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Non-ignorable fuzziness in granular counts: the case of RNA-seq data

Antonio Calcagnì, Arianna Consiglio, Przemyslaw Grzegorzewski, Corrado Mencar

Abstract

RNA-seq count data are often affected by read-to-gene alignment ambiguity, especially in high-dimensional transcriptomics. This type of ambiguity can be conveniently expressed through granular counts, namely fuzzy-valued observations of latent discrete quantities. We study a class of fuzzy-reporting mechanisms and show that, when reporting exploits graded membership, ignorability fails generically, leading to a coarsening-not-at-random structure. A hierarchical model is then introduced as a tractable instance of this construction and illustrated using RNA-seq data.

Non-ignorable fuzziness in granular counts: the case of RNA-seq data

Abstract

RNA-seq count data are often affected by read-to-gene alignment ambiguity, especially in high-dimensional transcriptomics. This type of ambiguity can be conveniently expressed through granular counts, namely fuzzy-valued observations of latent discrete quantities. We study a class of fuzzy-reporting mechanisms and show that, when reporting exploits graded membership, ignorability fails generically, leading to a coarsening-not-at-random structure. A hierarchical model is then introduced as a tractable instance of this construction and illustrated using RNA-seq data.

Paper Structure

This paper contains 12 sections, 1 theorem, 1 equation, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Fuzziness as Coarsening-Not-At-Random
  4. The statistical problem
  5. A Zadeh-oriented construction
  6. The CNAR nature of the construction
  7. A CNAR model instance
  8. Case study
  9. Data description
  10. Data analysis
  11. Results
  12. Conclusions

Key Result

Proposition 1

Assume $\nu(\xi)>0$ and $c(y)>0$. Under the Zadeh-oriented construction, the mechanism is CAR in the singleton sense for the outcome $\xi$ if and only if $\xi(y)/c(y)$ is constant over $S_\xi$. $\blacktriangleleft$$\blacktriangleleft$

Theorems & Definitions (11)

  • Definition 1
  • Definition 2
  • Remark 1
  • Definition 3
  • Definition 4
  • Definition 5
  • Remark 2
  • Definition 6
  • Remark 3
  • Proposition 1: Characterization of outcome-wise CAR
  • ...and 1 more