  Symbolic data analysis has been proposed as a technique for summarising large
and complex datasets into a much smaller and tractable number of distributions
-- such as random rectangles or histograms -- each describing a portion of the
larger dataset. Recent work has developed likelihood-based methods that permit
fitting models for the underlying data while only observing the distributional
summaries. However, while powerful, when working with random histograms this
approach rapidly becomes computationally intractable as the dimension of the
underlying data increases. We introduce a composite-likelihood variation of
this likelihood-based approach for the analysis of random histograms in $K$
dimensions, through the construction of lower-dimensional marginal histograms.
The performance of this approach is examined through simulated and real data
analysis of max-stable models for spatial extremes using millions of observed
datapoints in more than $K=100$ dimensions. Large computational savings are
available compared to existing model fitting approaches.
