Probability of Paternity (W)
Definition
The posterior probability that the alleged father is the biological father, calculated from the CPI and a prior probability using Bayes' theorem. Most laboratories used a neutral prior of 0.5. Expressed as a percentage in most court reports.
- Symbol
- W
- Field
- Forensic paternity testing, statistical serology
- Derived from
- Combined paternity index (CPI) and a prior probability
- Method
- Bayes' theorem
- Common prior used
- Neutral prior of 0.5
Common questions
Why do most laboratories default to a prior of 0.5 for W?+
A prior of 0.5 assumes the alleged father is, before any genetic testing, equally likely to be or not be the biological father, which keeps the reported figure a straightforward reflection of the genetic evidence rather than an assumption about the case's non-genetic facts that the lab has no way to evaluate.
What is the practical difference between the CPI and W?+
The CPI is the raw genetic likelihood ratio from comparing the tested loci, while W folds that CPI together with the chosen prior to produce a final percentage, which is the figure typically presented and understood in a paternity report.
Does a high W value, such as 99.9%, mean paternity is proven with certainty?+
It means the genetic evidence overwhelmingly favours paternity given the assumed prior, but it remains a probability rather than an absolute certainty, and the result should be read together with the assumptions, including the prior, that went into calculating it.
Related terms
- Combined Paternity Index (CPI)
- The product of all individual paternity indices across all marker systems tested. Assumes independence of the marker systems. The CPI is a...
- Paternity Index (PI)
- A likelihood ratio that compares the probability of the observed serological profile if the alleged father is the biological father to the...
- Deficient Paternity Test
- Paternity inferred from the alleged father's relatives (grandparents, siblings) when the alleged father himself is unavailable or deceased.
- Essen-Moller W
- The formula for probability of paternity derived by Erik Essen-Moller in 1938 and widely adopted by forensic laboratories. W = CPI /...
- Exclusion
- The categorical conclusion that one or more examined features are clearly inconsistent in a way that cannot be explained by projection angle,...
- Exclusion Probability (W)
- The proportion of the male reference population that would be excluded as the biological father by the marker panel tested. A high...
- Inclusion
- All obligate alleles are accounted for. Inclusion is probabilistic, never absolute, and is reported as a CPI plus probability of paternity.
- Motherless Paternity Test
- Paternity analysis where the mother's sample is unavailable. CPI thresholds are raised because the obligate paternal allele cannot be inferred from the...
- Mutation Rate
- STR loci mutate at roughly 0.001 to 0.005 per generation. A single one-step mismatch is typically scored as a possible mutation, not...
- Obligate Paternal Allele
- The allele in the child's genotype that did not come from the mother and therefore must have come from the biological father.
- Obligatory Paternal Allele
- The allele a child must have received from the biological father, identified by subtracting the mother's alleles from the child's genotype. The...
- Presumption of Legitimacy
- Statutory presumption that a child born during the continuance of a valid marriage is the legitimate child of the husband. Rebuttable only...
Explained in these topics
- Disputed Paternity and Maternity: Forensic Testing in IndiaBayesian posterior probability that the alleged father is the biological father, calculated as CPI / (CPI + 1) at a prior of 0.5. Most Indian reports require W...
- Statistical Interpretation of Serological Relationship Evidence