add beta_neg_binomial_cdf #3120

lingium · 2024-11-01T04:48:29Z

Summary

With this PR the cdf of beta negative binomial distribution are added.
See issue #3119

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

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

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

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

Then the function adjust for the formula for the derivative of a product since cdf([a, a, a]) == cdf(a) * cdf(a) * cdf(a).

Tests

Test is written follow the guide.

Side Effects

No.

Release notes

beta_neg_binomial_cdf is available if merged.

Checklist

Copyright holder: (fill in copyright holder information)

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

stan-buildbot · 2024-11-01T10:48:57Z

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.37	0.41	0.9	-10.86% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.05	5.16% faster
gp_regr/gen_gp_data.stan	0.03	0.03	1.09	8.16% faster
gp_regr/gp_regr.stan	0.12	0.1	1.22	18.02% faster
sir/sir.stan	71.85	72.38	0.99	-0.74% slower
irt_2pl/irt_2pl.stan	4.28	4.15	1.03	3.07% faster
eight_schools/eight_schools.stan	0.06	0.06	1.02	1.91% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.26	0.27	0.96	-3.99% slower
pkpd/one_comp_mm_elim_abs.stan	20.78	19.56	1.06	5.89% faster
garch/garch.stan	0.47	0.42	1.11	10.24% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.84	2.66	1.07	6.62% faster
arK/arK.stan	1.9	1.75	1.09	8.04% faster
gp_pois_regr/gp_pois_regr.stan	2.95	2.79	1.06	5.32% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	9.27	8.6	1.08	7.19% faster
performance.compilation	194.56	189.98	1.02	2.35% faster
Mean result: 1.05088945601077

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

SteveBronder

One big Q but everything else looks good

SteveBronder · 2024-11-11T20:09:34Z

stan/math/prim/prob/beta_neg_binomial_cdf.hpp

+        1.0);
+    auto C = lgamma(r_plus_n + 1.0) + lbeta(a_plus_r, b_plus_n + 1.0)
+             - lgamma(r_dbl) - lbeta(alpha_dbl, beta_dbl) - lgamma(n_dbl + 2.0);
+    auto ccdf = stan::math::exp(C) * F;


How is this for large values of C? Would it be better to do this calculation on the log scale and then exp the end result? i.e. stan::math::exp(C + log(F)). Or can F be <= 0?

You're right, stan::math::exp(C + log(F)) is indeed a better way. Will change it.

SteveBronder · 2024-11-11T20:10:23Z

stan/math/prim/prob/beta_neg_binomial_cdf.hpp

+          auto partial_lccdf = digamma(r_plus_n + 1.0)
+                               + (digamma_r_alpha - digamma_n_r_alpha_beta)
+                               + (dF[2] + dF[4]) / F - digamma(r_dbl);
+          partials<0>(ops_partials)[i] += partial_lccdf * chain_rule_term;


imo I think it's find to just have one line for this

Same for the other partial accumulations

Will move them in one line

stan/math/prim/prob/beta_neg_binomial_cdf.hpp

SteveBronder

Good!

stan-buildbot · 2024-11-14T05:51:18Z

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.36	0.33	1.08	7.71% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.02	2.32% faster
gp_regr/gen_gp_data.stan	0.03	0.03	1.07	6.23% faster
gp_regr/gp_regr.stan	0.1	0.09	1.04	3.8% faster
sir/sir.stan	69.71	71.41	0.98	-2.44% slower
irt_2pl/irt_2pl.stan	4.18	4.02	1.04	3.81% faster
eight_schools/eight_schools.stan	0.06	0.06	1.03	2.85% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.25	1.02	1.66% faster
pkpd/one_comp_mm_elim_abs.stan	19.54	19.03	1.03	2.58% faster
garch/garch.stan	0.43	0.41	1.06	5.65% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.71	2.61	1.04	3.55% faster
arK/arK.stan	1.79	1.72	1.04	3.68% faster
gp_pois_regr/gp_pois_regr.stan	2.79	2.73	1.02	1.93% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.77	8.36	1.05	4.69% faster
performance.compilation	180.62	177.62	1.02	1.66% faster
Mean result: 1.0348313406745062

Jenkins Console Log
Blue Ocean
Commit hash: 33e2a9b0643b749c04e63d6ae4d820d17920d0d6

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

SteveBronder

Thanks!

add beta_neg_binomial_cdf

fe8055d

WardBrian requested a review from SteveBronder November 6, 2024 17:50

SteveBronder requested changes Nov 11, 2024

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SteveBronder previously approved these changes Nov 12, 2024

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fix issues

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lingium dismissed SteveBronder’s stale review via 9594228 November 13, 2024 14:52

fix issues

9750889

WardBrian requested a review from SteveBronder November 13, 2024 17:03

WardBrian mentioned this pull request Nov 14, 2024

Expose beta_neg_binomial_lccdf, beta_neg_binomial_lcdf, beta_neg_binomial_cdf stan-dev/stanc3#1459

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add beta_neg_binomial_cdf #3120

add beta_neg_binomial_cdf #3120

lingium commented Nov 1, 2024

stan-buildbot commented Nov 1, 2024

SteveBronder left a comment

SteveBronder Nov 11, 2024

lingium Nov 12, 2024

SteveBronder Nov 11, 2024

SteveBronder Nov 11, 2024

lingium Nov 12, 2024

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stan-buildbot commented Nov 14, 2024

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add beta_neg_binomial_cdf #3120

add beta_neg_binomial_cdf #3120

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lingium commented Nov 1, 2024

Summary

Tests

Side Effects

Release notes

Checklist

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