Laplace: Add mean argument to helper distributions

[WardBrian]

Summary

Closes #3202. Note that this is branched off of #3209, since doing the two changes independently would lead to a great many merge conflicts.

Tests

Existing tests updated to pass 0 as the mean. It would be nice to add some tests with a non-zero mean, if there are suggestions (@avehtari @charlesm93)

Side Effects

Release notes

Checklist

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  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

[avehtari]

This example https://discourse.mc-stan.org/t/embedded-laplace-numerical-problem/39700 uses non-zero mean (mu) and Poisson. So with the helper it should look something like (not certain what is the argument order now)

laplace_marginal_poisson_log_lpmf(y | mu, [1], cov_fun, (sigmaz, N), theta_0)

[WardBrian]

Thanks @avehtari.

Writing that test made me realize something else: The y_index argument to laplace_marginal_poisson_log_lpmf is currently 0-indexed rather than 1-indexed. Is that intentional @charlesm93 @SteveBronder?

[charlesm93]

Writing that test made me realize something else: The y_index argument to laplace_marginal_poisson_log_lpmf is currently 0-indexed rather than 1-indexed. Is that intentional @charlesm93 @SteveBronder?

It should be 1-indexed to be consistent with the rest of Stan.

[WardBrian]

@charlesm93 y_index is now 1-indexed and I removed the newly redundant poisson_2_log helper

[WardBrian]

@SteveBronder similar to the last PR, the tests for math are passing, the failure is just because the compiler update needs to be merged simultaneously. So this is ready to review

[WardBrian]

@SteveBronder https://github.com/stan-dev/stanc3/pull/1523 still needs to be reviewed as well so they can be merged together