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Reading an article I came across the following expression:

'' $\overline{X}$ is constructed by sampling uniformly along the straight line between the pair of $X$ and $\hat{X}$."

I know what a uniform distribution is but I have never come across the expression "sampling uniformly". I was first wondering if they just mean randomly sampling any point which lies on that straight line between the two points $X$ and $\hat{X}$ but I assume, that randomly sampling is unrelated to uniformly sampling.

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It sounds like they they are placing a uniform distribution on the line segment between $X$ and $\hat{X}$, and sampling from this distribution, just as you sample from the uniform distribution on $[0, 1]$, for example.

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