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FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model

Author

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  • Gusto Gaelle

    (INRA)

  • Schbath Sophie

    (INRA)

Abstract

We propose an original statistical method to estimate how the occurrences of a given process along a genome, genes or motifs for instance, may be influenced by the occurrences of a second process. More precisely, the aim is to detect avoided and/or favored distances between two motifs, for instance, suggesting possible interactions at a molecular level. For this, we consider occurrences along the genome as point processes and we use the so-called Hawkes' model. In such model, the intensity at position t depends linearly on the distances to past occurrences of both processes via two unknown profile functions to estimate. We perform a non parametric estimation of both profiles by using B-spline decompositions and a constrained maximum likelihood method. Finally, we use the AIC criterion for the model selection. Simulations show the excellent behavior of our estimation procedure. We then apply it to study (i) the dependence between gene occurrences along the E. coli genome and the occurrences of a motif known to be part of the major promoter for this bacterium, and (ii) the dependence between the yeast S. cerevisiae genes and the occurrences of putative polyadenylation signals. The results are coherent with known biological properties or previous predictions, meaning this method can be of great interest for functional motif detection, or to improve knowledge of some biological mechanisms.

Suggested Citation

  • Gusto Gaelle & Schbath Sophie, 2005. "FADO: A Statistical Method to Detect Favored or Avoided Distances between Occurrences of Motifs using the Hawkes' Model," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-28, September.
    • Handle: RePEc:bpj:sagmbi:v:4:y:2005:i:1:n:24
    DOI: 10.2202/1544-6115.1119
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    Citations

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    Cited by:

    1. Zailei Cheng & Youngsoo Seol, 2020. "Diffusion Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 555-571, June.
    2. Chevallier, Julien, 2017. "Mean-field limit of generalized Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3870-3912.
    3. Laure Sansonnet, 2014. "Wavelet Thresholding Estimation in a Poissonian Interactions Model with Application to Genomic Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 200-226, March.
    4. Zailei Cheng & Youngsoo Seol, 2018. "Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims," Papers 1801.07595, arXiv.org, revised Aug 2019.
    5. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    6. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    7. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.

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