Suppose we wish to estimate the integral of a positive function $f:\mathbb{Z}_k\to\mathbb{R}_{>0}$ using samples from some proposal distribution $q$ over $\mathbb{Z}_k$. Importance sampling tells us that the best proposal is $q=f\big/\int f$, which is unfortunately unknown. Does there exist a better estimator for $\int f$ than the Monte Carlo estimator $\hat{f}=\frac{1}{n}\sum_{i=1}^n f(x_i)/q(x_i)$ for a given fixed proposal $q$ ?
2026-03-30 04:24:01.1774844641
Optimality of Monte Carlo estimator
31 Views Asked by user17762 https://math.techqa.club/user/user17762/detail AtRelated Questions in INTEGRATION
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