Coverage
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Certain of a coin that is not there
Bayes' theorem is exact, and it is only as good as the list of hypotheses it is given. Hand it a list that leaves out the truth and it does not hesitate: it becomes certain of the entry that is least wrong, in a precise sense — the one closest in Kullback–Leibler divergence — and if two entries are equally wrong it never settles at all. Hand it a model that assumes independence where there is none, and its intervals shrink as fast as they would for honest data while covering the truth less and less often.
Where random discs change sign
Scatter discs at random over the plane and their union breaks into pieces with holes in them. Pieces minus holes has an exact average, η e^(−η)(1 − η) per disc area, where η is how many discs cover a point on average, and it changes sign at exactly η = 1, with 63.2% of the plane covered. The discs first join up across the whole plane later, at η ≈ 1.128. The sign change looks like the moment the union connects and is not; and for squares or long rectangles turned at random it comes earlier still, at 4πA/L², which only a disc reaches one.
Named alongside it
The objects these essays reach for when they reach for this one.
Bayes' theoremCredible intervalEuler characteristicIndependenceIntegral geometryIsoperimetric inequalityModel misspecificationPercolationPosteriorRandom walkRelative entropySimulation