期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2018
页码：1-21
DOI：10.1007/s13171-018-0136-8
语种：English
出版社：Indian Statistical Institute
摘要：Regression models for size-and-shape analysis are developed, where the model is specified in the Euclidean space of the landmark coordinates. Statistical models in this space (which is known as the top space or ambient space) are often easier for practitioners to understand than alternative models in the quotient space of size-and-shapes. We consider a Bayesian linear size-and-shape regression model in which the response variable is given by labelled configuration matrix, and the covariates represent quantities such as gender and age. It is important to parameterize the model so that it is identifiable, and we use the LQ decomposition in the intercept term in the model for this purpose. Gamma priors for the inverse variance of the error term, matrix Fisher priors for the random rotation matrix, and flat priors for the regression coefficients are used. Markov chain Monte Carlo algorithms are used for sampling from the posterior distribution, in particular by using combinations of Metropolis-Hastings updates and a Gibbs sampler. The proposed Bayesian methodology is illustrated with an application to forensic facial data in three dimensions, where we investigate the main changes in growth by describing relative movements of landmarks for each gender over time.
关键词：Bayesian ; Markov chain Monte Carlo ; Principal components analysis ; Size-and-shape regression.
