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Merge pull request #3116 from lingium/feature/issue-3115-beta-neg-binomial-lcdf
add beta_neg_binomial_lcdf
2 parents 8ab9760 + 7514516 commit 7ada875

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Lines changed: 248 additions & 3 deletions

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‎stan/math/prim/prob.hpp‎

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#include <stan/math/prim/prob/beta_lcdf.hpp>
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#include <stan/math/prim/prob/beta_lpdf.hpp>
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#include <stan/math/prim/prob/beta_neg_binomial_lccdf.hpp>
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#include <stan/math/prim/prob/beta_neg_binomial_lcdf.hpp>
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#include <stan/math/prim/prob/beta_neg_binomial_lpmf.hpp>
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#include <stan/math/prim/prob/beta_proportion_ccdf_log.hpp>
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#include <stan/math/prim/prob/beta_proportion_cdf_log.hpp>

‎stan/math/prim/prob/beta_neg_binomial_lccdf.hpp‎

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@@ -34,15 +34,15 @@ namespace math {
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* @param alpha prior success parameter
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* @param beta prior failure parameter
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* @param precision precision for `grad_F32`, default \f$10^{-8}\f$
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* @param max_steps max iteration allowed for `grad_F32`, default \f$10^{-8}\f$
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* @param max_steps max iteration allowed for `grad_F32`, default \f$10^{8}\f$
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* @return log probability or log sum of probabilities
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* @throw std::domain_error if r, alpha, or beta fails to be positive
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* @throw std::invalid_argument if container sizes mismatch
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*/
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template <typename T_n, typename T_r, typename T_alpha, typename T_beta>
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inline return_type_t<T_r, T_alpha, T_beta> beta_neg_binomial_lccdf(
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const T_n& n, const T_r& r, const T_alpha& alpha, const T_beta& beta,
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const double precision = 1e-8, const int max_steps = 1e6) {
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const double precision = 1e-8, const int max_steps = 1e8) {
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static constexpr const char* function = "beta_neg_binomial_lccdf";
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check_consistent_sizes(
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function, "Failures variable", n, "Number of successes parameter", r,
@@ -100,7 +100,7 @@ inline return_type_t<T_r, T_alpha, T_beta> beta_neg_binomial_lccdf(
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std::initializer_list<b_t>{n_dbl + 2.0, a_plus_r + b_plus_n + 1.0},
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1.0);
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auto C = lgamma(r_plus_n + 1.0) + lbeta(a_plus_r, b_plus_n + 1.0)
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- lgamma(r_dbl) - lbeta(alpha_dbl, beta_dbl) - lgamma(n_dbl + 2);
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- lgamma(r_dbl) - lbeta(alpha_dbl, beta_dbl) - lgamma(n_dbl + 2.0);
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log_ccdf += C + stan::math::log(F);
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if constexpr (!is_constant_all<T_r, T_alpha, T_beta>::value) {

‎stan/math/prim/prob/beta_neg_binomial_lcdf.hpp‎

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#ifndef STAN_MATH_PRIM_PROB_BETA_NEG_BINOMIAL_LCDF_HPP
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#define STAN_MATH_PRIM_PROB_BETA_NEG_BINOMIAL_LCDF_HPP
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#include <stan/math/prim/meta.hpp>
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#include <stan/math/prim/err.hpp>
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#include <stan/math/prim/fun/constants.hpp>
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#include <stan/math/prim/fun/digamma.hpp>
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#include <stan/math/prim/fun/hypergeometric_3F2.hpp>
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#include <stan/math/prim/fun/grad_F32.hpp>
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#include <stan/math/prim/fun/lbeta.hpp>
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#include <stan/math/prim/fun/lgamma.hpp>
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#include <stan/math/prim/fun/max_size.hpp>
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#include <stan/math/prim/fun/scalar_seq_view.hpp>
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#include <stan/math/prim/fun/size.hpp>
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#include <stan/math/prim/fun/size_zero.hpp>
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#include <stan/math/prim/functor/partials_propagator.hpp>
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#include <cmath>
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namespace stan {
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namespace math {
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/** \ingroup prob_dists
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* Returns the log CDF of the Beta-Negative Binomial distribution with given
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* number of successes, prior success, and prior failure parameters.
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* Given containers of matching sizes, returns the log sum of probabilities.
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*
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* @tparam T_n type of failure parameter
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* @tparam T_r type of number of successes parameter
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* @tparam T_alpha type of prior success parameter
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* @tparam T_beta type of prior failure parameter
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*
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* @param n failure parameter
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* @param r Number of successes parameter
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* @param alpha prior success parameter
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* @param beta prior failure parameter
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* @param precision precision for `grad_F32`, default \f$10^{-8}\f$
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* @param max_steps max iteration allowed for `grad_F32`, default \f$10^{8}\f$
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* @return log probability or log sum of probabilities
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* @throw std::domain_error if r, alpha, or beta fails to be positive
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* @throw std::invalid_argument if container sizes mismatch
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*/
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template <typename T_n, typename T_r, typename T_alpha, typename T_beta>
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inline return_type_t<T_r, T_alpha, T_beta> beta_neg_binomial_lcdf(
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const T_n& n, const T_r& r, const T_alpha& alpha, const T_beta& beta,
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const double precision = 1e-8, const int max_steps = 1e8) {
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static constexpr const char* function = "beta_neg_binomial_lcdf";
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check_consistent_sizes(
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function, "Failures variable", n, "Number of successes parameter", r,
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"Prior success parameter", alpha, "Prior failure parameter", beta);
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if (size_zero(n, r, alpha, beta)) {
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return 0;
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}
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using T_r_ref = ref_type_t<T_r>;
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T_r_ref r_ref = r;
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using T_alpha_ref = ref_type_t<T_alpha>;
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T_alpha_ref alpha_ref = alpha;
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using T_beta_ref = ref_type_t<T_beta>;
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T_beta_ref beta_ref = beta;
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check_positive_finite(function, "Number of successes parameter", r_ref);
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check_positive_finite(function, "Prior success parameter", alpha_ref);
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check_positive_finite(function, "Prior failure parameter", beta_ref);
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scalar_seq_view<T_n> n_vec(n);
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scalar_seq_view<T_r_ref> r_vec(r_ref);
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scalar_seq_view<T_alpha_ref> alpha_vec(alpha_ref);
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scalar_seq_view<T_beta_ref> beta_vec(beta_ref);
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int size_n = stan::math::size(n);
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size_t max_size_seq_view = max_size(n, r, alpha, beta);
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// Explicit return for extreme values
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// The gradients are technically ill-defined, but treated as zero
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for (int i = 0; i < size_n; i++) {
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if (n_vec.val(i) < 0) {
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return negative_infinity();
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}
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}
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using T_partials_return = partials_return_t<T_n, T_r, T_alpha, T_beta>;
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T_partials_return log_cdf(0.0);
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auto ops_partials = make_partials_propagator(r_ref, alpha_ref, beta_ref);
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for (size_t i = 0; i < max_size_seq_view; i++) {
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// Explicit return for extreme values
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// The gradients are technically ill-defined, but treated as zero
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if (n_vec.val(i) == std::numeric_limits<int>::max()) {
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return 0.0;
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}
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auto n_dbl = n_vec.val(i);
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auto r_dbl = r_vec.val(i);
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auto alpha_dbl = alpha_vec.val(i);
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auto beta_dbl = beta_vec.val(i);
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auto b_plus_n = beta_dbl + n_dbl;
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auto r_plus_n = r_dbl + n_dbl;
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auto a_plus_r = alpha_dbl + r_dbl;
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using a_t = return_type_t<decltype(b_plus_n), decltype(r_plus_n)>;
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using b_t = return_type_t<decltype(n_dbl), decltype(a_plus_r),
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decltype(b_plus_n)>;
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auto F = hypergeometric_3F2(
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std::initializer_list<a_t>{1.0, b_plus_n + 1.0, r_plus_n + 1.0},
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std::initializer_list<b_t>{n_dbl + 2.0, a_plus_r + b_plus_n + 1.0},
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1.0);
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auto C = lgamma(r_plus_n + 1.0) + lbeta(a_plus_r, b_plus_n + 1.0)
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- lgamma(r_dbl) - lbeta(alpha_dbl, beta_dbl) - lgamma(n_dbl + 2.0);
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auto ccdf = stan::math::exp(C) * F;
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log_cdf += log1m(ccdf);
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if constexpr (!is_constant_all<T_r, T_alpha, T_beta>::value) {
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auto chain_rule_term = -ccdf / (1.0 - ccdf);
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auto digamma_n_r_alpha_beta = digamma(a_plus_r + b_plus_n + 1.0);
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T_partials_return dF[6];
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grad_F32<false, !is_constant<T_beta>::value, !is_constant_all<T_r>::value,
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false, true, false>(dF, 1.0, b_plus_n + 1.0, r_plus_n + 1.0,
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n_dbl + 2.0, a_plus_r + b_plus_n + 1.0, 1.0,
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precision, max_steps);
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if constexpr (!is_constant<T_r>::value || !is_constant<T_alpha>::value) {
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auto digamma_r_alpha = digamma(a_plus_r);
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if constexpr (!is_constant<T_r>::value) {
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auto partial_lccdf = digamma(r_plus_n + 1.0)
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+ (digamma_r_alpha - digamma_n_r_alpha_beta)
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+ (dF[2] + dF[4]) / F - digamma(r_dbl);
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partials<0>(ops_partials)[i] += partial_lccdf * chain_rule_term;
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}
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if constexpr (!is_constant<T_alpha>::value) {
125+
auto partial_lccdf = digamma_r_alpha - digamma_n_r_alpha_beta
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+ dF[4] / F - digamma(alpha_dbl);
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partials<1>(ops_partials)[i] += partial_lccdf * chain_rule_term;
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}
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}
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if constexpr (!is_constant<T_alpha>::value
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|| !is_constant<T_beta>::value) {
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auto digamma_alpha_beta = digamma(alpha_dbl + beta_dbl);
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if constexpr (!is_constant<T_alpha>::value) {
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partials<1>(ops_partials)[i] += digamma_alpha_beta * chain_rule_term;
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}
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if constexpr (!is_constant<T_beta>::value) {
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auto partial_lccdf = digamma(b_plus_n + 1.0) - digamma_n_r_alpha_beta
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+ (dF[1] + dF[4]) / F
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- (digamma(beta_dbl) - digamma_alpha_beta);
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partials<2>(ops_partials)[i] += partial_lccdf * chain_rule_term;
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}
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}
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}
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}
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return ops_partials.build(log_cdf);
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}
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} // namespace math
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} // namespace stan
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#endif

‎test/prob/beta_neg_binomial/beta_neg_binomial_cdf_log_test.hpp‎

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// Arguments: Ints, Doubles, Doubles, Doubles
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#include <stan/math/prim/prob/beta_neg_binomial_lcdf.hpp>
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#include <stan/math/prim/fun/lbeta.hpp>
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#include <stan/math/prim/fun/lgamma.hpp>
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using stan::math::var;
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using std::numeric_limits;
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using std::vector;
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class AgradCdfLogBetaNegBinomial : public AgradCdfLogTest {
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public:
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void valid_values(vector<vector<double>>& parameters,
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vector<double>& cdf_log) {
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vector<double> param(4);
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param[0] = 0; // n
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param[1] = 1.0; // r
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param[2] = 5.0; // alpha
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param[3] = 1.0; // beta
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parameters.push_back(param);
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cdf_log.push_back(std::log(0.833333333333333)); // expected cdf_log
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}
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void invalid_values(vector<size_t>& index, vector<double>& value) {
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// n
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// r
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index.push_back(1U);
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value.push_back(0.0);
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index.push_back(1U);
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value.push_back(-1.0);
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index.push_back(1U);
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value.push_back(std::numeric_limits<double>::infinity());
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// alpha
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index.push_back(2U);
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value.push_back(0.0);
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index.push_back(2U);
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value.push_back(-1.0);
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index.push_back(2U);
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value.push_back(std::numeric_limits<double>::infinity());
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// beta
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index.push_back(3U);
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value.push_back(0.0);
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index.push_back(3U);
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value.push_back(-1.0);
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index.push_back(3U);
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value.push_back(std::numeric_limits<double>::infinity());
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}
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// BOUND INCLUDED IN ORDER FOR TEST TO PASS WITH CURRENT FRAMEWORK
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bool has_lower_bound() { return false; }
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bool has_upper_bound() { return false; }
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template <typename T_n, typename T_r, typename T_size1, typename T_size2,
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typename T4, typename T5>
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stan::return_type_t<T_r, T_size1, T_size2> cdf_log(const T_n& n, const T_r& r,
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const T_size1& alpha,
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const T_size2& beta,
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const T4&, const T5&) {
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return stan::math::beta_neg_binomial_lcdf(n, r, alpha, beta);
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}
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template <typename T_n, typename T_r, typename T_size1, typename T_size2,
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typename T4, typename T5>
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stan::return_type_t<T_r, T_size1, T_size2> cdf_log_function(
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const T_n& n, const T_r& r, const T_size1& alpha, const T_size2& beta,
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const T4&, const T5&) {
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using stan::math::lbeta;
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using stan::math::lgamma;
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using stan::math::log_sum_exp;
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using std::vector;
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vector<stan::return_type_t<T_r, T_size1, T_size2>> lpmf_values;
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for (int i = 0; i <= n; i++) {
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auto lpmf = lbeta(i + r, alpha + beta) - lbeta(r, alpha)
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+ lgamma(i + beta) - lgamma(i + 1) - lgamma(beta);
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lpmf_values.push_back(lpmf);
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}
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return log_sum_exp(lpmf_values);
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}
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};

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