Research paper| Volume 54, 102563, September 2021

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The a posteriori probability of the number of contributors when conditioned on an assumed contributor

  • Catherine M. Grgicak
    Correspondence to: Department of Chemistry, Rutgers University, 315 Penn Street R306A, Camden, NJ 08102, USA.
    Department of Chemistry, Rutgers University, Camden, NJ 08102, USA

    Center for Computational and Integrative Biology, Rutgers University, Camden, NJ 08102, USA
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  • Ken R. Duffy
    Hamilton Institute, Maynooth University, Ireland
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  • Desmond S. Lun
    Center for Computational and Integrative Biology, Rutgers University, Camden, NJ 08102, USA

    Department of Computer Science, Rutgers University, Camden, NJ 08102, USA

    Department of Plant Biology, Rutgers University, New Brunswick, NJ 08901, USA
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      • We report the distribution of the number of contributors conditioned on context.
      • Conditioning on an assumed contributor can shift the distribution to a larger n.
      • The degree of change depends on whether the assumed contributor is major or minor.
      • Computing a LR treating the NOC as a nuisance variable requires consistent context.


      Forensic DNA signal is notoriously challenging to assess, requiring computational tools to support its interpretation. Over-expressions of stutter, allele drop-out, allele drop-in, degradation, differential degradation, and the like, make forensic DNA profiles too complicated to evaluate by manual methods. In response, computational tools that make point estimates on the Number of Contributors (NOC) to a sample have been developed, as have Bayesian methods that evaluate an A Posteriori Probability (APP) distribution on the NOC. In cases where an overly narrow NOC range is assumed, the downstream strength of evidence may be incomplete insofar as the evidence is evaluated with an inadequate set of propositions.
      In the current paper, we extend previous work on NOCIt, a Bayesian method that determines an APP on the NOC given an electropherogram, by reporting on an implementation where the user can add assumed contributors. NOCIt is a continuous system that incorporates models of peak height (including degradation and differential degradation), forward and reverse stutter, noise, and allelic drop-out, while being cognizant of allele frequencies in a reference population. When conditioned on a known contributor, we found that the mode of the APP distribution can shift to one greater when compared with the circumstance where no known contributor is assumed, and that occurred most often when the assumed contributor was the minor constituent to the mixture.
      In a development of a result of Slooten and Caliebe (FSI:G, 2018) that, under suitable assumptions, establishes the NOC can be treated as a nuisance variable in the computation of a likelihood ratio between the prosecution and defense hypotheses, we show that this computation must not only use coincident models, but also coincident contextual information. The results reported here, therefore, illustrate the power of modern probabilistic systems to assess full weights-of-evidence, and to provide information on reasonable NOC ranges across multiple contexts.


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