Importance sampling is a Monte Carlo method which samples from an alternative probability
density function and reweights the observations to estimate an expectation
under the target statistical distribution.
If the target and sampling probability
density functions are 
and 
, respectively, the estimator is
 |
where the 
are independent and identically
distributed with density 
. If 
wherever 
and 
is integrable under 
, this is an unbiased estimator
of 
(Owen 2013). A well-chosen 
can reduce the variance, but
an inappropriate choice can increase it.
