Kirsner, Scott, Contributor has reference to this Academic Journal, PHwiki organized this Journal INTERPRETING COMPLEX DNA PROFILE EVIDENCE: BAYESIAN NETWORKS TO THE RESCUE Philip Dawid University of Cambridge TexPoint fonts used in EMF. Read the TexPoint manual be as long as e you delete this box.: A Difficulties of Formalizing Reasoning Classical logic does not readily h in addition to le “non-monotonic” reasoning Reasoning with uncertainty is especially delicate but specification in addition to manipulation of probabilities appears problematic Example: “Explaining Away” Burglar alarm is ringing Break-in Earthquake Radio reports earthquake in vicinity report earthquake earthquake alarm alarm break-in So report break-in

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PROBABILISTIC REASONING IN INTELLIGENT SYSTEMS Networks of Plausible Inference Pearl 1988 Go with the (causal) flow BAYESIAN NETWORKS H in addition to le complex problems involving probabilistic uncertainty Modular structure Intuitive graphical representation Precise semantics relevance (conditional independence) Correct accounting as long as evidence Computational algorithms elegant in addition to efficient

AN APPLICATION Forensic Identification DNA Profiling Disputed Paternity FORENSIC USES FOR DNA PROFILES Murder/Rape/ : Is A the culprit Paternity: Is A the father of B Immigration: Is A the mother of B How are A in addition to B related Disasters: 9/11, tsunami, Romanovs, DNA Profile From blood, saliva, semen, hair root, Can be amplified from a single cell Record genotypes as long as 12–20 DNA markers unlinked (different chromosomes)

A typical DNA profile Short T in addition to em Repeat markers: hypervariable “junk” (nuclear) DNA GTACGTACGTACGTAC 4 repeats (allele) genotype, e.g. 7/13 or 14 D7S820 D7S880 is one of the 13 core CODIS STR genetic loci. This DNA is found on human chromosome 7. The DNA sequence of a representative allele of this locus is shown below. The tetrameric repeat sequence of D7S280 is GATA. Different alleles of this locus have from 6 to 15 t in addition to em repeats of the GATA sequence. 001 AATTTTTGTATTTTTTTTAGAGACGGGGTTTCACCATGTTGGTCAGGCTGACTATGGAGT 061 TATTTTAAGGTTAATATATATAAAGGGTATGATAGAACACTTGTCATAGTTTAGAACGAA 121 CTAACGATAGATAGATAGATAGATAGATAGATAGATAGATAGATAGATAGATAGATAGAT 181 TGATAGTTTTTTTTTATCTCACTAAATAGTCTATAGTAAACATTTAATTACCAATATTTG 241 GTGCAATTCTGTCAATGAGGATAAATGTGGAATCGTTATAATTCTTAAGAATATATATTC 301 CCTCTGAGTTTTTGATACCTCAGATTTTAAGGCC

Disputed Paternity We have DNA data D from a disputed child c, its mother m in addition to the putative father pf If the true father tf is not pf, he is a “r in addition to om” alternative father af Straight as long as ward to compute the evidence (LIKELIHOOD RATIO) in favor of paternity (Essen-Möller 1938) Disputed Paternity LIKELIHOOD RATIO (Essen-Möller 1938) MISSING DNA DATA What if we can not obtain DNA from the suspect (or other relevant individual) Sometimes we can obtain indirect in as long as mation by DNA profiling of relatives But analysis is complex in addition to subtle

Network Representation We have DNA data D from a disputed child c, its mother m in addition to the putative father pf Building blocks: founder, child query founder Disputed Paternity Case Building blocks: founder, child, query child Complex Paternity Case We have DNA from a disputed child c1 in addition to its mother m1 but not from the putative father pf. We do have DNA from c2 an undisputed child of pf, in addition to from her mother m2 as well as from two undisputed full brothers b1 in addition to b2 of pf. query hypothesis Building blocks: founder, child, query

Criminal Identification Case A body has been found, burnt beyond recognition, but there is reason to believe it might be that of a missing criminal CR. DNA is available from the body, from the wife of CR, in addition to from two children c1 in addition to c2 of CR in addition to wife founder founder child founder query child hypothesis Building blocks: founder, child, query Each building block (founder / child / query) in a pedigree can be an INSTANCE of a generic CLASS network — which can itself have further structure The pedigree is built up using simple mouse clicks to insert new nodes/instances in addition to connect them up Genotype data are entered in addition to propagated using simple mouse clicks Object-Oriented Bayesian Network HUGIN 6 Under the microscope Each CLASS is itself a Bayesian Network, with internal structure Recursive: can contain instances of further class networks Communication via input in addition to output nodes

Marker vWA (Austro-German population allele frequencies) Single-marker analysis (multiply LR’s across markers) Lowest Level Building Blocks founder FOUNDER INDIVIDUAL represented by a pair of genes pgin in addition to mgin (instances of gene) sampled independently from population distribution, in addition to combined in instance gt of genotype

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child CHILD INDIVIDUAL paternal [maternal] gene selected by instances fmeiosis [mmeiosis] of mendel from father’s [mother’s] two genes, in addition to combined in instance cgt of genotype query query QUERY INDIVIDUAL Choice of true father’s paternal gene tfpg [maternal gene mfpg] as either that of f1 or that of f2, according as tf=f1 is true or false. Complex Paternity Case query hypothesis Measurements as long as 12 DNA markers on all 6 individuals Enter data, “propagate” through system Overall Likelihood Ratio in favour of paternity: 1300

MORE COMPLEX DNA CASES Mutation Silent/missed alleles, Mixed crime stains rape scuffle Multiple perpetrators in addition to stains Database search Contamination, laboratory errors MUTATION mendel + appropriate network mut to describe mutation process e.g. proportional mutation: founder Prob(otherg) ~ mutation rate mut – or build other, more realistic, models

in addition to especially to JUDEA PEARL who made it all possible

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