Likelihood-Based Inference for Modelling Packet Transit From Thinned Flow Summaries

Rahman, Prosha A.; Beranger, Boris; Roughan, Matthew; Sisson, Scott A.

doi:10.1109/tsipn.2022.3188457

Cited by 2 publications

(1 citation statement)

References 45 publications

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“…These include regression models (Irpino and Verde 2015;Le-Rademacher and Billard 2013), time series (Lin and González-Rivera 2016), clustering and classification (Whitaker et al 2021), discriminant analysis (Duarte Silva and Brito 2015) and Bayesian hierarchical modelling (Lin et al 2022). Likelihoodbased inference was introduced by Le-Rademacher and Billard (2011) and Brito and Duarte Silva (2012) with further development and application by Zhang et al (2020), Rahman et al (2022), Lin et al (2022).…”

Section: Introductionmentioning

confidence: 99%

New models for symbolic data analysis

Beranger

Lin

Sisson

2022

Adv Data Anal Classif

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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.

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