Distribution of distributions Could anybody point me towards material for dealing with data when your sample points are distributions in themselves? To be more specific each data point I am sampling has a mean and a variance, so I am basically drawing them from a distribution of distributions.
I couldn't really find anything not the least because I don't know the right terminology for what I am looking at.
[Update] Description of data:
I have GPS points that come with an estimated measurement of the variance for each point.
 A: Rather than your observations being distributions, it sounds like you have some uncertainty or variability about your observations. This kind of observations can be modelled using hierarchical models. For example, you can say
\begin{eqnarray}
y_j &\sim& Normal(\mu,\sigma^2),\,\,\, j=1,...,n,\\
\mu &\sim& F,\\
\sigma^2 &\sim& G.
\end{eqnarray}
where $F$ is a distribution on ${\mathbb R}$ and $G$ is a distribution on ${\mathbb R}_+$. A discussion on the choice for $F$ and $G$ can be found in:

Prior distributions for variance parameters in hierarchical models

Update If you have the estimated variance, you can still use hierarchical models. Take a look at Chapter 5 of the book:

Bayesian Data Analysis

and the aforementioned paper.
Consider also the case when the observations are measured with a certain error. This is, an observation $y_j$ means that you are actually observing $y_j\pm \epsilon$. In this case the treatment might be a little different. For a proper modelling of your data, you  need to clearly understand the measurement mechanism.
A: Perhaps you are looking for analysis which can treat imprecise input data? I would look for terms like metaanalysis and:
statistics working with imprecise input parameters
statistics working with imprecise input data
statistics fuzzy input data

Here are some resources:
http://www.lix.polytechnique.fr/~adje/uploads/vstte_13.pdf
http://www.tandfonline.com/doi/abs/10.1080/17415977.2012.675505#.VDepYmd_vcw
http://dl.acm.org/citation.cfm?id=778922
http://sci2s.ugr.es/keel/pdf/keel/articulo/gfs-extendido-IEEE.pdf
http://gnedenko-forum.org/Journal/2008/022008/RATA_2_2008-09.pdf
http://www.sciencedirect.com/science/article/pii/S0167947302001160
