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A puzzle of two unreliable sensors
Suppose you are trying to measure a value P and you have two unreliable sensors. Sensor A returns 0.5P + 0.5U, where U is uniform random noise over the same domain as P. Sensor B will return either…
In other words, sensor A is a noisy measurement of your variable, and B is sometimes the correct value and sometimes pure noise. We could theoretically improve the precision of this estimate with a ternary search, but in practice numerical accuracy becomes a problem and I can’t nail it down much tighter than 0.586 or so. Here the location of the dip is enough to make anyone suspect good ol’ 1/e ≈ 0.367, but sadly numerical data points clearly to a minimum near 0.41, instead.
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