Composite likelihood methods for histogram-valued random variables

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 tha...

Full description

Saved in:
Bibliographic Details
Published in:Statistics and computing 2020-09, Vol.30 (5), p.1459-1477
Main Authors: Whitaker, T., Beranger, B., Sisson, S. A.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computer simulation
Data analysis
Datasets
Histograms
Mathematics and Statistics
Probability and Statistics in Computer Science
Random variables
Rectangles
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-020-09955-5