4
$\begingroup$

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.
Improve this question
$\endgroup$
1
  • $\begingroup$ 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 ♦
    Commented Dec 22, 2023 at 17:32

2 Answers 2

Reset to default
3
$\begingroup$

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

Improve this answer
$\endgroup$
2
$\begingroup$

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.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.