I have collected positional data. To visualize the data, I'd like to draw a 'typical' outcome of an experiment.
The data comes from a few hundred experiments, where I identify a variable number of objects at different positions relative to the origin in 2D. Thus, I can calculate the average number of objects, as well as estimate the empirical distribution of the objects. A plot of the 'typical' outcome would then have the average (or possibly mode) number of objects, say, 5. What I'm not sure about is where to position these 5 objects.
To simplify the problem, assume that the data follows a 2D normal distribution. If I were just to randomly draw 5 points from the distribution, I might get one point at [3,3], which would be a very rare outcome, and would thus not reflect the 'typical', or 'average' outcome. However, just drawing 5 points at [0,0] would also not make sense - even though [0,0] is the average position of the objects, 5 overlapping points are not an 'average' outcome of the process, either.
In other words, how can I get a 'likely' draw from a distribution?
It looks like I should mention why I don't want to use the usual methods (like a 2D smoothed histogram, or plotting all the many points) to look at the 2D distribution.
- The objects (which are vesicles (i.e. little spheres) inside cells) vary in number, size and position (distribution of the distance from the cell center, amount of clustering). I would like to display all these features in one graph. Since there are several hundred cells containing many vesicles each, it is not very useful to combine them all in a single plot. I am well aware that I could use a multipanel graph showing the distributions of all parameters, but this would be a lot less intuitive.
- I would like to show a 'typical' cell that shows all the salient features that characterize a specific phenotype. This way, if I want to image a particular phenotype in a mixed population, I know what kind of cell I'm looking for.
- I think such a plot would be a cool way to display a lot of information at once, and I just want to try.
Maybe it would be clearer If I said that I want to simulate a likely experimental result based on my measurements?