Mahalanobis Distance
Definition
A multivariate distance measure that expresses the separation between two observations in units of the population standard deviation, accounting for covariance; used in glass comparison to assess dissimilarity between questioned and known element vectors.
- Handles
- Correlated variables and multiple measurement dimensions
- Scales by
- Variance of each dimension and population standard deviation
- Common uses
- Glass element profiles, soil chemical comparisons
Common questions
What problem does Mahalanobis distance solve in forensic trace evidence?+
In glass or soil comparisons, forensic elements often vary together. Mahalanobis distance lets you measure how different two samples are while accounting for those correlations. This gives a fair comparison regardless of whether one element is naturally more variable than another.
How is Mahalanobis distance different from simple Euclidean distance?+
Simple Euclidean distance treats all dimensions equally. Mahalanobis distance scales each dimension by its variance and accounts for correlations between variables, so it avoids inflating the distance just because one element naturally has bigger swings than another.
What forensic evidence types use Mahalanobis distance?+
Glass comparison using refractive index and element data from LA-ICP-MS, and soil analysis comparing multiple chemical or mineral properties. It works whenever you have multiple correlated measurements to compare between a questioned sample and a reference.
Related terms
- Likelihood Ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Principal Component Analysis (PCA)
- A multivariate statistical method used in fire debris research to reduce chromatographic data matrices to principal components that capture major variance. Used...
- ASTM E1967
- The ASTM International standard for forensic glass RI measurement; specifies three acceptable methods (automated, semi-automated, manual), minimum precision of ±0.0001 RI units,...
- ASTM E2927
- Standard test method for the determination of trace elements in glass samples using LA-ICP-MS; specifies the element suite, calibration standards (NIST SRM...
- Bayesian Inference
- A framework for updating probability estimates in the light of new evidence; in forensic science, used to combine the prior probability of...
- Bayesian Likelihood Ratio (LR)
- The statistical framework that evaluates glass-fragment evidence by comparing the probability of the observed fragment population assuming contact with the source glass...
- Control Sample
- A water sample collected from the suspected drowning environment at or shortly after the time of body recovery. Its diatom assemblage is...
- ENFSI ENG-FG1
- The European Network of Forensic Science Institutes' guidelines for forensic geological evidence, published in 2018 by the Expert Working Group on Forensic...
- ENFSI ENG3-2013
- The ENFSI Glass Expert Working Group guideline for glass comparison casework; specifies the examination sequence, within-source variation requirements, statistical comparison framework, and...
- False-Positive Rate
- The proportion of authentic media files that a detection tool incorrectly classifies as manipulated or synthetic. Deepfake detectors and ELA tools both...
- FBI Soil Examination Unit
- The specialist unit at the FBI Laboratory in Quantico, Virginia, that has conducted forensic soil comparisons in federal criminal cases since the...
- GRIM-3
- Glass Refractive Index Measurement, third-generation instrument by Foster + Freeman (UK); an automated phase-contrast hot-stage system that identifies the RI match point...
Explained in these topics
- Glass Comparison: RI, Density and LA-ICP-MSA multivariate distance measure that expresses the separation between two observations in units of the population standard deviation, accounting for covariance...
- Soil Comparison Casework and Statistical InferenceA multivariate statistical distance measure that quantifies the separation between two data points (or between a data point and a distribution mean) in units o...
- Statistical Comparison and the Reference Population ProblemA multivariate distance measure that accounts for correlations between variables and scales each dimension by its variance, allowing comparison of data points...