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

[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: [email protected]

[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.

[bob-carpenter]

Hi, @Franzi2114 --- could you clean up the conflicts in these files? It looks like they're not just superficial formatting. I'm diving into the code review now.

[bob-carpenter]

For reference, here's a paper defining the partial derivatives of the pdf and cdf:

Hartmann, R. and Klauer, K.C., 2021. Partial derivatives for the first-passage time distribution in Wiener diffusion models. Journal of Mathematical Psychology.

They released an R package with code, wienR.

[bob-carpenter]

Thanks for fixing the conflict.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.34	0.3	1.14	11.9% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.07	6.6% faster
gp_regr/gen_gp_data.stan	0.03	0.02	1.09	8.17% faster
gp_regr/gp_regr.stan	0.1	0.09	1.07	6.27% faster
sir/sir.stan	72.13	68.04	1.06	5.67% faster
irt_2pl/irt_2pl.stan	4.22	3.94	1.07	6.66% faster
eight_schools/eight_schools.stan	0.06	0.05	1.07	6.88% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.24	1.06	6.03% faster
pkpd/one_comp_mm_elim_abs.stan	19.48	18.32	1.06	5.92% faster
garch/garch.stan	0.44	0.4	1.1	8.74% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.86	2.56	1.11	10.25% faster
arK/arK.stan	1.83	1.71	1.07	6.47% faster
gp_pois_regr/gp_pois_regr.stan	2.87	2.67	1.07	6.93% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	9.08	8.33	1.09	8.26% faster
performance.compilation	179.67	178.26	1.01	0.78% faster
Mean result: 1.0763698073841381

---

Jenkins Console Log
Blue Ocean
Commit hash: e4209047880771b486dfe532503f536918e27083

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

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NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78
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Vulnerability Gather data sampling: Mitigation; Microcode
Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled
Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable
Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Meltdown: Mitigation; PTI
Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable
Vulnerability Reg file data sampling: Not affected
Vulnerability Retbleed: Mitigation; IBRS
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl
Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected
Vulnerability Srbds: Not affected
Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable
Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++:
g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0
Copyright (C) 2019 Free Software Foundation, Inc.
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang:
clang version 10.0.0-4ubuntu1
Target: x86_64-pc-linux-gnu
Thread model: posix
InstalledDir: /usr/bin