| Several topics on hidden variable models and their applications are discussed in this dissertation. First, misspecification of the hidden variables in the proportional hazards model with frailty is briefly discussed. Second, two new classes of frailty models are proposed, namely, the scale mixture frailty models and the hidden Markov frailty models for local dependence. Third, we present a minimal class of non-stationary stochastic processes that can be detected from observations. Fourth, we suggest a classifier using a binary hidden Markov model, which is robust to unknown noise structure in testing images. Finally, the identifiability of several binary hidden Markov models, including the model used in the robust classifier, is studied. |
