I've got a set of observations, each consisting of seven two-dimensional values. So each observation looks something like this:

(58, 73)

(114, 97)

(34, 116)

(59, 37)

(83, 115)

(23, 91)

(77, 66)

Also, I know that the points depend on one another in various ways (e.g. no two points can be too close), so we can't assume independence.

How can I characterize the probability distribution of a set of observations like this? I am getting particularly bogged down in trying to understand how to deal with a set of two-dimensional points: Can I simply treat each observation as a 14 dimensional vector, or do I have to retain the 7x2 shape of the data?

Ultimately I'd also like to measure the distance between individual observations in addition to characterizing the distribution, but when I use multivariate distance measures like mahalanobis I still run into this question about handing a set of points.

Please please please any help would be great. Thanks so much!!