Why are elite samples weighted by likelihood ratios when updating the proposal parameters in the cross-entropy method?

Conditions

• Elite samples are those with values above the iteration threshold $\gamma_i$.
• The likelihood ratios are computed as the original density divided by the proposal density.

Reasoning, step by step

1. Identify the elite samples from the current batch.
2. Compute the likelihood ratio for each elite sample.
3. Use these ratios as weights when calculating the new proposal parameters.

Example

The speaker says they update the v parameters to be the maximum likelihood estimates of the elite samples, and must weight the samples by their likelihood ratios. The code shows weighted averages for `mu_i` and `sigma_i` using `weights=eliteLRs`.

Common misconceptions

• Forgetting to weight the samples, treating them as if they were drawn from the original distribution.
• Assuming the likelihood ratio is the proposal density divided by the original density.

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Explore next

• What is the final estimator after the cross-entropy loop finishes, and how is its confidence interval computed?
• How is the iteration threshold $\gamma_i$ defined and when does the cross-entropy loop stop?