Detection boundaries for sparse gamma scale mixture models
Time: 2-3PM 8 April
Location: Carslaw 829 (University of Sydney) or Zoom at https://uni-sydney.zoom.us/j/87417817957
Speaker: Michael Stewart - University of Sydney
Mixtures of distributions from a parametric family are useful for various statistical problems, including nonparametric density estimation, as well as model-based clustering. In clustering an enduringly difficult problem is choosing the number of clusters; when using mixtures models for model-based clustering this corresponds (roughly) to choosing the number of components in the mixture. The simplest version of this model selection problem is choosing between a known single-component mixture, and a "contaminated" version where a second unknown component is added. Due to certain structural irregularities, many standard asymptotic results from hypothesis testing do not apply in these "mixture detection" problems, including those relating to power under local alternatives. Detection boundaries have arisen over the past few decades as useful ways to describe what kinds of local alternatives are and are not detectable (asymptotically) in these problems, in particular in the "sparse" case where the mixing proportion of the contaminant is very small. We review early work on simple normal location mixtures, some interesting generalisations and also recent results for a gamma scale mixture model.
Mixtures of distributions from a parametric family are useful for various statistical problems, including nonparametric density estimation, as well as model-based clustering. In clustering an enduringly difficult problem is choosing the number of clusters; when using mixtures models for model-based clustering this corresponds (roughly) to choosing the number of components in the mixture. The simplest version of this model selection problem is choosing between a known single-component mixture, and a "contaminated" version where a second unknown component is added. Due to certain structural irregularities, many standard asymptotic results from hypothesis testing do not apply in these "mixture detection" problems, including those relating to power under local alternatives. Detection boundaries have arisen over the past few decades as useful ways to describe what kinds of local alternatives are and are not detectable (asymptotically) in these problems, in particular in the "sparse" case where the mixing proportion of the contaminant is very small. We review early work on simple normal location mixtures, some interesting generalisations and also recent results for a gamma scale mixture model.