Feature/issue 2966 add 7 parameter ddm cdf and ccdf

[Franzi2114]

Summary

With this PR the CDF and the CCDF of the 7-parameter diffuion model are added.
See issue #2966
Relates to issue #2822

Tests

We implemented analogous tests as for the PDF

Side Effects

no

Release notes

CDF and CCDF for the 7-parameter diffusion model. Allows modeling truncated and censored data.

Checklist

• Copyright holder: Franziska Henrich, Christoph Klauer

  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/)

• 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)

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

• the new changes are tested

[SteveBronder]

tbc what I made a branch to show what I did

git pull
git checkout wiener_lpdf/test-vals
## These tests pass
python3 ./runTests.py -j20 ./test/unit/math/mix/prob/ -f wiener_full_lcdf
## Some of these tests fail
python3 ./runTests.py -j20 ./test/unit/math/prim/prob/ -f wiener_full_lc

[Franzi2114]

Only your suggested changes above for wiener4_lccdf yielded errors. The changes I made in wiener4_lcdf are all fine.

I changed the lines in winer4_lccdf to the following three lines:

  const auto exponent = -sign(v) * 2.0 * v * a * w;
  auto prob_grad_w = (v != 0) ? exp(LOG_TWO + log(fabs(v)) + log(a) - log1m_exp(exponent)) : ret_t(1 / w);
  prob_grad_w = (v > 0) ? prob_grad_w * exp(exponent) : prob_grad_w;

Now, all tests should pass. Let's see. Then, you can say, what I shall change next.

[Franzi2114]

Hey Steve, now the errors from before should be fixed and the wildcards are deleted. What next?

[Franzi2114]

Hey @SteveBronder, any news?

[Franzi2114]

Hello together, I would kindly like to ask, how we can proceed with this PR?

[Franzi2114]

Hey @SteveBronder, any news on this PR?

[Franzi2114]

Dear @SteveBronder, @andrjohns, @bob-carpenter,

I would kindly like to ask whether it would be possible to continue this PR?

[bob-carpenter]

I'm sorry this got hung up without a response. There's no excuse for us leaving PRs hanging. If they're impossible or too much work, we need to make that clear earlier rather than later.

In the future, please feel free to email me about this kind of thing and I can talk to our devs and try to figure out what's going on: bcarpenter@flatironinstitute.org

[SteveBronder]

Hey! I'm terribly sorry. We've been doing a bunch of stuff to get laplace working in Stan and I kind of got tunnel vision. Honestly I felt like some of the math and robustness checks were above my paygrade so I pinged @andrjohns or @bob-carpenter to have a look at some things here. I'm not totally sure how to continue because I don't think I'm the right reviewer for this at this point

[bob-carpenter]

The C++ in Stan is way too complicated for me, which I find sad because I wrote around half of the first release (@syclik wrote most of the rest). I'm also not enough of a statistician or applied mathematician to even understand what this function is supposed to be doing.

The only two candidates among active Stan developers would be:

• @SteveBronder
• @andrjohns

Though he didn't come out and say this directly, I think you should interpret @SteveBronder's message above as saying he is not going to do it. I don't know how much time @andrjohns has to work on Stan these days. We can see if he responds. Our other C++ developers have all departed for industry.

I wish I could help myself, but I gave up trying to understand or code Stan's C++ code years ago when I couldn't finish a simple PR of my own. I think we've dug ourselves into a deep hole of complexity and I don't see any way out of it other than starting over. I've personally moved to developing samplers outside the context of Stan because integrating anything with Stan is such a headache these days.

I feel terrible that we left you hanging for so long, but I can't think of a way we can review this. In retrospect, we should've realized this was going to be too complex for us due to the form of the density (none of our testing is set up for this many arguments) and the lack of understanding of Wiener processes among our active developers. In the future, we're going to try to do better at telling people their issue isn't one we can support.