Bayesian analysis of multivariate mixture models via factor analyzer
인자분해를 통한 다변량 혼합 모형의 베이지안 분석
- 자연과학대학 통계학과
- Issue Date
- 서울대학교 대학원
- 학위논문 (박사)-- 서울대학교 대학원 : 통계학과, 2012. 8. 김용대.
- We consider a new Bayesian finite mixture model for multivariate data.
A problem is to estimate the covariance matrix since the number of parameters
for the covariance matrix is squarely proportional to the dimension of data.
Also, the inverting large dimensional covariate, which is necessary for
MCMC algorithms, is very time consuming and practically almost prohibited.
In this thesis, we propose a way of reducing the parameters in the
covariance matrices by use of the factor model. That is, the dependence structure of each component is assumed to be represented by linear
combinations of factors. To simply the model and improve interpretability further, we allow some factors can be shared across the components.
From numerical studies, we confirmed that our method well perform with different component covariance structure.