New models for symbolic data analysis

Boris Beranger, Huan Lin, Scott Sisson

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
10 Downloads (Pure)


Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is required at this level. Here we consider a different perspective, which opens a new research direction in the field of SDA. We assume that, as with a standard statistical analysis, inference is required at the level of individual-level data. However, the individual-level data are unobserved, and are aggregated into observed symbols—group-based distributional-valued summaries—prior to the analysis. We introduce a novel general method for constructing likelihood functions for symbolic data based on a desired probability model for the underlying measurement-level data, while only observing the distributional summaries. This approach opens the door for new classes of symbol design and construction, in addition to developing SDA as a viable tool to enable and improve upon classical data analyses, particularly for very large and complex datasets. We illustrate this new direction for SDA research through several real and simulated data analyses, including a study of novel classes of multivariate symbol construction techniques.
Original languageEnglish
Pages (from-to)659-699
Number of pages41
JournalAdvances in Data Analysis and Classification
Issue number3
Early online date19 Sept 2022
Publication statusPublished - Sept 2023

Bibliographical note

© The Author(s) 2022. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Binned data
  • Interval data
  • Likelihoods
  • Summary statistics
  • Symbol design


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