 Score-function gradient estimator

For a parameter-independent integrand $h$, the displayed score-function gradient estimator follows by differentiating the sampling probability density function or probability mass function, using $\nabla q=q\nabla \log q$. It requires conditions permitting differentiation under the integral sign, or the corresponding sum, and control of support changes. It applies to discrete choices without pretending that their sampled values are differentiable paths. If $h=h_{\lambda }$, add ${\mathbb{E}}_{q_{\lambda }}[{\nabla }_{\lambda }{h}_{\lambda }]$.