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add beta_neg_binomial_lcdf #3116

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lingium
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@lingium lingium commented Oct 27, 2024

Summary

With this PR the lcdf of beta negative binomial distribution are added.
See issue #3115

Fix a few typos in beta_neg_binomial_lccdf, pr #3114.

Expressions involved (almost the same as #3114 , just add the chain rule from log ccdf to log cdf):

$$ \begin{align} & P(Y \leq y) = F(r,\alpha,\beta) = 1-C(r,\alpha,\beta) = 1-\frac{\Gamma (r+y +1) B(r+\alpha ,\beta +y +1) {}_3F_2(...)}{\Gamma (r) B(\alpha ,\beta ) \Gamma (y +2)} \end{align} $$

where $C(r,\alpha,\beta)$ is ccdf, we denote ${}_3F_2({1,r+y +1,\beta +y +1}; {y +2,r+\alpha +\beta +y +1};1)$ as ${}_3F_2(...)$

Then the partial derivatives w.r.t log ccdf:

$$ \begin{align} \frac{\partial \log C(r,\alpha,\beta)}{\partial r} &= \psi(r+y+1) + \psi(\alpha+r) - \psi(\alpha+\beta+r+y+1) - \psi(r) + \frac{\partial \log {}_3F_2(...)}{\partial r}, \\ \frac{\partial \log C(r,\alpha,\beta)}{\partial \alpha} &= \psi(\alpha+r) - \psi(\alpha+\beta+r+y+1) + \frac{\partial \log {}_3F_2(...)}{\partial \alpha} - \psi(\alpha) + \psi(\alpha+\beta), \\ \frac{\partial \log C(r,\alpha,\beta)}{\partial \beta} &= \psi(\beta+y+1) - \psi(\alpha+\beta+r+y+1) + \frac{\partial \log {}_3F_2(...)}{\partial \beta} - \psi(\beta) + \psi(\alpha+\beta). \end{align} $$

where

$$ \begin{align} \frac{\partial \log {}_3F_2(...)}{\partial r} &= \frac{\partial {}_3F_2(...)}{\partial r} / {}_3F_2(...) \\ &= \left[ _3F_2(...)^{({0,1,0},{0,0},0)}(...) + _3F_2(...)^{({0,0,0},{0,1},0)}(...) \right] / _3F_2(...), \\ \frac{\partial \log {}_3F_2(...)}{\partial \alpha} &= {}_3F_2(...)^{({0,0,0},{0,1},0)}(...) / {}_3F_2(...), \\ \frac{\partial \log {}_3F_2(...)}{\partial \beta} &= \left[ _3F_2(...)^{({0,0,1},{0,0},0)}(...) + _3F_2(...)^{({0,0,0},{0,1},0)}(...) \right] / _3F_2(...). \end{align} $$

By chain rule,

$$ \begin{align} \frac{\partial \log F(r,\alpha,\beta)}{\partial r} &= - \frac{1}{F(r,\alpha,\beta)} \cdot \frac{\partial C(r,\alpha,\beta)}{\partial r} &= - \frac{C(r,\alpha,\beta)}{1-C(r,\alpha,\beta)} \cdot \frac{\partial \log C(r,\alpha,\beta)}{\partial r} \end{align} $$

Therefore, the partial derivatives w.r.t log cdf:

$$ \begin{align} \frac{\partial \log F(r,\alpha,\beta)}{\partial r} &= - \frac{C(r,\alpha,\beta)}{1-C(r,\alpha,\beta)} \cdot\frac{\partial \log C(r,\alpha,\beta)}{\partial r} , \\ \frac{\partial \log F(r,\alpha,\beta)}{\partial \alpha} &= - \frac{C(r,\alpha,\beta)}{1-C(r,\alpha,\beta)} \cdot\frac{\partial \log C(r,\alpha,\beta)}{\partial \alpha}, \\ \frac{\partial \log F(r,\alpha,\beta)}{\partial \beta} &= - \frac{C(r,\alpha,\beta)}{1-C(r,\alpha,\beta)} \cdot\frac{\partial \log C(r,\alpha,\beta)}{\partial \beta}. \end{align} $$

Tests

Test is written follow the guide.

Side Effects

No.

Release notes

beta_neg_binomial_lcdf is available if merged.

Checklist

  • Copyright holder: Zhi Ling

    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

@WardBrian
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@lingium while it is very useful to keep each feature in a separate PR (thanks for doing this!), if you do have multiple things you want to add you can open several PRs at once, which might help with review lag-time. I think you said you also have an RNG for this distribution, and if so feel free to open a separate PR before this one is merged

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lingium commented Oct 28, 2024

Hi @WardBrian , got you, Just thought this modification is too minor so I didn't open another PR. I'll make sure to open separate PRs for different things next time. Yes, there is a RNG. I can open it in parallel.
BTW I'm encountering problems adding signatures to the compiler, still trying to understand the OCaml thing. Would you mind me to submit a PR anyway later and then you can tell me where the problem lies?

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Name Old Result New Result Ratio Performance change( 1 - new / old )
arma/arma.stan 0.36 0.34 1.06 5.88% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.11 9.64% faster
gp_regr/gen_gp_data.stan 0.03 0.02 1.09 8.0% faster
gp_regr/gp_regr.stan 0.1 0.09 1.08 7.79% faster
sir/sir.stan 70.01 71.92 0.97 -2.73% slower
irt_2pl/irt_2pl.stan 4.19 4.27 0.98 -1.8% slower
eight_schools/eight_schools.stan 0.06 0.06 1.01 1.2% faster
pkpd/sim_one_comp_mm_elim_abs.stan 0.25 0.26 0.98 -2.41% slower
pkpd/one_comp_mm_elim_abs.stan 19.44 19.39 1.0 0.25% faster
garch/garch.stan 0.43 0.41 1.06 5.6% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.81 2.6 1.08 7.64% faster
arK/arK.stan 1.8 1.7 1.06 5.47% faster
gp_pois_regr/gp_pois_regr.stan 2.84 2.69 1.06 5.31% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.73 8.47 1.03 3.03% faster
performance.compilation 182.14 179.64 1.01 1.37% faster
Mean result: 1.039233657339016

Jenkins Console Log
Blue Ocean
Commit hash: c148b0c9a356ceda75f6c6ee381d5d8ffc12bca0


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

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 3372.909
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
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
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
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

SteveBronder
SteveBronder previously approved these changes Oct 30, 2024
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No notes!

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Blocking the merge on the test speed

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Name Old Result New Result Ratio Performance change( 1 - new / old )
arma/arma.stan 0.36 0.33 1.07 6.96% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.05 5.15% faster
gp_regr/gen_gp_data.stan 0.03 0.02 1.1 8.75% faster
gp_regr/gp_regr.stan 0.1 0.09 1.07 6.12% faster
sir/sir.stan 70.13 70.71 0.99 -0.83% slower
irt_2pl/irt_2pl.stan 4.12 4.09 1.01 0.63% faster
eight_schools/eight_schools.stan 0.06 0.06 1.03 3.17% faster
pkpd/sim_one_comp_mm_elim_abs.stan 0.25 0.26 0.95 -5.43% slower
pkpd/one_comp_mm_elim_abs.stan 19.44 19.19 1.01 1.27% faster
garch/garch.stan 0.44 0.52 0.84 -18.76% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.7 2.66 1.01 1.39% faster
arK/arK.stan 1.8 1.74 1.03 3.24% faster
gp_pois_regr/gp_pois_regr.stan 2.82 2.73 1.03 3.21% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.93 8.57 1.04 4.03% faster
performance.compilation 182.14 180.79 1.01 0.74% faster
Mean result: 1.0169765867864264

Jenkins Console Log
Blue Ocean
Commit hash: b88ac6535111d0a72e585fc78fc4fa664aeadc51


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

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 2400.000
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
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
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
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

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Thanks, looks good!

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Name Old Result New Result Ratio Performance change( 1 - new / old )
arma/arma.stan 0.35 0.33 1.06 5.45% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.04 4.25% faster
gp_regr/gen_gp_data.stan 0.03 0.02 1.18 14.92% faster
gp_regr/gp_regr.stan 0.09 0.09 1.06 5.47% faster
sir/sir.stan 69.89 73.24 0.95 -4.79% slower
irt_2pl/irt_2pl.stan 4.13 4.24 0.97 -2.56% slower
eight_schools/eight_schools.stan 0.06 0.06 0.99 -0.51% slower
pkpd/sim_one_comp_mm_elim_abs.stan 0.25 0.28 0.89 -12.33% slower
pkpd/one_comp_mm_elim_abs.stan 19.4 19.34 1.0 0.29% faster
garch/garch.stan 0.44 0.4 1.08 7.72% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.72 2.58 1.05 4.91% faster
arK/arK.stan 1.85 1.7 1.09 8.22% faster
gp_pois_regr/gp_pois_regr.stan 2.78 2.67 1.04 3.93% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.84 8.49 1.04 3.87% faster
performance.compilation 178.79 185.38 0.96 -3.69% slower
Mean result: 1.0282088496373505

Jenkins Console Log
Blue Ocean
Commit hash: b88ac6535111d0a72e585fc78fc4fa664aeadc51


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

CPU:
Architecture: x86_64
CPU op-mode(s): 32-bit, 64-bit
Byte Order: Little Endian
Address sizes: 46 bits physical, 48 bits virtual
CPU(s): 80
On-line CPU(s) list: 0-79
Thread(s) per core: 2
Core(s) per socket: 20
Socket(s): 2
NUMA node(s): 2
Vendor ID: GenuineIntel
CPU family: 6
Model: 85
Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz
Stepping: 4
CPU MHz: 2400.000
CPU max MHz: 3700.0000
CPU min MHz: 1000.0000
BogoMIPS: 4800.00
Virtualization: VT-x
L1d cache: 1.3 MiB
L1i cache: 1.3 MiB
L2 cache: 40 MiB
L3 cache: 55 MiB
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
NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79
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

@lingium lingium merged commit 7ada875 into stan-dev:develop Nov 1, 2024
8 checks passed
@lingium lingium deleted the feature/issue-3115-beta-neg-binomial-lcdf branch November 1, 2024 03:56
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