The term jurimetrics was coined by Lee Loevinger in 1949 to describe the scientific investigation of legal problems. In its modern usage, jurimetrics encompasses the application of probability theory, statistics, and particularly Bayesian reasoning to the evaluation of evidence in legal proceedings. The field addresses a fundamental challenge: how should judges and juries rationally combine multiple pieces of evidence — DNA profiles, eyewitness testimony, motive, opportunity — to reach a verdict?
Bayesian reasoning provides the most rigorous framework for this task. The likelihood ratio quantifies the strength of each piece of evidence, the prior represents the presumption of innocence or prior information, and the posterior is the updated belief in guilt or liability. Yet the introduction of formal probability into the courtroom has been controversial, raising deep questions about the nature of legal proof, the role of subjective judgment, and the risk of mathematical fallacies misleading non-expert juries.
The Likelihood Ratio Framework
The central tool of Bayesian forensic inference is the likelihood ratio (LR) — the ratio of the probability of observing the evidence under two competing hypotheses, typically prosecution (H) and defense (not-H).
Bayesian Update in Odds Form Posterior Odds = LR × Prior Odds
O(guilty | E) = [P(E | guilty) / P(E | innocent)] × O(guilty)
Where O(guilty) → Prior odds (reflecting presumption of innocence and other evidence)
LR → Evidential strength of this particular piece of evidence
O(guilty|E) → Updated odds after considering the evidence
The likelihood ratio separates the roles of expert witness and trier of fact. The forensic expert reports the LR — how much more (or less) probable the evidence is under each hypothesis — without opining on guilt. The jury or judge combines this with prior odds (reflecting other evidence, presumption of innocence, and background information) to arrive at a posterior. This division of labor is the logically correct framework and is endorsed by the European Network of Forensic Science Institutes (ENFSI) and the Royal Statistical Society.
Forensic Fallacies
Misuse of probability in the courtroom has led to documented miscarriages of justice. Two fallacies are particularly dangerous.
The Prosecutor's Fallacy
Confusing P(evidence | innocent) with P(innocent | evidence). A DNA match probability of one in a million does not mean the defendant is guilty with probability 999,999/1,000,000. If the suspect was identified by searching a database of 100,000 people, the expected number of coincidental matches is 0.1 — making the evidence far less conclusive than it appears. The fallacy consists of ignoring the prior probability and equating the likelihood with the posterior.
The Defense Attorney's Fallacy
Arguing that because many people share a trait, the evidence against this particular defendant is worthless. If 5,000 people in a city match a DNA profile, the defense might argue the evidence implicates the defendant no more than any of the other 4,999. But this ignores other evidence — motive, opportunity, witness identification — that may dramatically narrow the field.
In 1999, Sally Clark was convicted of murdering her two infant sons, partly on the basis of expert testimony that the probability of two natural sudden infant deaths in one family was "one in 73 million." This figure was obtained by squaring the single-event probability — assuming independence — and was presented as if it were the probability of innocence. The Royal Statistical Society issued a public statement condemning the misuse of statistics. Clark's conviction was eventually overturned in 2003, but the case remains a cautionary tale about probabilistic reasoning in court.
DNA Evidence
DNA profiling is the area where Bayesian reasoning in law has had the greatest impact. A DNA profile match between a crime scene sample and a suspect's sample is characterized by a random match probability (RMP) — the probability that a randomly selected unrelated individual would share the same profile. Modern STR (short tandem repeat) profiles can have RMPs on the order of one in a billion or smaller.
The Bayesian framework correctly treats the RMP as part of the likelihood ratio, not as the probability of innocence. The LR for a DNA match is approximately 1/RMP under the prosecution hypothesis versus defense hypothesis of a random match. But the posterior odds depend on the prior — which reflects how the suspect came to the attention of police (targeted investigation vs. database search) and all other evidence in the case.
≈ 1 / RMP
Example RMP = 10⁻⁹ → LR ≈ 10⁹ (one billion)
Prior odds = 1/10,000 (one suspect in a city of 10,000 candidates)
Posterior odds = 10⁹ × (1/10,000) = 100,000 to 1 in favor of guilt
"The likelihood ratio is the logically correct measure of the probative value of scientific evidence. It is the duty of the forensic scientist to present the evidence in this form and to leave the assessment of prior odds to the court." — Colin Aitken and Franco Taroni, Statistics and the Evaluation of Evidence for Forensic Scientists (2004)
Beyond DNA: Other Applications
Handwriting and Document Analysis
Bayesian methods are used to evaluate questioned documents — comparing handwriting samples, assessing the probability of authorship, and evaluating the evidential value of ink analysis and paper dating.
Accident Reconstruction
Bayesian networks can model the causal relationships among factors in traffic accidents, industrial incidents, and medical malpractice cases, combining physical evidence, witness statements, and expert knowledge into a coherent probabilistic assessment.
Prediction of Recidivism
Statistical risk assessment instruments, increasingly used in sentencing and parole decisions, produce probabilistic predictions of reoffending. Bayesian calibration of these instruments — and Bayesian analysis of their fairness across demographic groups — is an active area of research at the intersection of jurimetrics and algorithmic fairness.
Legal scholars are divided. Proponents argue that Bayes' theorem makes reasoning transparent and avoids fallacies. Critics worry that jurors cannot meaningfully assign numerical prior odds, that the appearance of mathematical precision is misleading, and that the adversarial system is better served by narrative reasoning. In practice, most courts allow Bayesian reasoning by expert witnesses (especially for DNA evidence) but do not require juries to perform explicit calculations. The likelihood ratio framework is increasingly accepted as the standard for expert presentation, even if the final integration is left to human judgment.
The Legal Standard of Proof
Different legal standards — "beyond reasonable doubt" (criminal), "balance of probabilities" (civil), "clear and convincing evidence" (intermediate) — can be interpreted as different posterior probability thresholds. While courts rarely assign explicit numbers, Bayesian analysis clarifies what these standards mean in probabilistic terms and reveals when evidence is sufficient or insufficient to meet them.