. Currently, its awkward to select multiple parameters for some of the same plots. I would like to have a simpler parameter selection interface. This notebook could be the test bed.
• Use flow matching instead of coupling flow. I had some errors during inference on my mac this morning so I switched just to run it for now. (Was an issue with JAX and Mac GPUs)

[codecov-commenter]

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Codecov Report

Attention: Patch coverage is 8.18182% with 101 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
bayesflow/utils/dict_utils.py	8.82%	31 Missing ⚠️
bayesflow/diagnostics/plots/pairs_samples.py	12.50%	21 Missing ⚠️
bayesflow/diagnostics/plots/pairs_posterior.py	15.78%	16 Missing ⚠️
bayesflow/diagnostics/plots/recovery.py	0.00%	6 Missing ⚠️
...yesflow/diagnostics/plots/calibration_histogram.py	0.00%	5 Missing ⚠️
bayesflow/diagnostics/plots/z_score_contraction.py	0.00%	5 Missing ⚠️
bayesflow/diagnostics/metrics/calibration_error.py	0.00%	4 Missing ⚠️
bayesflow/diagnostics/plots/calibration_ecdf.py	0.00%	4 Missing ⚠️
...sflow/diagnostics/metrics/posterior_contraction.py	0.00%	3 Missing ⚠️
...low/diagnostics/metrics/root_mean_squared_error.py	0.00%	3 Missing ⚠️
... and 2 more

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Files with missing lines	Coverage Δ
bayesflow/workflows/basic_workflow.py	24.26% <ø> (ø)
bayesflow/utils/plot_utils.py	20.77% <0.00%> (ø)
bayesflow/diagnostics/plots/mc_calibration.py	22.72% <0.00%> (ø)
...sflow/diagnostics/metrics/posterior_contraction.py	40.00% <0.00%> (ø)
...low/diagnostics/metrics/root_mean_squared_error.py	33.33% <0.00%> (ø)
bayesflow/diagnostics/metrics/calibration_error.py	22.22% <0.00%> (ø)
bayesflow/diagnostics/plots/calibration_ecdf.py	14.89% <0.00%> (ø)
...yesflow/diagnostics/plots/calibration_histogram.py	24.24% <0.00%> (ø)
bayesflow/diagnostics/plots/z_score_contraction.py	21.73% <0.00%> (ø)
bayesflow/diagnostics/plots/recovery.py	22.22% <0.00%> (ø)
... and 3 more

... and 1 file with indirect coverage changes

[paul-buerkner]

I have made some progress in making the diagnostic plots prettier and easier to use. Specifically, I added back the filter_keys. We should also discuss the name of this but I will make more edits first.

I know it's not super clean that I will put all of this in one PR but I don't have the time to make both the starter notebook pretty and fix all the plots at the same time if they are not on the same branch.

[paul-buerkner]

More updates. I have now cleaned up the interface of the diagnostics and some of the related backend code.

In particular, pairs_posterior is now much less awkward to use. For example, previously we would have had to do something like:

draws_stacked = bf.utils.dict_utils.dicts_to_arrays(
    post_draws, val_sims,
)

f = bf.diagnostics.plots.pairs_posterior(
    post_samples = draws_stacked["targets"][0], 
    true_params = draws_stacked["references"][0],
)

which also required users to know the deeply hidden function bf.utils.dict_utils.dicts_to_arrays. Now, we can just write:

f = bf.diagnostics.plots.pairs_posterior(
    post_draws, val_sims,
    dataset_id=0,
)

So the interface of pairs_posteriors is now the same as that of the other diagnostics for NPE except that is does require the dataset_id argument because it can only handle the posterior of a single dataset at once.

Tomorrow, I will work on the renamining. Here is the summary of what I propose to rename, must of which we discussed already:

• targets -> estimates
• references -> targets
• filter_keys -> variable_keys
• pretty naming will be continue to done via variable_names

You can check all the current diagnostics at work in the updated linear regression notebook on this branch.

I would love to hear your thoughts and comments :-)

[paul-buerkner]

This PR is now ready for review. It closes #307, #308, and #309.

@stefanradev93 would you mind taking a look and merging if you are happy?

I left some remaining ToDos in the code, which would further improve the plots but are not essential at the moment. I will take care of them at a later point.

[LarsKue]

Made some adjustments with feedback from @paul-buerkner. IMO, the notebook looks great. Ready to merge from my side @stefanradev93.