Hidden markov models for time series: an introduction using R
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
|
| Series: | Monographs on statistics and applied probability
110 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXII, 275 S. |
| ISBN: | 9781584885733 |
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MARC
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| 245 | 1 | 0 | |a Hidden markov models for time series |b an introduction using R |c Walter Zucchini ; Iain L. MacDonald |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2009 | |
| 300 | |a XXII, 275 S. | ||
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| 490 | 1 | |a Monographs on statistics and applied probability |v 110 | |
| 650 | 4 | |a Markov processes | |
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|---|---|
| adam_text | Contents
Preface
xvii
Notation
and abbreviations
xxi
PART ONE Model structure, properties and methods
1
Preliminaries: mixtures and Markov chains
3
1.1
Introduction
3
1.2
Independent mixture models
6
1.2.1
Definition and properties
6
1.2.2
Parameter estimation
9
1.2.3
Unbounded likelihood in mixtures
10
1.2.4
Examples of fitted mixture models
11
1.3
Markov chains
15
1.3.1
Definitions and example
16
1.3.2
Stationary distributions
18
1.3.3
Reversibility
19
1.3.4
Autocorrelation function
19
1.3.5
Estimating transition probabilities
20
1.3.6
Higher-order Markov chains
22
Exercises
24
Hidden Markov models: definition and properties
29
2.1
A simple hidden Markov model
29
2.2
The
basics
30
2.2.1
Definition and notation
30
2.2.2
Marginal distributions
32
2.2,3
Moments
34
2.3
The
likelihood
35
2.3.1
The likelihood of a two-state Bemoulli-HMM
35
2.3.2
The likelihood in general
ЗУ
2.3.3
The likelihood when data are missing at
random
39
2.3.4
The likelihood when observations are interval-
censored
40
Exercises
41
3
Estimation by direct maximization of the likelihood
45
3.1
Introduction
45
3.2
Scaling the likelihood computation
46
3.3
Maximization subject to constraints
47
3.3.1
Reparametrization to avoid constraints
47
3.3.2
Embedding in a continuous-time Markov chain
49
3.4
Other problems
49
3.4.1
Multiple maxima in the likelihood
49
3.4.2
Starting values for the iterations
50
3.4.3
Unbounded likelihood
50
3.5
Example: earthquakes
50
3.6
Standard errors and confidence intervals
53
3.6.1
Standard errors via the Hessian
53
3.6.2
Bootstrap standard errors and confidence
intervals
55
3.7
Example: parametric bootstrap
55
Exercises
57
4
Estimation by the EM algorithm
59
4.1
Forward and backward probabilities
59
4.1.1
Forward probabilities
60
4.1.2
Backward probabilities
61
4.1.3
Properties of forward and backward probabili¬
ties
62
4.2
The EM algorithm
63
4.2.1
EM in general
63
4.2.2
EM for HMMs
64
4.2.3
M
step for
Poisson-
and normal-HMMs
66
4.2.4
Starting from a specified state
67
4.2.5
EM for the case in which the Markov chain is
stationary
67
4.3
Examples of EM applied to Poisson-HMMs
68
4.3.1
Earthquakes
68
4.3.2
Foetal movement counts
70
4.4
Discussion
72
Exercises
73
5
Forecasting, decoding and state prediction
75
5.1
Conditional distributions
76
5.2
Forecast distributions
77
5.3
Decoding
80
5.3.1
State probabilities and local decoding
80
5.3.2
Global decoding
82
5.4
State prediction
- 86
Exercises
87
6
Model selection and checking
89
6.1
Model selection by AIC and BIG
89
6.2
Model checking with pseudo-residuals
92
6.2.1
Introducing pseudo-residuals
93
6.2.2
Ordinary pseudo-residuals
96
6.2.3
Forecast pseudo-residuals
97
6.3
Examples
98
6.3.1
Ordinary pseudo-residuals for the earthquakes
98
6.3.2
Dependent ordinary pseudo-residuals
98
6.4
Discussion
100
Exercises
101
7
Bayesian inference for
Poisson—
HMMs
103
7.1
Applying the Gibbs sampler to Poisson-HMMs
103
7.1.1
Generating sample paths of the Markov chain
105
7.1.2
Decomposing observed counts
106
7.1.3
Updating the parameters
106
7.2
Bayesian estimation of the number of states
106
7.2.1
Use of the integrated likelihood
107
7.2.2
Model selection by parallel sampling
108
7.3
Example: earthquakes
108
7.4
Discussion
110
Exercises
112
8
Extensions of the basic hidden Markov model
115
8.1
Introduction
115
8.2
HMMs with general univariate state-dependent distri¬
bution
116
8.3
HMMs based on a second-order Markov chain
118
8.4
HMMs for multivariate series
119
8.4.1
Series of rnultinomiaHike observations
119
8.4.2
A model for categorical series
121
8.4.3
Other multivariate models
122
8.5
Series that depend on covariates
125
8.5.1
Covariates in the state-dependent distributions
125
8.5.2
Covariates in the transition probabilities
126
8.6 Models
with additional dependencies
128
Exercises
129
PART TWO Applications
133
9
Epileptic seizures
135
9.1
Introduction
135
9.2
Models fitted
135
9.3
Model checking by pseudo-residuals
138
Exercises
140
10
Eruptions of the Old Faithful geyser
141
10.1
Introduction
141
10.2
Binary time series of short and long eruptions
141
10.2.1
Markov chain models
142
10.2.2
Hidden Markov models
144
10.2.3
Comparison of models
147
10.2.4
Forecast distributions
148
10.3
Normal-HMMs for durations and waiting times
149
10.4
Divariate
model for durations and waiting times
152
Exercises
153
11
Drosophila
speed and change of direction
155
11.1
Introduction
155
11.2 Von
Mises
distributions
156
11.3 Von
Mises-HMMs for the two subjects
157
11.4
Circular autocorrelation functions
158
11.5
Bivaxiate model
161
Exercises
165
12
Wind direction at Koeberg
167
12.1
Introduction
167
12.2
Wind direction classified into
16
categories
167
12.2.1
Three HMMs for hourly averages of wind
direction
167
12.2.2
Model comparisons and other possible models
170
12.2.3
Conclusion
173
12.3
Wind direction as a circular variable
174
12.3.1
Daily at hour
24: von
Mises-HMMs
174
12.3.2
Modelling hourly change of direction
176
12.3.3
Transition probabilities varying with lagged
speed
176
12.3.4
Concentration
parameter varying with
speed
177
Exercises
180
13
Models for financial series
181
13.1
Thinly traded shares
181
13.1.1
Univariate models
181
13.1.2
Multivariate models
183
13.1.3
Discussion
185
13.2
Multivariate
HMM
for returns on four shares
186
13.3
Stochastic volatility models
190
13.3.1
Stochastic volatility models without leverage
190
13.3.2
Application: FTSE
100
returns
192
13.3.3
Stochastic volatility models with leverage
193
13.3.4
Application: TOPIX returns
195
13.3.5
Discussion
197
14
Births at Edendale Hospital
199
14.1
Introduction
199
14.2
Models for the proportion Caesarean
199
14.3
Models for the total number of deliveries
205
14.4
Conclusion
208
15
Homicides and suicides in Cape Town
209
15.1
Introduction
209
15.2
Firearm homicides as a proportion of all homicides,
suicides and legal intervention homicides
209
15.3
The number of firearm homicides
211
15.4
Firearm homicide and suicide proportions
213
15.5
Proportion in each of the five categories
217
16
Animal behaviour model with feedback
219
16.1
Introduction
219
16.2
The model
220
16.3
Likelihood evaluation
22.2
16.3.1
The likelihood as a multiple sum
223
16.3.2
Recursive evaluation
223
16.4
Parameter estimation by maximum likelihood
224
16.5
Model checking
224
16.6
Inferring the underlying state
225
16.7
Models for a heterogeneous group of subjects
226
16.7.1
Models assuming some parameters to be
constant across subjects
226
16.7.2
Mixed models
227
16.7.3
Inclusion of covariates
227
16.8
Other modifications or extensions
228
16.8.1
Increasing the number of states
228
16.8.2
Changing the nature of the state-dependent
distribution
228
16.9
Application to caterpillar feeding behaviour
229
16.9.1
Data description and preliminary analysis
229
16.9.2
Parameter estimates and model checking
229
16.9.3
Runlength distributions
233
16.9.4
Joint models for seven subjects
235
16.10
Discussion
236
A Examples of
R
code
239
A.I Stationary Poisson-HMM, numerical maximization
239
A.
1.1
Transform natural parameters to working
240
A.
1.2
Transform working parameters to natural
240
A.
1.3
Log-likelihood of a stationary Poisson-HMM
240
A.
1.4
ML estimation of a stationary Poisson-HMM
241
A.2 More on Poisson-HMMs, including EM
242
A.
2.1
Generate a realization of a Poisson-HMM
242
A.
2.2
Forward and backward probabilities
242
A.2.3 EM estimation of a Poisson-HMM
243
A.
2.4
Viterbi algorithm
244
A.
2.5
Conditional state probabilities
244
A.
2.6
Local decoding
245
A.
2.7
State prediction
245
A.
2.8
Forecast distributions
246
A.
2.9
Conditional distribution of one observation
given the rest
246
A.2.
10
Ordinary pseudo-residuals
247
A.3 Bivariate normal state-dependent distributions
248
A.
3.1
Transform natural parameters to working
248
A.
3.2
Transform working parameters to natural
249
A.
3.3
Discrete log-likelihood
249
A.
3.4
MLEs of the parameters
250
A.
4
Categorical
HMM.
constrained optimization
250
A.4.1 Log-likelihood
251
A.
4.2
MLEs of the parameters
252
В
Some proofs
253
B.I Factorization needed for forward probabilities
253
B.2 Two results for backward probabilities
255
В.
3
Conditional independence of X^ and Xj^
256
References
257
Author index
267
Subject index
271
Statistics
Reveals How HMMs Can Be Used as General-Purpose Time Series Models
Hidden Markov Models for Time Series: An Introduction Using
R
applies
hidden Markov models (HMMs) to a wide range of time series types, from
continuous-valued, circular, and multivariate series to binary data, bounded
and unbounded counts, and categorical observations. It also discusses how to
employ the freely available computing environment
R
to carry out computations
for parameter estimation, model selection and checking, decoding, and
forecasting.
After presenting the simple
Poisson —
HMM,
the book covers estimation,
forecasting, decoding, prediction, model selection, and Bayesian inference.
Through examples and applications, the authors describe how to extend and
generalize the basic model so it can be applied in a rich variety of situations.
They also provide
R
code for some of the examples, enabling the use of the
codes in similar applications.
This book illustrates the wonderful flexibility of HMMs as general-purpose
models for time series data. It provides a broad understanding of the models
and their uses.
Features
•
Presents an accessible overview of HMMs for analyzing time series data
•
Covers continuous-valued, circular, and multivariate time series data
•
Explores a variety of applications in animal behavior, finance,
epidemiology, climatology, and sociology
•
Shows how to apply the methods using
R
•
Includes numerous theoretical and programming exercises at the end of
most chapters
•
Provides all of the analyzed data sets online
|
| adam_txt |
Contents
Preface
xvii
Notation
and abbreviations
xxi
PART ONE Model structure, properties and methods
1
Preliminaries: mixtures and Markov chains
3
1.1
Introduction
3
1.2
Independent mixture models
6
1.2.1
Definition and properties
6
1.2.2
Parameter estimation
9
1.2.3
Unbounded likelihood in mixtures
10
1.2.4
Examples of fitted mixture models
11
1.3
Markov chains
15
1.3.1
Definitions and example
16
1.3.2
Stationary distributions
18
1.3.3
Reversibility
19
1.3.4
Autocorrelation function
19
1.3.5
Estimating transition probabilities
20
1.3.6
Higher-order Markov chains
22
Exercises
24
Hidden Markov models: definition and properties
29
2.1
A simple hidden Markov model
29
2.2
The
basics
30
2.2.1
Definition and notation
30
2.2.2
Marginal distributions
32
2.2,3
Moments
34
2.3
The
likelihood
35
2.3.1
The likelihood of a two-state Bemoulli-HMM
35
2.3.2
The likelihood in general
ЗУ
2.3.3
The likelihood when data are missing at
random
39
2.3.4
The likelihood when observations are interval-
censored
40
Exercises
41
3
Estimation by direct maximization of the likelihood
45
3.1
Introduction
45
3.2
Scaling the likelihood computation
46
3.3
Maximization subject to constraints
47
3.3.1
Reparametrization to avoid constraints
47
3.3.2
Embedding in a continuous-time Markov chain
49
3.4
Other problems
49
3.4.1
Multiple maxima in the likelihood
49
3.4.2
Starting values for the iterations
50
3.4.3
Unbounded likelihood
50
3.5
Example: earthquakes
50
3.6
Standard errors and confidence intervals
53
3.6.1
Standard errors via the Hessian
53
3.6.2
Bootstrap standard errors and confidence
intervals
55
3.7
Example: parametric bootstrap
55
Exercises
57
4
Estimation by the EM algorithm
59
4.1
Forward and backward probabilities
59
4.1.1
Forward probabilities
60
4.1.2
Backward probabilities
61
4.1.3
Properties of forward and backward probabili¬
ties
62
4.2
The EM algorithm
63
4.2.1
EM in general
63
4.2.2
EM for HMMs
64
4.2.3
M
step for
Poisson-
and normal-HMMs
66
4.2.4
Starting from a specified state
67
4.2.5
EM for the case in which the Markov chain is
stationary
67
4.3
Examples of EM applied to Poisson-HMMs
68
4.3.1
Earthquakes
68
4.3.2
Foetal movement counts
70
4.4
Discussion
72
Exercises
73
5
Forecasting, decoding and state prediction
75
5.1
Conditional distributions
76
5.2
Forecast distributions
77
5.3
Decoding
80
5.3.1
State probabilities and local decoding
80
5.3.2
Global decoding
82
5.4
State prediction
- 86
Exercises
87
6
Model selection and checking
89
6.1
Model selection by AIC and BIG
89
6.2
Model checking with pseudo-residuals
92
6.2.1
Introducing pseudo-residuals
93
6.2.2
Ordinary pseudo-residuals
96
6.2.3
Forecast pseudo-residuals
97
6.3
Examples
98
6.3.1
Ordinary pseudo-residuals for the earthquakes
98
6.3.2
Dependent ordinary pseudo-residuals
98
6.4
Discussion
100
Exercises
101
7
Bayesian inference for
Poisson—
HMMs
103
7.1
Applying the Gibbs sampler to Poisson-HMMs
103
7.1.1
Generating sample paths of the Markov chain
105
7.1.2
Decomposing observed counts
106
7.1.3
Updating the parameters
106
7.2
Bayesian estimation of the number of states
106
7.2.1
Use of the integrated likelihood
107
7.2.2
Model selection by parallel sampling
108
7.3
Example: earthquakes
108
7.4
Discussion
110
Exercises
112
8
Extensions of the basic hidden Markov model
115
8.1
Introduction
115
8.2
HMMs with general univariate state-dependent distri¬
bution
116
8.3
HMMs based on a second-order Markov chain
118
8.4
HMMs for multivariate series
119
8.4.1
Series of rnultinomiaHike observations
119
8.4.2
A model for categorical series
121
8.4.3
Other multivariate models
122
8.5
Series that depend on covariates
125
8.5.1
Covariates in the state-dependent distributions
125
8.5.2
Covariates in the transition probabilities
126
8.6 Models
with additional dependencies
128
Exercises
129
PART TWO Applications
133
9
Epileptic seizures
135
9.1
Introduction
135
9.2
Models fitted
135
9.3
Model checking by pseudo-residuals
138
Exercises
140
10
Eruptions of the Old Faithful geyser
141
10.1
Introduction
141
10.2
Binary time series of short and long eruptions
141
10.2.1
Markov chain models
142
10.2.2
Hidden Markov models
144
10.2.3
Comparison of models
147
10.2.4
Forecast distributions
148
10.3
Normal-HMMs for durations and waiting times
149
10.4
Divariate
model for durations and waiting times
152
Exercises
153
11
Drosophila
speed and change of direction
155
11.1
Introduction
155
11.2 Von
Mises
distributions
156
11.3 Von
Mises-HMMs for the two subjects
157
11.4
Circular autocorrelation functions
158
11.5
Bivaxiate model
161
Exercises
165
12
Wind direction at Koeberg
167
12.1
Introduction
167
12.2
Wind direction classified into
16
categories
167
12.2.1
Three HMMs for hourly averages of wind
direction
167
12.2.2
Model comparisons and other possible models
170
12.2.3
Conclusion
173
12.3
Wind direction as a circular variable
174
12.3.1
Daily at hour
24: von
Mises-HMMs
174
12.3.2
Modelling hourly change of direction
176
12.3.3
Transition probabilities varying with lagged
speed
176
12.3.4
Concentration
parameter varying with
speed
177
Exercises
180
13
Models for financial series
181
13.1
Thinly traded shares
181
13.1.1
Univariate models
181
13.1.2
Multivariate models
183
13.1.3
Discussion
185
13.2
Multivariate
HMM
for returns on four shares
186
13.3
Stochastic volatility models
190
13.3.1
Stochastic volatility models without leverage
190
13.3.2
Application: FTSE
100
returns
192
13.3.3
Stochastic volatility models with leverage
193
13.3.4
Application: TOPIX returns
195
13.3.5
Discussion
197
14
Births at Edendale Hospital
199
14.1
Introduction
199
14.2
Models for the proportion Caesarean
199
14.3
Models for the total number of deliveries
205
14.4
Conclusion
208
15
Homicides and suicides in Cape Town
209
15.1
Introduction
209
15.2
Firearm homicides as a proportion of all homicides,
suicides and legal intervention homicides
209
15.3
The number of firearm homicides
211
15.4
Firearm homicide and suicide proportions
213
15.5
Proportion in each of the five categories
217
16
Animal behaviour model with feedback
219
16.1
Introduction
219
16.2
The model
220
16.3
Likelihood evaluation
22.2
16.3.1
The likelihood as a multiple sum
223
16.3.2
Recursive evaluation
223
16.4
Parameter estimation by maximum likelihood
224
16.5
Model checking
224
16.6
Inferring the underlying state
225
16.7
Models for a heterogeneous group of subjects
226
16.7.1
Models assuming some parameters to be
constant across subjects
226
16.7.2
Mixed models
227
16.7.3
Inclusion of covariates
227
16.8
Other modifications or extensions
228
16.8.1
Increasing the number of states
228
16.8.2
Changing the nature of the state-dependent
distribution
228
16.9
Application to caterpillar feeding behaviour
229
16.9.1
Data description and preliminary analysis
229
16.9.2
Parameter estimates and model checking
229
16.9.3
Runlength distributions
233
16.9.4
Joint models for seven subjects
235
16.10
Discussion
236
A Examples of
R
code
239
A.I Stationary Poisson-HMM, numerical maximization
239
A.
1.1
Transform natural parameters to working
240
A.
1.2
Transform working parameters to natural
240
A.
1.3
Log-likelihood of a stationary Poisson-HMM
240
A.
1.4
ML estimation of a stationary Poisson-HMM
241
A.2 More on Poisson-HMMs, including EM
242
A.
2.1
Generate a realization of a Poisson-HMM
242
A.
2.2
Forward and backward probabilities
242
A.2.3 EM estimation of a Poisson-HMM
243
A.
2.4
Viterbi algorithm
244
A.
2.5
Conditional state probabilities
244
A.
2.6
Local decoding
245
A.
2.7
State prediction
245
A.
2.8
Forecast distributions
246
A.
2.9
Conditional distribution of one observation
given the rest
246
A.2.
10
Ordinary pseudo-residuals
247
A.3 Bivariate normal state-dependent distributions
248
A.
3.1
Transform natural parameters to working
248
A.
3.2
Transform working parameters to natural
249
A.
3.3
Discrete log-likelihood
249
A.
3.4
MLEs of the parameters
250
A.
4
Categorical
HMM.
constrained optimization
250
A.4.1 Log-likelihood
251
A.
4.2
MLEs of the parameters
252
В
Some proofs
253
B.I Factorization needed for forward probabilities
253
B.2 Two results for backward probabilities
255
В.
3
Conditional independence of X^ and Xj^
256
References
257
Author index
267
Subject index
271
Statistics
Reveals How HMMs Can Be Used as General-Purpose Time Series Models
Hidden Markov Models for Time Series: An Introduction Using
R
applies
hidden Markov models (HMMs) to a wide range of time series types, from
continuous-valued, circular, and multivariate series to binary data, bounded
and unbounded counts, and categorical observations. It also discusses how to
employ the freely available computing environment
R
to carry out computations
for parameter estimation, model selection and checking, decoding, and
forecasting.
After presenting the simple
Poisson —
HMM,
the book covers estimation,
forecasting, decoding, prediction, model selection, and Bayesian inference.
Through examples and applications, the authors describe how to extend and
generalize the basic model so it can be applied in a rich variety of situations.
They also provide
R
code for some of the examples, enabling the use of the
codes in similar applications.
This book illustrates the wonderful flexibility of HMMs as general-purpose
models for time series data. It provides a broad understanding of the models
and their uses.
Features
•
Presents an accessible overview of HMMs for analyzing time series data
•
Covers continuous-valued, circular, and multivariate time series data
•
Explores a variety of applications in animal behavior, finance,
epidemiology, climatology, and sociology
•
Shows how to apply the methods using
R
•
Includes numerous theoretical and programming exercises at the end of
most chapters
•
Provides all of the analyzed data sets online |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Zucchini, Walter MacDonald, Iain L. |
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| building | Verbundindex |
| bvnumber | BV022545255 |
| callnumber-first | Q - Science |
| callnumber-label | QA280 |
| callnumber-raw | QA280 |
| callnumber-search | QA280 |
| callnumber-sort | QA 3280 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 515 ST 601 |
| classification_tum | DAT 368f MAT 634f MAT 607f |
| ctrlnum | (OCoLC)144565537 (DE-599)BVBBV022545255 |
| dewey-full | 519.5/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/5 |
| dewey-search | 519.5/5 |
| dewey-sort | 3519.5 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV022545255 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:11:40Z |
| indexdate | 2024-07-09T20:59:56Z |
| institution | BVB |
| isbn | 9781584885733 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015751638 |
| oclc_num | 144565537 |
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| physical | XXII, 275 S. |
| publishDate | 2009 |
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| publisher | CRC Press |
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| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability |
| spelling | Zucchini, Walter Verfasser aut Hidden markov models for time series an introduction using R Walter Zucchini ; Iain L. MacDonald Boca Raton [u.a.] CRC Press 2009 XXII, 275 S. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 110 Markov processes R (Computer program language) Time-series analysis Hidden-Markov-Modell (DE-588)4352479-5 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Hidden-Markov-Modell (DE-588)4352479-5 s Zeitreihenanalyse (DE-588)4067486-1 s R Programm (DE-588)4705956-4 s b DE-604 MacDonald, Iain L. Verfasser (DE-588)131475290 aut Monographs on statistics and applied probability 110 (DE-604)BV002494005 110 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751638&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751638&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Zucchini, Walter MacDonald, Iain L. Hidden markov models for time series an introduction using R Monographs on statistics and applied probability Markov processes R (Computer program language) Time-series analysis Hidden-Markov-Modell (DE-588)4352479-5 gnd R Programm (DE-588)4705956-4 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4352479-5 (DE-588)4705956-4 (DE-588)4067486-1 |
| title | Hidden markov models for time series an introduction using R |
| title_auth | Hidden markov models for time series an introduction using R |
| title_exact_search | Hidden markov models for time series an introduction using R |
| title_exact_search_txtP | Hidden markov models for time series an introduction using R |
| title_full | Hidden markov models for time series an introduction using R Walter Zucchini ; Iain L. MacDonald |
| title_fullStr | Hidden markov models for time series an introduction using R Walter Zucchini ; Iain L. MacDonald |
| title_full_unstemmed | Hidden markov models for time series an introduction using R Walter Zucchini ; Iain L. MacDonald |
| title_short | Hidden markov models for time series |
| title_sort | hidden markov models for time series an introduction using r |
| title_sub | an introduction using R |
| topic | Markov processes R (Computer program language) Time-series analysis Hidden-Markov-Modell (DE-588)4352479-5 gnd R Programm (DE-588)4705956-4 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Markov processes R (Computer program language) Time-series analysis Hidden-Markov-Modell R Programm Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751638&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015751638&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
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