Farklı bağımlılık varsayımlarına dayalı saklı Markov modelleri

Hidden Markov models are widely used to model the probabilistic structures with latent random variables. The main assumption of hidden Markov models is that; observations are conditionally independent and identically distributed random variables. There may exist some cases where this assumption may not be valid in practice. That is, an observation that occurs in the current state may depend on the previous observation symbol that occurred in the previous state. In this thesis, two types of hidden Markov models are introduced which differ from the classical hidden Markov model based on different first-order Markov dependence assumptions. The introduced models are capable of capturing a possible first-order Markov dependence between the successive observations or successive system informations. They can provide better representation for the appropriate real-life problems where, if the observations have some conditional dependencies among them. The two proposed models are defined with their assumptions and using appropriate notation. Modifications to the algorithms used for parameter estimates and hidden state sequence estimates are explained. In addition, an experimental study is conducted to show the performance of the introduced models compared to the classical hidden Markov model. According to the results of the experimental study, the proposed models outperform in generated observation sequences that have appropriate assumptions. Besides, two different case studies are conducted namely the occurrences of strong earthquakes and daily stock prices. They are modelled with both the classical hidden Markov model and the proposed models, and the results are compared.