joint-distributions #

Shows a discrete joint distribution p_{X,Y}(x,y) as a 5×5 probability grid. The animation cycles through (1) summing a highlighted row to form the marginal p_Y(y), (2) summing a highlighted column to form p_X(x), and (3) fixing a y* row and normalizing by p_Y(y*) to produce the conditional p_{X|Y}(x|y*). The right panel reinforces the identities p_{X,Y}=p_{X|Y}·p_Y and Bayes’ rule as an algebraic rearrangement.

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⏮◀◀▶▶STEP0.25x1xZOOM

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practical uses #

01.Computing marginals from a learned or measured joint distribution (e.g., sensor fusion tables)
02.Turning joint models into conditional predictors p(Y|X) for classification/diagnosis
03.Understanding independence/correlation structure by comparing joint vs marginals and conditionals

technical notes #

Renders a blocky heatmap on a snapped grid (4px*scale). Joint probabilities are generated from a small correlated discrete model that smoothly morphs over time, then normalized. Marginals and conditionals are computed each frame and visualized as bar charts and normalized strips; narrative segments are timed over a 4s cycle using smoothstep/ease for emphasis.

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