Abstract

Model-based clustering represents a population as a mixture of sub-populations, with each component modeled by a probability distribution and interpreted as a cluster. The choice of component distribution is therefore crucial. Although the multivariate normal distribution is widely used, it assumes symmetric cluster shapes and can be strongly affected by outlying observations. Greater flexibility can be achieved through heavy-tailed distributions, many of which arise as normal-scale mixtures, where a link and weight function determine the resulting distributional shape while preserving symmetry. Examples include the multivariate Student-t distribution. To allow for asymmetric clusters, skew normal-scale mixtures provide a natural extension and include flexible families such as skew-t and generalized hyperbolic-type models.
This talk explores how normal-scale mixtures and skew normal-scale mixtures can be adapted for model-based clustering when data contain values missing at random. Missing values, skewness, heavy tails, and outlying observations are common features of environmental data, where measurements may be incomplete because of detection limits, sensor failures, sampling constraints, or heterogeneous natural processes. Particular attention is given to the distributional properties that make these families suitable for handling incomplete observations. These properties allow the expected values required in expectation-maximization-like algorithms to be computed naturally, enabling clustering without discarding partially observed data. Examples will focus on environmental data and will illustrate the approach and demonstrate its implementation using the recently proposed MixtureMissing R package.