Statistical Interpretation

Statistical Interpretation - Numbers Game

• Allele Frequency: Proportion of a specific allele in a population.
• Genotype Frequency: Proportion of a specific genotype.
• Hardy-Weinberg Equilibrium (HWE): Predicts genotype frequencies from allele frequencies. Equation: $p^2 + 2pq + q^2 = 1$.
  • Assumes: Random mating; No MMSG (Mutation, Migration, Selection, Genetic drift). 📌
• Random Match Probability (RMP): Chance a random unrelated person matches evidence DNA.
  • Uses population allele frequencies. ↓RMP = ↑Evidence strength.
• Likelihood Ratio (LR): Compares evidence probability: Prosecution hypothesis vs. Defense hypothesis.
  • LR > 1: Favors prosecution.
  • LR < 1: Favors defense.
  • LR = 1: Neutral.

⭐ The Hardy-Weinberg Equilibrium principle is fundamental for calculating expected genotype frequencies from allele frequencies in a population, assuming random mating and no evolutionary influences.

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Statistical Interpretation - Weighing Evidence

• Likelihood Ratio (LR): Central component of Case Assessment and Interpretation (CAI) methodology using Bayes' theorem for DNA evidence evaluation under BSA.
• Compares evidence probability (E) under:
  • $H_p$ (Prosecution): Suspect is source.
  • $H_d$ (Defense): Another is source.
• Formula: $LR = \frac{P(E|H_p)}{P(E|H_d)}$
  • $P(E|H_p)$: $P(E)$ if $H_p$.
  • $P(E|H_d)$: $P(E)$ if $H_d$.
• Interpretation:
  • LR > 1: Supports $H_p$.
  • LR < 1: Supports $H_d$.
  • LR = 1: Neutral.
• CAI methodology helps decision-makers update beliefs by rationally incorporating prior odds and evidence within case context for BNSS proceedings.

⭐ A Likelihood Ratio (LR) greater than 1 supports the prosecution's hypothesis ($H_p$), while an LR less than 1 supports the defense's hypothesis ($H_d$); an LR of 1 means the evidence is neutral and assists legal practitioners in evaluating DNA data under BSA framework.

Statistical Interpretation - Mixed & Matched

⭐ DNA mixture interpretation often involves calculating the Combined Probability of Inclusion (CPI) or using Likelihood Ratios (LR). The Combined Probability of Inclusion (CPI) is a widely used statistic for DNA mixtures, but its reliability for complex or 'irresolvable' mixtures has been questioned. Probabilistic Genotyping Software (PGS) is increasingly preferred for such cases as it offers a more robust statistical approach by modeling various genotype combinations and calculating likelihood ratios.

• Mixed DNA Samples: DNA from >1 individual.

  • Challenges: Allele stacking, stutter, drop-out (undetected true alleles), drop-in (contaminant DNA).
  • Interpretation:
    • Combined Probability of Inclusion (CPI): Probability a random person is a contributor. The formula for Combined Probability of Inclusion (CPI) for one locus is typically presented as $P(\text{Inclusion}) = (\sum p_i)^2$ for homozygous alleles and $2p_ip_j$ for heterozygous alleles, where $p_i$ and $p_j$ are allele frequencies. However, the application of this formula, especially in complex or low-template mixtures, is often superseded by more sophisticated probabilistic genotyping methods.
    • Likelihood Ratio (LR): Compares probability of evidence (E) given prosecution hypothesis ($H_p$) vs. defense hypothesis ($H_d$). $LR = P(E|H_p) / P(E|H_d)$. An LR > 1 favors $H_p$.
    • Probabilistic Genotyping Software (PGS): e.g., STRmix™, TrueAllele™; statistically models complex mixtures.

• Database Matches (Matched Profiles):

  • Random Match Probability (RMP): Statistical frequency of the DNA profile in a relevant population.
  • Issues:
    • Adventitious matches: Chance coincidental hits; risk ↑ with larger database size.
    • Familial searching: Uses partial matches to identify potential relatives; raises ethical concerns.

Statistical Interpretation - Stats Traps

• Key errors in DNA statistics, leading to misinterpretation in modern forensic analysis with probabilistic genotyping and diverse databases.
• Prosecutor's Fallacy:

  ⭐ The 'Prosecutor's Fallacy' incorrectly transposes the conditional probability, equating P(E|S) (probability of evidence given source) with P(S|E) (probability of source given evidence), often by misinterpreting the Random Match Probability as the probability of guilt.

• Defence Attorney's Fallacy: Downplays match significance by citing large population matches or focusing on others who might match.
• Base Rate Fallacy: Ignores prior probabilities or the underlying frequency of a characteristic in the population.
• Uniqueness Fallacy: Assumes a DNA profile is unique without considering population substructures or database limitations.
• Database Issues:
  • Cold hits (database trawling): ↑ Risk of adventitious (chance) matches.
  • Inappropriate reference population: Leads to biased Random Match Probability (RMP).
• Likelihood Ratio (LR): Preferred statistical method using validated probabilistic software for complex mixtures, considering allele drop-in/drop-out and stutter: $LR = \frac{P(E|H_p)}{P(E|H_d)}$.
• Pattern-matching disciplines (firearms identification) require transparent error rate reporting and objective validation under BSA evidence standards.

High‑Yield Points - ⚡ Biggest Takeaways

• Likelihood Ratio (LR) is paramount: Compares evidence probability under prosecution vs. defence hypotheses.
• Random Match Probability (RMP): Estimates DNA profile frequency in a relevant population.
• Hardy-Weinberg Principle ($p^2 + 2pq + q^2 = 1$) calculates genotype frequencies from allele frequencies.
• Avoid Prosecutor's Fallacy: Confusing P(Match|Innocent) with P(Innocent|Match).
• Defence Fallacy downplays match significance using large population numbers.
• Bayes' Theorem combines prior odds with LR for posterior probability of a hypothesis.