Improve Numerical Stability of Bernoulli CDF functions

[andrjohns]

Summary

This PR updates the Bernoulli CDF functions (_cdf, _lcdf, and _lccdf) to operate on the log scale as much as possible, to avoid issues with underflow and resolution around 1

Tests

Additional mix/prob tests have been added to ensure that the gradients aren't impacted (prim behaviour covered by the distribution tests)

Side Effects

N/A

Release notes

Improved numerical stability of Bernoulli CDF functions

Checklist

• [x] Math issue #2783

• [x] Copyright holder: Andrew Johnson

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses: - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause) - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• [x] the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• [x] the code is written in idiomatic C++ and changes are documented in the doxygen

• [x] the new changes are tested

[bob-carpenter]

@andrjohns: please let me know when this is ready to review and merge. Thanks!

[andrjohns]

Thanks @bob-carpenter! This is ready for another look. I've updated the vectorisation by adding a prim implementation of the select function that is currently used by the OpenCL code for the same purpose (ternary operations that can be agnostic between scalar and Eigen inputs)

[andrjohns]

@SteveBronder when you have a minute (no rush at all), can you have a look at this PR? It involves re-implementing the the OpenCL code's select function, so would be great to have eyes on from someone that knows how it should be behaving

[spinkney]

@bob-carpenter are you able to re-review this?

@SteveBronder are you able to double check the opencl select code?

[spinkney]

dismiss the closed/reopened, I hit the trackpad on my laptop by accident

[bob-carpenter]

Thanks for the heads up. I just dismissed my review so that someone else could review it. I still don't feel I understand our new C++ conventions well enough to review PRs.

[SteveBronder]

Sorry didn't have time today but Tuesday I can look at this

[andrjohns]

@SteveBronder I'll add an any() function, since I agree that would be super handy. Should I open a separate PR for the select() and any() functions and tests, or are you happy for me to include them in this one?

[andrjohns]

I'll update this PR once the helper functions from #2852 have been added and merged

[andrjohns]

@SteveBronder would you mind having another look at this when you get a minute? No rush

[WardBrian]

develop tests have been failing in the distribution tests since this was merged (https://jenkins.flatironinstitute.org/blue/organizations/jenkins/Stan%2FMath/detail/develop/194/pipeline/500)

I'm guessing this is due to -DSTAN_TEST_ROW_VECTORS which we don't use in CI for PRs

In file included from test/prob/bernoulli/bernoulli_cdf_00000_generated_ffv_test.cpp:3:
In file included from ./test/prob/test_fixture_distr.hpp:4:
In file included from ./stan/math/mix.hpp:4:
In file included from ./stan/math/mix/meta.hpp:6:
In file included from ./stan/math/fwd/core.hpp:4:
In file included from ./stan/math/fwd/core/fvar.hpp:4:
In file included from ./stan/math/prim/meta.hpp:72:
In file included from ./stan/math/prim/meta/append_return_type.hpp:4:
In file included from ./stan/math/prim/fun/Eigen.hpp:22:
In file included from lib/eigen_3.4.0/Eigen/Dense:1:
In file included from lib/eigen_3.4.0/unsupported/Eigen/../../Eigen/Core:295:
lib/eigen_3.4.0/Eigen/src/Core/PlainObjectBase.h:970:7: error: static_assert failed "INVALID_MATRIX_TEMPLATE_PARAMETERS"
      EIGEN_STATIC_ASSERT((EIGEN_IMPLIES(MaxRowsAtCompileTime==1 && MaxColsAtCompileTime!=1, (int(Options)&RowMajor)==RowMajor)
      ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
lib/eigen_3.4.0/Eigen/src/Core/util/StaticAssert.h:33:40: note: expanded from macro 'EIGEN_STATIC_ASSERT'
    #define EIGEN_STATIC_ASSERT(X,MSG) static_assert(X,#MSG);
                                       ^             ~
lib/eigen_3.4.0/Eigen/src/Core/Map.h:159:30: note: in instantiation of member function 'Eigen::PlainObjectBase<Eigen::Array<stan::math::var_value<double, void>, 1, -1, 0, 1, -1> >::_check_template_params' requested here
      PlainObjectType::Base::_check_template_params();
                             ^
./stan/math/rev/core/arena_matrix.hpp:62:9: note: in instantiation of member function 'Eigen::Map<Eigen::Array<stan::math::var_value<double, void>, 1, -1, 0, 1, -1>, 0, Eigen::Stride<0, 0> >::Map' requested here
      : Base::Map(

@andrjohns are you able to take a look at this soon? Otherwise I think we may need to revert this to unblock our CI

[andrjohns]

Ah damn, yeah I'll have a look now