Delta method for important sampling variances

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This post is mainly about one technique I used in my undergraduate dissertation, which mainly follows and slightly extends [1].

Outline:

  • Self-normalized importance sampling (SNIS).
  • Variance estimation for SNIS.
  • Covariance estimation for SNIS.
  • Variance estimation for sum of SNIS estimators.

[1] Owen, A. B. (2013). Monte Carlo theory, methods and examples.