- #1
Jameson
Gold Member
MHB
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Problem:
Use importance sampling to estimate the quantity:
, where and . Plot the converge of the estimator versus sample size. Note: You may consider as the density for importance sampling.
Attempt:
This is a new topic that I digesting but as far as I understand it, this technique is used to reduce variance in Monte Carlo estimation and has a much faster convergence for small values. For example, if we want to estimate the if is a standard normal random variable, then it will take a very large amount of samples to get this value so it's not practical.
If we are trying to estimate we can rewrite this as
This problem appears to take a similar form but I'm not sure what my first step is. According to my notes I should be trying find by the following:
.
Can anyone provide some insight into the idea here or tips to get started?
Use importance sampling to estimate the quantity:
Attempt:
This is a new topic that I digesting but as far as I understand it, this technique is used to reduce variance in Monte Carlo estimation and has a much faster convergence for small values. For example, if we want to estimate the
If we are trying to estimate
This problem appears to take a similar form but I'm not sure what my first step is. According to my notes I should be trying find
Can anyone provide some insight into the idea here or tips to get started?
Last edited: