EM Algorithm and Related Statistical Models

Michiko Watanabe, Kazunori Yamaguchi

• Incomplete data and the generation mechanisms; type of incomplete data and its analysis; statistical models for incomplete data; analysis of data with missing values; missing data in multinominal data; algorithms for MLE for multivariate normal datawith missing values; scoring method; EM algorithm; basics of EM algorithm; extension of EM algorithm and acceleration; EM algorithm as an optimization tool robust model and outlier detection; scale mixture model of normal distributions; multivariate andcontaminated normal distribution; robust tobit model; robust factor model; statistical model with latent variables; latent structure model and EM algorithm; latent class model and latent trait model; structured equations model with latent variables;extensions of EM algorithm; ECM algorithm; ECME algorithm; optimal EM algorithm; MCEM algorithm; covergence speed of EM algorithm; convergence speed; comparisons of EM and other optimization algorithms quasi Newton method; acceleration methods of the EMalgorithm; neural networks and EM algorithm; EM algorithm in neural networks; geometric interpretation of EM algorithm; Marcov chain Monte Carlo; Bayes estimation; Marcov chain; Metropolis-Hastings algorithm; data augmentation algorithm; poor man's dataaugmentation algorithm; Gibbs sampling algorithm. Appendices: SOLAS for missing data analysis; Lem.