k₁ = −log(r) Estimator: Unbiased but High Variance
μ
p
0.50
True KL =
0.125
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Sampling x ~ q = N(0,1), computing r = p(x)/q(x) where p = N(μ
p
,1). The red shaded region shows where k₁ < 0 (r > 1) — roughly half the samples fall here, causing high variance.