Add quantile function for Student-T distribution #3211

andrjohns · 2025-06-19T14:24:04Z

Summary

This PR adds the (vectorised) student-t quantile function with signature:

reals student_t_qf(reals p, reals nu, reals mu, reals sigma)

The current implementation directly estimates the quantile using the inverse of the incomplete beta, but implementing approximations (like those used by R) are a planned future improvement

Tests

Both prim and mix tests (using the AD framework) are added

Side Effects

An additional utility type has been added: common_container_type to detect the right container type to return for vectorised inputs.

Release notes

Added quantile function for student-t distribution

Checklist

Copyright holder: Andrew Johnson

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 · 2025-06-20T06:48:43Z

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.33	0.38	0.89	-12.78% slower
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.01	0.86% faster
gp_regr/gen_gp_data.stan	0.02	0.02	1.07	6.57% faster
gp_regr/gp_regr.stan	0.09	0.09	1.07	6.17% faster
sir/sir.stan	70.97	67.96	1.04	4.24% faster
irt_2pl/irt_2pl.stan	4.2	3.95	1.06	6.1% faster
eight_schools/eight_schools.stan	0.06	0.05	1.05	4.48% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.24	1.04	4.17% faster
pkpd/one_comp_mm_elim_abs.stan	20.2	18.71	1.08	7.41% faster
garch/garch.stan	0.43	0.41	1.04	4.09% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.75	2.63	1.04	4.23% faster
arK/arK.stan	1.82	1.74	1.05	4.46% faster
gp_pois_regr/gp_pois_regr.stan	2.94	2.75	1.07	6.69% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.85	9.91	0.89	-11.94% slower
performance.compilation	177.48	177.46	1.0	0.01% faster
Mean result: 1.0273234881588633

Jenkins Console Log
Blue Ocean
Commit hash: 9d0e74af54c729b15ce95fcce935a889c4306822

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

spinkney · 2025-06-26T10:21:08Z

Thanks @andrjohns for tackling this! Do you happen to know any particular ranges which are problematic for the current implementation?

andrjohns · 2025-06-26T11:10:47Z

Thanks @andrjohns for tackling this! Do you happen to know any particular ranges which are problematic for the current implementation?

I haven't done any proper testing at this point, it was more just getting an initial implementation in to be refined. Because it's just directly estimating, I'd say that the problematic ranges for both the values and gradients are going to mostly match those for boost's incomplete beta inverse

Definitely want to move to more stable approximations for both the gradient and value at some point though!

andrjohns · 2025-06-27T08:29:45Z

@spinkney on a semi-related note - after being annoyed by the need to compile c++ whenever I'm validating against Boost's Math functions, I've started exposing them in an R package: https://github.com/andrjohns/boostmath

Just an FYI in case it helps with any of your validation/testing as well!

spinkney · 2025-06-28T19:03:25Z

That's great!

SteveBronder

Sorry this took so long for me to look at. Looks good imo!

Should we have a higher order function to be able to call this with vectors?

SteveBronder · 2025-09-23T18:55:33Z

stan/math/prim/prob/student_t_qf.hpp

+template <typename T_p, typename T_nu, typename T_mu, typename T_sigma,
+          typename T_container = common_container_t<T_p, T_nu, T_mu, T_sigma>,
+          require_any_vector_t<T_p, T_nu, T_mu, T_sigma>* = nullptr,
+          require_not_t<std::is_void<T_container>>* = nullptr>


What is this line doing?

SteveBronder · 2025-09-23T18:57:19Z

stan/math/rev/prob/student_t_qf.hpp

+template <typename T_p, typename T_nu, typename T_mu, typename T_sigma,
+          require_all_stan_scalar_t<T_p, T_mu, T_sigma, T_nu>* = nullptr,
+          require_any_var_t<T_p, T_mu, T_sigma, T_nu>* = nullptr>
+var student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,


Suggested change

var student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

inline var student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

SteveBronder · 2025-09-23T18:59:16Z

stan/math/rev/prob/student_t_qf.hpp

+      Eigen::VectorXd hyper_arg_a(3);
+      hyper_arg_a << 0.5, half_nu, half_nu;
+      Eigen::VectorXd hyper_arg_b(2);
+      hyper_arg_b << 1 + half_nu, 1 + half_nu;


Suggested change

Eigen::VectorXd hyper_arg_a(3);

hyper_arg_a << 0.5, half_nu, half_nu;

Eigen::VectorXd hyper_arg_b(2);

hyper_arg_b << 1 + half_nu, 1 + half_nu;

Eigen::VectorXd hyper_arg_a{{0.5, half_nu, half_nu}};

Eigen::VectorXd hyper_arg_b{{1 + half_nu, 1 + half_nu}};

SteveBronder · 2025-09-23T19:00:37Z

stan/math/prim/prob/student_t_qf.hpp

+          typename T_container = common_container_t<T_p, T_nu, T_mu, T_sigma>,
+          require_any_vector_t<T_p, T_nu, T_mu, T_sigma>* = nullptr,
+          require_not_t<std::is_void<T_container>>* = nullptr>
+auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,


inline for functions so we can have multiple definitions of the same function across compilation units

Suggested change

auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

inline auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

andrjohns and others added 9 commits June 19, 2025 13:50

Initial implementation

76ba303

Compile fixs

f8c6701

Initial tests

d8ba50c

Working scalar implementations

44aed3e

Proper container

bd9e001

Update doc

774cd41

[Jenkins] auto-formatting by clang-format version 10.0.0-4ubuntu1

f0174e6

Dynamic

63004a7

[Jenkins] auto-formatting by clang-format version 10.0.0-4ubuntu1

332c74f

SteveBronder requested changes Sep 23, 2025

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Add quantile function for Student-T distribution #3211

Add quantile function for Student-T distribution #3211

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andrjohns commented Jun 19, 2025

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spinkney commented Jun 26, 2025

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	var student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,
	inline var student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

	auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,
	inline auto student_t_qf(const T_p& p, const T_nu& nu, const T_mu& mu,

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Add quantile function for Student-T distribution #3211

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Conversation

andrjohns commented Jun 19, 2025

Summary

Tests

Side Effects

Release notes

Checklist

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stan-buildbot commented Jun 20, 2025

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spinkney commented Jun 26, 2025

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andrjohns commented Jun 26, 2025

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