Kernel Density Estimate (KDE)
Definition
A non-parametric smooth probability density function fitted to a set of measurements by placing a kernel (usually Gaussian) over each data point and summing them. Used in glass and other trace evidence LR models to convert a set of reference measurements into a continuous density that can be evaluated at any measurement value.
- Type
- Non-parametric probability density estimate
- Typical kernel
- Gaussian
- Common use
- Glass and trace evidence likelihood ratio models
- Input
- A set of reference measurements
Common questions
Why choose a KDE over fitting a normal distribution to reference data?+
A KDE makes no assumption that the underlying data follows a particular shape such as a normal curve, so it can capture skewed or multi-modal patterns that a single parametric distribution would misrepresent. This matters for trace evidence populations, such as refractive index measurements, that do not always follow a simple bell curve.
What choice most affects the accuracy of a KDE-based likelihood ratio?+
The bandwidth, which controls how much smoothing is applied around each data point, has the largest effect. Too narrow a bandwidth overfits to the specific reference sample and produces a jagged, unreliable density; too wide a bandwidth oversmooths and can understate how distinctive a measurement really is.
Related terms
- Bandwidth
- The smoothing parameter in a kernel density estimate. A small bandwidth produces a jagged curve that follows every data point; a large...
- Box Plot (Box-and-Whisker Plot)
- A graphic showing the five-number summary of a distribution: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Whiskers...
- Defence Proposition (Hd)
- The alternative proposition, typically asserting that someone else is the source (e.g., 'the crime-scene DNA came from an unknown, unrelated person'). It...
- Histogram
- A bar chart in which data are grouped into contiguous equal-width intervals (bins) and the bar height represents the count or relative...
- Interquartile Range (IQR)
- The difference between the third quartile and the first quartile: IQR = Q3 - Q1. It measures the spread of the central...
- 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...
- Log-LR (Log Likelihood Ratio)
- The natural or base-10 logarithm of the LR. Log-LRs are additive for independent evidence types, making them convenient for combining across disciplines....
- Prosecution Proposition (Hp)
- The proposition advanced by the prosecution, typically asserting that the defendant is the source of the questioned material (e.g., 'the crime-scene DNA...
- Random Match Probability (RMP)
- The probability that a randomly chosen unrelated person from the relevant population would match the evidence profile by chance. A very small...
- Scatter Plot
- A two-dimensional graph in which each observation is plotted as a point at coordinates (x, y), where x and y are two...
Explained in these topics
- Computing Likelihood Ratios: Worked Examples
- Visualising Forensic DataA non-parametric method that estimates a probability density function by placing a smooth kernel function, commonly Gaussian, at each observed data point and s...