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Forensic experts are required to quantify their findings and to assess the range of uncertainties associated with the inferences that may be drawn from different genetic evidence. The practical application of probabilistic reasoning in forensic science can be assisted through the use of the formalism known as Bayesian networks. The aim of the study was to implement existing ways of probabilistic evaluation of DNA evidence in building appropriate network structures. We present a network models for identification of human remains and paternity investigation cases using different kinds of genetic markers, which have a different inheritance mode.
The logical approach to interpreting the weight of forensic evidence has been implemented for paternity cases since the 1930s. Now it dominates in the many kinds of forensic disciplines. The advantage of the logical approach is that the likelihood ratio can be put in a context of the entire case [
]. Such approach requires some assumptions as to the prior knowledge about possible paternity or identity of chosen person. We present two simple Bayesian networks for evaluating a complicated identity and paternity investigation using a panel of autosomal, mitochondrial and Y chromosome genetic markers. The proposed networks are theoretical models, which can be updated to real case by incorporating the probabilities of particular evidences given chosen hypotheses [
]. Conditional probability tables assigned to the particular nodes were set according to the knowledge from our practice. In routine casework involving identity and paternity investigation we use AmpFl Identifiler, AmpFl Yfiler, AmpFl MiniFiler STR kits and Big Dye Terminator Cycle Sequencing Ready Reaction Kit (Applera).
3. Results and discussion
3.1 Identity investigation model
Hypothesis node “identity” has four uniformly probable states: “He”, “his maternal relative”, “his paternal relative” and “unrelated”. Autosomal match probabilities depend on the kind of accessible reference material; the closer the possible relatives the stronger the impact on the truth of the hypothesis that the remains origins from “He”. The proposed structure of the network is illustrated by the Fig. 1.
Fig. 1Bayesian network for evaluating a hypothesis about identity of human remains after propagation of the “hard evidences” on the “mt DNA” and “ChrY” nodes, which means that after examination of some relatives using only those DNA markers there is a high probability of the match. One can see that simultaneously the probability of the match in autosomal markers is increased.
Hypothesis node “paternity” has four states: “He”, “his close paternal relative”, “his distant relative” and “unrelated” to the alleged man that could be the biological fathers. The Y chromosomal match node is influenced by the “haplotype” node representing the kind of the haplotype (“unseen before”, “rare”, “common” in the population). It is also influenced by the information about the possible mutation process during spermatozoa production. The overall network structure is illustrated by the Fig. 2.
Fig. 2The proposed Bayesian network for evaluating hypotheses as to alleged father paternity using two kinds of DNA markers: autosomal STR and ChrY ones. On the left: the results of entering “hard evidence” (that is the observed no exclusion in autosomal markers) and propagation it throughout the network. It should be remarked that the probability of the match in Chr Y markers simultaneously grown to near 100%.
Described Bayesian networks are seem to be usable for addressing a wide range of different scenarios simply by changing the assumed conditional probabilities assigned to the particular nodes to that adequate to the specified case [
This work was financially supported by grant 0 T00C 028 29 of the Ministry of Education and Science, Poland - but without any involvement in the development of this paper.
Acknowledgment
This work was financially supported by grant 0 T00C 028 29 of the Ministry of Education and Science, Poland.
References
Aitken C.G.G.
Taroni F.
Statistics and the Evaluation of Evidence for Forensic Scientists. Statistics in Practice.
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