distributed and reduced precision bootstrap

[palday]

The idea for the reduced precision bootstrap came out of my work looking at the optimizer/convergence behavior.

• add entry in NEWS.md
• after opening this PR, add a reference and run docs/NEWS-update.jl to update the cross-references.
• I've bumped the version appropriately

[codecov]

Codecov Report

Patch coverage: 100.00% and project coverage change: +0.04 🎉

Comparison is base (491f7a7) 95.64% compared to head (92d0177) 95.68%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #694      +/-   ##
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+ Coverage   95.64%   95.68%   +0.04%     
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  Files          35       35              
  Lines        3190     3225      +35     
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+ Hits         3051     3086      +35     
  Misses        139      139              

Flag	Coverage Δ
current	95.68% <100.00%> (+0.04%)	⬆️
minimum	95.58% <100.00%> (+0.04%)	⬆️
nightly	?

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/MixedModels.jl	100.00% <ø> (ø)
src/bootstrap.jl	94.87% <100.00%> (+0.93%)	⬆️
src/optsummary.jl	100.00% <100.00%> (ø)

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[dmbates]

The example of changing ftol_rel on the parametric bootstrap for the "maximal" kb07 model is most impressive! On my computer it took 33 minutes to generate 1000 samples with the default tolerance, 1 minute with 1e-3 tolerance and 6 minutes with 1e-6. And the conclusions from each of these samples are substantively the same.

[dmbates]

@palday Is there anything in particular that you would like me to concentrate on when reviewing this PR?

[palday]

@dmbates whether the general reduced precision approach is valid statistically.

[dmbates]

@palday Sorry for making commits to your branch rather than creating suggestions. I used to know how to create a suggestion that would just require you to click on a button to accept it but I can't seem to work out how to do that now. After flailing around for far too long, I eventually just made the commits.

[dmbates]

Regarding the validity of allowing more slack in ftol_abs, the whole rationale of the parametric bootstrap is that of drawing a sample from a population of possible parameter values. In everything that we have seen the progress of the iterations is to make big gains initially then settle down to a long, drawn-out validation of being at a local optimum. If we are just generating a sample, a high level of precision of the estimates is unnecessary because it is just one result of several simulated results.

[dmbates]

The check on the nightly version failed to compile some of the dependencies of BSplineKit.jl I saw that on a locally compiled nightly too and I don't think we will need to take action on it.

[dmbates]

Thanks for doing this. I think the optsum_overrides will be very useful.

[palday]

Regarding the validity of allowing more slack in ftol_abs, the whole rationale of the parametric bootstrap is that of drawing a sample from a population of possible parameter values. In everything that we have seen the progress of the iterations is to make big gains initially then settle down to a long, drawn-out validation of being at a local optimum. If we are just generating a sample, a high level of precision of the estimates is unnecessary because it is just one result of several simulated results.

@dmbates Exactly my thoughts! I just wanted a sanity check.

Thanks for the other edits. 😄