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Fix the finite-difference scale of grad_hess_log_prob (Hessian 10⁻⁶ too small) #3442

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Fix the finite-difference scale of grad_hess_log_prob (Hessian 10⁻⁶ too small) #3442

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08dbc8f
Fix the finite-difference scale in grad_hess_log_prob
jachymb Oct 17, 2026
cdf4814
Merge branch 'develop' into bugfix/grad-hess-log-prob-scale
jachymb Oct 25, 2026
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11 changes: 6 additions & 5 deletions src/stan/model/grad_hess_log_prob.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -37,15 +37,16 @@ double grad_hess_log_prob(const M& model, std::vector<double>& params_r,
std::vector<double>& hessian,
std::ostream* msgs = 0) {
static const double epsilon = 1e-3;
static const double half_epsilon = 0.5 * epsilon;
// each estimate is added to both H(d, dd) and H(dd, d), hence the 0.5
static const double half_inv_epsilon = 0.5 / epsilon;
static const int order = 4;
static const double perturbations[order]
= {-2 * epsilon, -1 * epsilon, epsilon, 2 * epsilon};
static const double coefficients[order]
= {1.0 / 12.0, -2.0 / 3.0, 2.0 / 3.0, -1.0 / 12.0};
static const double half_epsilon_coeff[order]
= {half_epsilon * coefficients[0], half_epsilon * coefficients[1],
half_epsilon * coefficients[2], half_epsilon * coefficients[3]};
static const double scaled_coefficients[order] = {
half_inv_epsilon * coefficients[0], half_inv_epsilon * coefficients[1],
half_inv_epsilon * coefficients[2], half_inv_epsilon * coefficients[3]};
double result = log_prob_grad<propto, jacobian_adjust_transform>(
model, params_r, params_i, gradient, msgs);
hessian.assign(params_r.size() * params_r.size(), 0);
Expand All @@ -58,7 +59,7 @@ double grad_hess_log_prob(const M& model, std::vector<double>& params_r,
log_prob_grad<propto, jacobian_adjust_transform>(model, perturbed_params,
params_i, temp_grad);
for (size_t dd = 0; dd < params_r.size(); ++dd) {
const double increment = half_epsilon_coeff[i] * temp_grad[dd];
const double increment = scaled_coefficients[i] * temp_grad[dd];
const int col_iter = dd * params_r.size();
hessian[dd + row_iter] += increment;
hessian[d + col_iter] += increment;
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17 changes: 17 additions & 0 deletions src/test/unit/model/grad_hess_log_prob_test.cpp
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Expand Up @@ -45,3 +45,20 @@ TEST(ModelUtil, grad_hess_log_prob) {
EXPECT_EQ("", stan::test::cout_ss.str());
EXPECT_EQ("", stan::test::cerr_ss.str());
}

TEST(ModelUtil, grad_hess_log_prob_values) {
// log density -x^2 / 2: gradient -x, Hessian -1 (the Hessian used to come
// out scaled by 1e-6)
stan::io::empty_var_context data_var_context;
stan_model model(data_var_context, 0, static_cast<std::stringstream*>(0));
std::vector<double> params_r{1.5};
std::vector<int> params_i;
std::vector<double> gradient, hessian;
double lp = stan::model::grad_hess_log_prob<true, true, stan_model>(
model, params_r, params_i, gradient, hessian, 0);
EXPECT_FLOAT_EQ(-1.125, lp);
ASSERT_EQ(1, gradient.size());
EXPECT_FLOAT_EQ(-1.5, gradient[0]);
ASSERT_EQ(1, hessian.size());
EXPECT_NEAR(-1, hessian[0], 1e-10);
}