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  "body": "\n## Summary\n\nOptimal experimental design chooses the conditions of an experiment so that the parameters of a given model are estimated as precisely as possible.\nPrecision is measured by the information matrix of the design, and an optimality criterion turns that matrix into a number.\nD-optimality maximises its determinant, A-optimality minimises the trace of its inverse, and E-optimality maximises its smallest eigenvalue.\nThe approximate theory, where a design is a probability measure on the design region, makes these problems convex.\nThe [[Kiefer–Wolfowitz equivalence theorem|71XBFB49HE]] shows that D-optimal and G-optimal designs coincide in that theory.\n\n## Explanations\n\n### L1 human\n\nTo estimate the slope of a straight line over an interval, where should one measure?\nSpreading the points evenly feels natural, but putting half of them at each end gives a more precise slope.\nOptimal design makes such choices systematic: it picks the measuring points that make the estimates as sharp as possible.\nDifferent goals, such as precise coefficients or precise predictions, lead to different criteria and sometimes to different designs.\n",
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