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The elite samples are weighted by likelihood ratios because they are drawn from the current proposal distribution, not the original target distribution. The likelihood ratio corrects for this discrepancy, ensuring that the updated proposal parameters accurately reflect the maximum likelihood estimates under the original distribution.

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.

The elite samples are weighted by likelihood ratios because they are drawn from the current proposal distribution, not the original target distribution. The likelihood ratio corrects for this discrepancy, ensuring that the updated proposal parameters accurately reflect the maximum likelihood estimates under the original distribution.

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.