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Suppose a gun is fired at the bullseye of a target a specific number of times.

Ignoring the accuracy (e.g. all the shots are well to the left and above the bullseye), is there a standard way of expressing the precision (i.e. how closely they cluster together) and the confidence of that value (based on the number of shots)?

  • Input: N (x,y) coordinates with arbitrary origin.
  • Output: precision, confidence.
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  • $\begingroup$ One standard definition of precision is the inverse of the variance-covariance matrix. It's not a single number because it needs to account for the precision in all dimensions. $\endgroup$
    – whuber
    Dec 22, 2023 at 17:32

2 Answers 2

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I would simply sum the variances of x and y coordinates to represent the precision.

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You could use the intra-cluster distance, which is the average distance between any two points in the cluster.

One way to measure the confidence of this value would be to bootstrap the intra-cluster distance. To do this, say you have N shots. Then take a bootstrap sample by randomly drawing N samples from the N shots with replacement and calculate the intra-cluster distance for the bootstrap sample. Repeat this a large number of times (at least 1000). The variation of the bootstrapped intra-cluster distances can be used to estimate a confidence interval.

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