Bandwidth
Definition
The smoothing parameter in a kernel density estimate. A small bandwidth produces a jagged curve that follows every data point; a large bandwidth over-smooths and can merge distinct subpopulations. Silverman's rule of thumb provides a common default: h = 0.9 min(s, IQR/1.34) n^(-1/5).
- Field
- Kernel density estimation, forensic statistics
- Role
- Smoothing parameter
- Default rule
- Silverman's rule of thumb
Common questions
What is the practical consequence of choosing too small a bandwidth in forensic data visualisation?+
A bandwidth that is too small produces a jagged, spiky density curve that closely tracks individual data points rather than the underlying population distribution, which can make random noise look like meaningful structure, such as false subpopulation peaks, when presenting statistical evidence.
How does an oversized bandwidth mislead an audience reviewing forensic statistical evidence?+
Too large a bandwidth over-smooths the density estimate, which can blur together two genuinely distinct subpopulations, such as different reference groups in a comparison, into what appears to be a single unified distribution, potentially hiding a real difference that matters to the interpretation.
Is Silverman's rule of thumb always the right choice for forensic data?+
Silverman's rule works well for roughly unimodal, bell-shaped data but can oversmooth multimodal or skewed distributions, so analysts sometimes use cross-validation or other adaptive bandwidth selection methods when the data are known or suspected to have more complex structure than a simple normal-like shape.
Related terms
- 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...
- 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...
- Kernel Density Estimate (KDE)
- A non-parametric smooth probability density function fitted to a set of measurements by placing a kernel (usually Gaussian) over each data point...
- 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...