Walter Zucchini (Germany University of Gottingen), Iain L. MacDonald, Roland Langrock

Hidden Markov Models for Time Series

An Introduction Using R, Second Edition

• Broschiertes Buch

Produktbeschreibung

Hidden Markov Models (HMMs) remains a vibrant area of research in statistics, with many new applications appearing since publication of the first edition.

Produktdetails

• Chapman & Hall/CRC Monographs on Statistics and Applied Probability
• Verlag: Taylor & Francis Ltd
• 2 ed
• Seitenzahl: 400
• Erscheinungstermin: 30. September 2021
• Englisch
• Abmessung: 157mm x 263mm x 26mm
• Gewicht: 598g
• ISBN-13: 9781032179490
• ISBN-10: 103217949X
• Artikelnr.: 62570889

Autorenporträt

Walter Zucchini, Iain K. MacDonald, Roland Langrock

Inhaltsangabe

Model structure, properties and methods
Preliminaries: mixtures and Markov chainsIntroduction
Independent mixture models
Markov chains
Exercises
Hidden Markov models: definition and properties
A simple hidden Markov model
The basics
The likelihood
Exercises
Direct maximization of the likelihood
Introduction
Scaling the likelihood computation
Maximization subject to constraints
Other problems
Example: earthquakes
Standard errors and confidence intervals
Example: parametric bootstrap
Exercises
Estimation by the EM algorithmForward and backward probabilities
The EM algorithm
Examples of EM applied to Poisson-HMMs
Discussion
Exercises
Forecasting, decoding and state predictionConditional distributions
Forecast distributions
Decoding
State prediction
HMMs for classification
Exercises
Model selection and checkingModel selection by AIC and BIC
Model checking with pseudo-residuals
Examples
Discussion
Exercises
Bayesian inference for Poisson-HMMsApplying the Gibbs sampler to
Poisson-HMMs
Bayesian estimation of the number of states
Example: earthquakes
Discussion
Exercises
R packagesThe package depmixS4The package HiddenMarkovThe package msmThe
package R20penBUGS
Discussion
Extensions
General state-dependent distributionsIntroduction
Univariate state-dependent distribution
Multinomial and categorical HMMs
Multivariate state-dependent distribution
Exercises
Covariates and other extra dependenciesIntroduction
HMMs with covariates
HMMs based on a second-order Markox chain
HMMs with other additional dependencies
Exercises
Continuous-valued state processesIntroduction
Models with continous-valued state process
Fitting an SSM to the earthquake data
Discussion
Hidden semi-Markov models as HMMsIntroduction
Semi-Markov processes, hidden semi-Markov models and approximating HMMs
Examples of HSMMs as HMMs
General HSMM
R code
Some examples of dwell-time distributions
Fitting HSMMs via the HMM representation
Example: earthquakes
Discussion
Exercises
HMMs for longitudinal dataIntroduction
Some parameters constant across components
Models with random effects
Discussion
Exercises
Applications
Introduction to applications
Epileptic seizuresIntroduction
Models fitted
Model checking by pseudo-residuals
Exercises
Daily rainfall occurrenceIntroduction
Models fitted
Eruptions of the Old Faithful geyserIntroduction
The data
Binary time series of short and long eruptions
Normal-HMMs for durations and waiting times
Bivariate model for durations and waiting times
Exercises
HMMs for animal movementIntroduction
Directional data
HMMs for movement data
Basic HMM for Drosophila movement
HMMs and HSMMs for bison movement
Mixed HMMs for woodpecker movement
Exercises
Wind direction at KoebergIntroduction
Wind direction classified into 16 categories
Wind direction as a circular variable
Exercises
Models for financial seriesMultivariate HMM for returns on four shares
Stochastic volatility models
Exercises
Births at Edendale HospitalIntroduction
Models for the proportion Caesarean
Models for the total number of deliveries
Conclusion
Homicides and suicides in Cape TownIntroduction
Firearm homicides as a proportion of all homicides, suicides and legal
intervention homicides
The number of firearm homicides
Firearm homicide and suicide proportions
Proportion in each of the five categories
Animal behaviour model with feedbackIntroduction
The model
Likelihood evaluation
Parameter estimation by maximum likelihood
Model checking
Inferring the underlying state
Models for a heterogeneous group of subjects
Other modifications or extensions
Application to caterpillar feeding behaviour
Discussion
Survival rates of Soay sheepIntroduction
MRR data without use of covariates
MRR data involving covariate information
Application to Soay sheep data
Conclusion
Examples of R codeThe functions
Examples of code using the above functions
Some proofsFactorization needed for forward probabilities
Two results for backward probabilities
Conditional independence of Xt1 and XTt+1
References
Author index
Subject index