Mixture Models and Networks -- Overview of Stochastic Blockmodelling

An Overview of Semiparametric Extensions of Finite Mixture Models

Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly introduced into traditional finite mixture models, and so semiparametric mixture models have experienced exciting development in methodologies, theories and applications. In this article, we provide a selective overview of newly-developed semiparametric mixture models, discuss their estimation methodologies, theoretical properties if applied, and some open questions.…

An Overview of Mixture Models

This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack these problems, some of which can be implemented in the area of mixture modeling. There is a great deal of literature on mixture models and this work attempts to provide a general overview of the subject, including the discussion of relevant issues and algorithms. The reader can hope to gain a broad understanding of concepts in mixture modeling and find the r…

On Mixtures of Skew Normal and Skew t-Distributions

Finite mixture of skew distributions have emerged as an effective tool in modelling heterogeneous data with asymmetric features. With various proposals appearing rapidly in the recent years, which are similar but not identical, the connections between them and their relative performance becomes rather unclear. This paper aims to provide a concise overview of these developments by presenting a systematic classification of the existing skew distributions into four types, thereby clarifying their close relationships. This also aids in understanding the link between some of the proposed expectatio…

Variance matrix priors for Dirichlet process mixture models with Gaussian kernels

The Dirichlet Process Mixture Model (DPMM) is a Bayesian non-parametric approach widely used for density estimation and clustering. In this manuscript, we study the choice of prior for the variance or precision matrix when Gaussian kernels are adopted. Typically, in the relevant literature, the assessment of mixture models is done by considering observations in a space of only a handful of dimensions. Instead, we are concerned with more realistic problems of higher dimensionality, in a space of up to 20 dimensions. We observe that the choice of prior is increasingly important as the dimensiona…

On the characterization of flowering curves using Gaussian mixture models

In this paper, we develop a statistical methodology applied to the characterization of flowering curves using Gaussian mixture models. Our study relies on a set of rosebushes flowering data, and Gaussian mixture models are mainly used to quantify the reblooming properties of each one. In this regard, we also suggest our own selection criterion to take into account the lack of symmetry of most of the flowering curves. Three classes are created on the basis of a principal component analysis conducted on a set of reblooming indicators, and a subclassification is made using a longitudinal $k$--mea…

基于模型的聚类

Model-based Clustering

本文介绍基于模型的聚类，通过混合模型在概率框架内定义簇结构，并与启发式方法对比，讨论后处理及应用领域。