In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (2001) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn.
The aim of the paper is to address Aitkin's concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations.
A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.
Bayesian Statistical Modeling in Action for Estimation and Forecasting in Low- and Middle-income Countries: The Case of the Family Planning Estimation Tool
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；NYU（纽约大学）；Hamilton Institute and Department of Mathematics and Statistics, Maynooth University（梅努斯大学数学与统计学院汉密尔顿研究所）；Avenir Health（Avi未来健康）；Track20 (India), Avenir Health（Track20（印度）/ Avi未来健康）；Ministry of Health, Uganda（乌干达卫生部）；United Nations Population Fund（联合国人口基金）；Track20 and Ministry of Health and Child Care（Track20及儿童保健卫生部）
Calda AI AB（Calda AI公司）；Oskar Klein Centre for Cosmoparticle Physics, Stockholm University（斯德哥尔摩大学奥斯卡·克莱因宇宙粒子物理中心）；William H. Miller III Department of Physics and Astronomy, Johns Hopkins University（约翰斯·霍普金斯大学威廉·H·米勒三世物理与天文学系）；Center for Computational Astrophysics, Flatiron Institute（熨斗研究所计算天体物理中心）；Sorbonne Université（索邦大学）；Institut d’Astrophysique de Paris（巴黎天体物理研究所）
An Interval-Based Bayesian Generative Model for Human Complex Activity Recognition
Chongqing University（重庆大学）；National University of Singapore（新加坡国立大学）；Bioinformatics Institute, A*STAR（A*STAR生物信息研究所）；Lanzhou University of Technology（兰州理工大学）；Lanzhou University（兰州大学）
