DENSITY ESTIMATION

[Continued...] (Gaussian) mixture models attempt to find the superposition of Gaussians which best accounts for the sample data.

Properties: Continuous and robust density estimates are obtained with good asymptotic properties. The method can in principle model any shape of cluster, and works best when the population is described well by a mixture of Gaussians. The method typically requires large sample sizes for accuracy. Serious degradation of results can occur as the number of variables increases. In practice the method also has difficulty modelling complex geometries and topologies.

In kernel-based methods, each point is spread out over a region determined by the “kernel” function (usually flat or bell-shaped).
Properties: Continuous normalised density estimates are obtained. The estimates have good asymptotic properties. The estimation quality depends on wise selection of the local spread? Too small a spread generates estimates which undulate greatly, and too large a spread leads to oversmooth estimates leading to loss of shape.

Seventh Sense Software actively researches into advanced density estimation techniques, and some of our discoveries are summarised on the Algorithms page.