Finite or infinite mixture models are routinely used in Bayesian statistical practice for tasks such as clustering or density estimation. Such models are very attractive due to their flexibility and tractability. However, a common problem in fitting these or other discrete models to data is that they tend to produce a large number of overlapping clusters. Some attention has been given in the statistical literature to models that include a repulsive feature, i.e., that encourage separation of mixture components. We study here a method that has been shown to achieve this goal without sacrificing flexibility or model fit. The model is a special case of Gibbs measures, with a parameter that controls the level of repulsion that allows construction of d-dimensional probability densities whose coordinates tend to repel each other. This approach was successfully used for density regression in Quinlan et al. (J Stat Comput Simul 88(15):2931–2947, 2018). We detail some of the global properties of the repulsive family of distributions and offer some further insight by means of a small simulation study.

贝叶斯统计实践中通常使用有限或无限混合模型来完成诸如聚类或密度估计之类的任务。这种模型由于其灵活性和易处理性而非常有吸引力。但是，将这些模型或其他离散模型拟合到数据中的一个普遍问题是它们倾向于产生大量重叠的簇。在统计文献中已经对包含排斥特征的模型给予了一些关注，即，该模型鼓励混合成分的分离。我们在这里研究了一种在不牺牲灵活性或模型拟合性的前提下实现这一目标的方法。该模型是Gibbs测度的特例，其参数控制排斥程度，可构造d坐标趋于相互排斥的三维概率密度。这种方法已成功用于Quinlan等人的密度回归中。（J Stat Comput Simul 88（15）：2931-2947年，2018年）。我们详细介绍了排斥性分布族的一些全局特性，并通过小型模拟研究提供了一些进一步的见解。