Unbiased exponential estimators

The penalty method allows a Metropolis random walk to be correct even with the presence of noise in the probability function being sampled.

It eventually dawned on me that this same method can be used to correct any exponential estimator.

Imagine we wish to compute the estimator, exp(x), where x is some sample point that is contaminated with noise. Suppose the variance of the noise is sigma, and we know the noise is gaussian. Then the estimator exp(x-sigma^2/2) will be unbiased.