I Misunderstood Rejection Sampling All This Time
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I Misunderstood Rejection Sampling All This Time is a September 2025 NULL BITMAP essay by Justin Jaffray that expands a common disk-sampling view of rejection sampling into the general algorithm.
It starts from rejecting points outside a circle, then samples an image by intensity, including unknown normalization. It states the rule where proposal density F dominates target G and acceptance uses G(r)/F(r), then improves efficiency with boxes sampled by max intensity, with keep rates moving from about 62 percent toward roughly 70 percent.
It is for intermediate readers who know basic probability and want Monte Carlo intuition used in graphics and statistics.
Access is a free Buttondown archive page with diagrams and links to related sampling posts.
It is useful when rejection sampling has only been seen as point-in-disk filtering and you need the density-ratio form.