Riassunto:
Discrete-valued time series are common in practice, but methods for their analysis are not well-known. In recent years, methods have been developed which are specifically designed for the analysis of discrete-valued time series. Hidden Markov and Other Models for Discrete-Valued Time Series introduces a new, versatile, and computationally tractable class of models, the "hidden Markov" models. It presents a detailed account of these models, then applies them to data from a wide range of diverse subject areas, including medicine, climatology, and geophysics. This book will be invaluable to researchers and postgraduate and senior undergraduate students in statistics. Researchers and applied statisticians who analyze time series data in medicine, animal behavior, hydrology, and sociology will also find this information useful.
Contenuti:
Survey of Models
A Survey of Models for Discrete-Valued Time Series
Introduction: The Need for Discrete-Valued Time Series Models
Markov Chains
Higher-Order Markov Chains
The DARMA models of Jacobs and Lewis
Models Based on Thinning
The Bivariate Geometric Models of Block, Langberg, and Stoffer
Markov Regression Models
Parameter-Driven Models
State-Spaced Models
Miscellaneous Models
Discussion
Hidden Markov Models
The Basic Models
Introduction
Some Theoretical Aspects of Hidden Markov Models in Speech Processing
Hidden Markov Time Series Models: Definition and Notation
Correlation Properties
Evaluation of the Likelihood Function
Distributional Properties
Parameter Estimation
Identification of Outliers
Reversibility
Discussion
Extensions and Modifications
Introduction
Models Based on a Second-Order Markov Chain
Multinomial-Hidden Markov Models
Multivariate Models
Models with State-Dependent Probabilities Depending on Covariates
Models in Which the Markov Chain Is Homogeneous but Not Assumed Stationary
Models in Which the Markov Chain Is Nonhomogeneous
Joint Models for the Numbers of Trials and the Numbers of Successes in Those Trials
Discussion
Applications
Introduction
The Durations of Successive Eruptions of the Old Faithful Geyser
Epileptic Seizure Counts
Births at Edendale Hospital
Locomotory Behaviour of Locusta migratoria
Wind Direction at Koeberg
Evapotranspiration
Thinly Traded Shares on the Johannesburt Stock Exchange
Daily Rainfall at Durban
Homicides and Suicides, Cape Town, 1986-1991
Conclusion
Appendices
A : Proofs of Results Used in the Derivation of the Baum-Welch Algorithm
B: Data
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