I have a dataset that describes the position and rotation of an object at different points in time using four dimensions. I want to use this sample of observations to get a sense of what positions and rotations are possible/likely for this object.
Ultimately, I want to be able to take a new measurement of the object and estimate how "likely" the new four-dimensional measurement is (e.g., is this measurement similar to those in the dataset or very different/rare?). What would be a good way to characterize the multivariate distribution of scores and compare a new measurement to this distribution?
I was thinking that maybe I could use multivariate kernel density estimation in the dataset. To estimate the "likelihood" of the new measurement, I would then take the density of the region corresponding to that new measurement.
Would this be a reasonable approach? What assumptions would it make? Can you think of a better or alternative approach? Thanks.