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[On hold] New formulas for derivatives of neg_binomial_lpmf after alpha cutoff #1579

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[On hold] New formulas for derivatives of neg_binomial_lpmf after alpha cutoff #1579

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3cf0219
Failing test for derivatives (adapted from PR #1497)
martinmodrak Jan 3, 2020
352e7f3
New formulas for derivatives after alpha cutoff
martinmodrak Jan 3, 2020
d900db6
Fixed typo in test
martinmodrak Jan 3, 2020
095974e
[Jenkins] auto-formatting by clang-format version 5.0.0-3~16.04.1 (ta…
stan-buildbot Jan 3, 2020
1188e91
Merge remote-tracking branch 'stan-dev/develop' into bugfix/1578-neg_…
martinmodrak Jan 6, 2020
ce88c83
Fixed for boost 1.72, tightened test accuracy
martinmodrak Jan 6, 2020
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[Jenkins] auto-formatting by clang-format version 5.0.0-3~16.04.1 (ta… 
…gs/RELEASE_500/final)
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stan-buildbot committed Jan 3, 2020
commit 095974e718e145215f3fad55fe4c5f6ee03a4f59
6 changes: 3 additions & 3 deletions stan/math/prim/prob/neg_binomial_lpmf.hpp
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Expand Up @@ -111,8 +111,8 @@ return_type_t<T_shape, T_inv_scale> neg_binomial_lpmf(const T_n& n,
if (alpha_vec[i] > internal::neg_binomial_alpha_cutoff) {
// reduces numerically to Poisson
// The derivatives are obtained via Taylor series at alpha -> Inf
// via Mathematica as:
// nb[n_,alpha_,beta_]:= LogGamma[n + alpha] - LogGamma[n + 1] -
// via Mathematica as:
// nb[n_,alpha_,beta_]:= LogGamma[n + alpha] - LogGamma[n + 1] -
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I don't think we should assume the readers of comments understand mathematica. So this should be put in Stan notation or just eliminated. I couldn't understand what LogGamma is or Log or D. If these comments stay, the functions used need to be explained.

// LogGamma[alpha ] + alpha * Log[beta/ (1 + beta)] - n * Log[1 + beta];
// nbdalpha[n_,alpha_,beta_]= D[nb[n, alpha, beta],alpha];
// nbdbeta[n_,alpha_,beta_]= D[nb[n, alpha, beta],beta];
Expand All @@ -127,7 +127,7 @@ return_type_t<T_shape, T_inv_scale> neg_binomial_lpmf(const T_n& n,

if (!is_constant_all<T_shape>::value) {
ops_partials.edge1_.partials_[i]
+= n_vec[i] / value_of(alpha_vec[i]) + log_beta_m_log1p_beta[i];
+= n_vec[i] / value_of(alpha_vec[i]) + log_beta_m_log1p_beta[i];
}
if (!is_constant_all<T_inv_scale>::value) {
ops_partials.edge2_.partials_[i]
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