= Unbiased likelihood estimator
{title2=$\mathbb E\widehat L(\theta)=L(\theta)$}
An <unbiased likelihood estimator> has expectation equal to the <likelihood function> at each parameter. A <pseudo-marginal algorithm> requires this estimator to be nonnegative. <Importance sampling> provides $\widehat L=M^{-1}\sum_j\ell(F_j)p_\theta(F_j)/g_\theta(F_j)$ for <independent random variables> $F_j\sim g_\theta$, provided the proposal covers the target support. Relative <variance> affects the <mixing time> even though unbiasedness guarantees the correct marginal target.
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