Mixture and Hidden Markov Models with R:
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| Hauptverfasser: | , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2022]
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| Schriftenreihe: | Use R!
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 267 Seiten |
| ISBN: | 9783031014383 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mixture and Hidden Markov Models with R |c Ingmar Visser, Maarten Speekenbrink |
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| 264 | 4 | |c © 2022 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents 1 Introduction and Preliminaries.................................................................... What Are Mixture and Hidden Markov Models?............................... 1.1.1 Outline................................................................................... 1.2 Getting Started with R........................................................................ 1.2.1 Help!..................................................................................... 1.2.2 Loading Packages and Data.................................................. 1.2.3 Object Types and Manipulation ........................................... 1.2.4 Visualizing Data.................................................................... 1.2.5 Summarizing Data................................................................. 1.2.6 Linear and Generalized Linear Models................................. 1.2.7 Multinomial Logistic Regression.......................................... 1.2.8 Time-Series........................................................................... 1.3 Datasets Used in the Book.................................................................. 1.3.1 Speed-Accuracy Data............................................................ 1.3.2 S P500 ................................................................................ 1.3.3 Perth Dams Data.................................................................... 1.3.4 Discrimination Learning Data............................................... 1.3.5 Balance
Data.......................................................................... 1.3.6 Repeated Measures on the Balance Scale Task..................... 1.3.7 Dimensional Change Card Sorting Task Data...................... 1.3.8 Weather Prediction Task Data............................................... 1.3.9 Conservation of Liquid Data.................................................. 1.3.10 Iowa Gambling Task Data ..................................................... 1.1 2 Mixture and Latent Class Models................................................................ 2.1 2.2 Introduction and Motivating Example............................................... Definitions and Notation..................................................................... 2.2.1 Mixture Distribution ............................................................ 2.2.2 Example: Generating Data from a Mixture Distribution .... 2.2.3 Parameters of the Mixture Model.......................................... 1 1 З 3 5 5 6 13 15 17 21 25 26 26 28 29 30 31 33 34 36 39 41 45 45 47 48 48 49 xiii
Contents xiv 2.2.4 Mixture Likelihood............................................................... 2.2.5 Posterior Probabilities........................................................... Parameter Estimation........................................................................ 2.3.1 Maximum Likelihood Estimation........................................ 2.3.2 Numerical Optimization of the Likelihood........................... 2.3.3 Expectation Maximization (EM).......................................... 2.3.4 Optimizing Parameters Subject to Constraints..................... 2.3.5 EM or Numerical Optimization?.......................................... 2.3.6 Starting Values for Parameters in Mixture Models.............. Parameter Inference: Likelihood Ratio Tests.................................... 2.4.1 Example: Equality Constraint on Standard Deviations......... Parameter Inference: Standard Errors and Confidence Intervals....... 2.5.1 Finite Difference Approximation of the Hessian................. 2.5.2 Parametric Bootstrap............................................................. 2.5.3 Correcting the Hessian for Linear Constraints...................... Model Selection................................................................................. 2.6.1 Likelihood-Ratio Tests.......................................................... 2.6.2 Information Criteria............................................................... 2.6.3 Example: Model Selection for the Speedl RT Data............. Covariates on the Prior
Probabilities................................................. Identifiability of Mixture Models ..................................................... Further Reading................................................................................ 49 50 52 52 54 56 66 69 70 72 73 74 76 77 79 80 80 85 89 90 92 93 Mixture and Latent Class Models: Applications..................................... 95 95 99 100 106 108 110 112 113 115 116 119 123 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 Gaussian Mixture for the S P500 Data........................................... Gaussian Mixture Model for Conservation Data.............................. Bivariate Gaussian Mixture Model for Conservation Data .............. Latent Class Model for Balance Scale Data..................................... 3.4.1 Model Selection and Checking........................................... 3.4.2 Testing Item Homogeneity Using Parameter Constraints ... 3.5 Binomial Mixture Model for Balance Scale Data............................. 3.5.1 Binomial Logistic Regression ............................................. 3.5.2 Mixture Models.................................................................... 3.5.3 Model Selection Model Checking....................................... 3.6 Model Selection with the Bootstrap Likelihood Ratio...................... 3.7 Further Reading.................................................................................. 3.1 3.2 3.3 3.4 4 Hidden Markov Models................................................................................ 4.1 Preliminaries: Markov
Models........................................................... 4.1.1 Definitions............................................................................ 4.1.2 Properties of Markov Models............................................... 4.2 Introducing the Hidden Markov Model............................................. 4.2.1 Definitions............................................................................ 4.2.2 Relation Between Hidden Markov and Mixture Model...... 4.2.3 Example: Bernoulli Hidden Markov Model ........................ 4.2.4 Likelihood and Inference Problems..................................... 125 126 126 127 135 135 136 137 139
Contents Filtering, Likelihood, Smoothingand Prediction............................... 4.3.1 Filtering................................................................................. 4.3.2 Likelihood............................................................................ 4.3.3 Smoothing............................................................................ 4.3.4 Scaling.................................................................................. 4.3.5 The Likelihood Revisited..................................................... 4.3.6 Multiple Timeseries.............................................................. 4.3.7 Prediction.............................................................................. Parameter Estimation........................................................................ 4.4.1 Numerical Optimization of the Likelihood........................... 4.4.2 Expectation Maximization (EM).......................................... Decoding .......................................................................................... 4.5.1 Local Decoding..................................................................... 4.5.2 Global Decoding ................................................................... Parameter Inference........................................................................... 4.6.1 Standard Errors...................................................................... Covariates on Initial and Transition Probabilities............................ Missing
Data..................................................................................... 4.8.1 Missing Data in Hidden Markov Models ............................. 4.8.2 Missing at Random................................................................ 4.8.3 State-Dependent Missingness................................................ 140 141 144 144 146 149 150 151 152 152 154 157 157 158 160 161 163 164 166 166 169 Univariate Hidden Markov Models............................................................ 173 173 177 182 183 184 186 189 4.3 4.4 4.5 4.6 4.7 4.8 5 XV Gaussian Hidden Markov Model for Financial Time Series............. Bernoulli HMM for the DCCS Data.................................................. Accounting for Autocorrelation Between Response Times............... 5.3.1 Response Times................................................................... 5.3.2 Models for Response Times ................................................ 5.3.3 Model Assessment and Selection of RT Models.................. 5.4 Change Point HMM for Climate Data............................................... 5.5 Generalized Linear Hidden Markov Models for Multiple Cue Learning............................................................................. 195 5.1 5.2 5.3 6 Multivariate Hidden Markov Models......................................................... 201 6.1 Latent Transition Model for Balance Scale Data............................... 201 6.1.1 Learning and Regression....................................................... 208 6.2 6.3 Switching Between Speed and
Accuracy.......................................... 209 6.2.1 Modeling Hysteresis ............................................................ 216 6.2.2 Testing Conditional Independence and Further Extensions.............................................................. 219 Dependency Between Binomial and Multinomial Responses: The IGT Data......................................................... 223
xvi 7 Contents Extensions.................................................................................................. 7.1 Higher-Order Markov Models............................................................ 7.1.1 Reformulating a Higher-Order HMM as a First-Order HMM.................................................. 233 7.1.2 Example: A Two-State Second-Order HMM for Discrimination Learning........................................ 234 7.2 Models with a Distributed State Representation................................ 7.3 Dealing with Practical Issues in Estimation....................................... 7.3.1 Unbounded Likelihood.......................................................... 7.4 The Classification Likelihood............................................................ 7.4.1 Mixture Models..................................................................... 7.4.2 Hidden Markov Models........................................................ 7.5 Bayesian Estimation.......................................................................... 7.5.1 Sampling States and Model Parameters................................ 7.5.2 Sampling Model Parameters by Marginalizing Over Hidden States............................................................... 231 231 237 241 241 242 243 247 248 249 256 References......................................................................................................... 257 Epilogue............................................................................................................ 263
Index.................................................................................................................. 265
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| adam_txt |
Contents 1 Introduction and Preliminaries. What Are Mixture and Hidden Markov Models?. 1.1.1 Outline. 1.2 Getting Started with R. 1.2.1 Help!. 1.2.2 Loading Packages and Data. 1.2.3 Object Types and Manipulation . 1.2.4 Visualizing Data. 1.2.5 Summarizing Data. 1.2.6 Linear and Generalized Linear Models. 1.2.7 Multinomial Logistic Regression. 1.2.8 Time-Series. 1.3 Datasets Used in the Book. 1.3.1 Speed-Accuracy Data. 1.3.2 S P500 . 1.3.3 Perth Dams Data. 1.3.4 Discrimination Learning Data. 1.3.5 Balance
Data. 1.3.6 Repeated Measures on the Balance Scale Task. 1.3.7 Dimensional Change Card Sorting Task Data. 1.3.8 Weather Prediction Task Data. 1.3.9 Conservation of Liquid Data. 1.3.10 Iowa Gambling Task Data . 1.1 2 Mixture and Latent Class Models. 2.1 2.2 Introduction and Motivating Example. Definitions and Notation. 2.2.1 Mixture Distribution . 2.2.2 Example: Generating Data from a Mixture Distribution . 2.2.3 Parameters of the Mixture Model. 1 1 З 3 5 5 6 13 15 17 21 25 26 26 28 29 30 31 33 34 36 39 41 45 45 47 48 48 49 xiii
Contents xiv 2.2.4 Mixture Likelihood. 2.2.5 Posterior Probabilities. Parameter Estimation. 2.3.1 Maximum Likelihood Estimation. 2.3.2 Numerical Optimization of the Likelihood. 2.3.3 Expectation Maximization (EM). 2.3.4 Optimizing Parameters Subject to Constraints. 2.3.5 EM or Numerical Optimization?. 2.3.6 Starting Values for Parameters in Mixture Models. Parameter Inference: Likelihood Ratio Tests. 2.4.1 Example: Equality Constraint on Standard Deviations. Parameter Inference: Standard Errors and Confidence Intervals. 2.5.1 Finite Difference Approximation of the Hessian. 2.5.2 Parametric Bootstrap. 2.5.3 Correcting the Hessian for Linear Constraints. Model Selection. 2.6.1 Likelihood-Ratio Tests. 2.6.2 Information Criteria. 2.6.3 Example: Model Selection for the Speedl RT Data. Covariates on the Prior
Probabilities. Identifiability of Mixture Models . Further Reading. 49 50 52 52 54 56 66 69 70 72 73 74 76 77 79 80 80 85 89 90 92 93 Mixture and Latent Class Models: Applications. 95 95 99 100 106 108 110 112 113 115 116 119 123 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 Gaussian Mixture for the S P500 Data. Gaussian Mixture Model for Conservation Data. Bivariate Gaussian Mixture Model for Conservation Data . Latent Class Model for Balance Scale Data. 3.4.1 Model Selection and Checking. 3.4.2 Testing Item Homogeneity Using Parameter Constraints . 3.5 Binomial Mixture Model for Balance Scale Data. 3.5.1 Binomial Logistic Regression . 3.5.2 Mixture Models. 3.5.3 Model Selection Model Checking. 3.6 Model Selection with the Bootstrap Likelihood Ratio. 3.7 Further Reading. 3.1 3.2 3.3 3.4 4 Hidden Markov Models. 4.1 Preliminaries: Markov
Models. 4.1.1 Definitions. 4.1.2 Properties of Markov Models. 4.2 Introducing the Hidden Markov Model. 4.2.1 Definitions. 4.2.2 Relation Between Hidden Markov and Mixture Model. 4.2.3 Example: Bernoulli Hidden Markov Model . 4.2.4 Likelihood and Inference Problems. 125 126 126 127 135 135 136 137 139
Contents Filtering, Likelihood, Smoothingand Prediction. 4.3.1 Filtering. 4.3.2 Likelihood. 4.3.3 Smoothing. 4.3.4 Scaling. 4.3.5 The Likelihood Revisited. 4.3.6 Multiple Timeseries. 4.3.7 Prediction. Parameter Estimation. 4.4.1 Numerical Optimization of the Likelihood. 4.4.2 Expectation Maximization (EM). Decoding . 4.5.1 Local Decoding. 4.5.2 Global Decoding . Parameter Inference. 4.6.1 Standard Errors. Covariates on Initial and Transition Probabilities. Missing
Data. 4.8.1 Missing Data in Hidden Markov Models . 4.8.2 Missing at Random. 4.8.3 State-Dependent Missingness. 140 141 144 144 146 149 150 151 152 152 154 157 157 158 160 161 163 164 166 166 169 Univariate Hidden Markov Models. 173 173 177 182 183 184 186 189 4.3 4.4 4.5 4.6 4.7 4.8 5 XV Gaussian Hidden Markov Model for Financial Time Series. Bernoulli HMM for the DCCS Data. Accounting for Autocorrelation Between Response Times. 5.3.1 Response Times. 5.3.2 Models for Response Times . 5.3.3 Model Assessment and Selection of RT Models. 5.4 Change Point HMM for Climate Data. 5.5 Generalized Linear Hidden Markov Models for Multiple Cue Learning. 195 5.1 5.2 5.3 6 Multivariate Hidden Markov Models. 201 6.1 Latent Transition Model for Balance Scale Data. 201 6.1.1 Learning and Regression. 208 6.2 6.3 Switching Between Speed and
Accuracy. 209 6.2.1 Modeling Hysteresis . 216 6.2.2 Testing Conditional Independence and Further Extensions. 219 Dependency Between Binomial and Multinomial Responses: The IGT Data. 223
xvi 7 Contents Extensions. 7.1 Higher-Order Markov Models. 7.1.1 Reformulating a Higher-Order HMM as a First-Order HMM. 233 7.1.2 Example: A Two-State Second-Order HMM for Discrimination Learning. 234 7.2 Models with a Distributed State Representation. 7.3 Dealing with Practical Issues in Estimation. 7.3.1 Unbounded Likelihood. 7.4 The Classification Likelihood. 7.4.1 Mixture Models. 7.4.2 Hidden Markov Models. 7.5 Bayesian Estimation. 7.5.1 Sampling States and Model Parameters. 7.5.2 Sampling Model Parameters by Marginalizing Over Hidden States. 231 231 237 241 241 242 243 247 248 249 256 References. 257 Epilogue. 263
Index. 265 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:27:45Z |
| indexdate | 2024-07-10T09:46:17Z |
| institution | BVB |
| isbn | 9783031014383 |
| language | English |
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| spelling | Visser, Ingmar 19XX- Verfasser (DE-588)1284583953 aut Mixture and Hidden Markov Models with R Ingmar Visser, Maarten Speekenbrink Cham Springer [2022] © 2022 XVI, 267 Seiten txt rdacontent n rdamedia nc rdacarrier Use R! R Programm (DE-588)4705956-4 gnd rswk-swf Hidden-Markov-Modell (DE-588)4352479-5 gnd rswk-swf Statistics Biometry Hidden-Markov-Modell (DE-588)4352479-5 s R Programm (DE-588)4705956-4 s DE-604 Speekenbrink, Maarten 19XX- Verfasser (DE-588)1284586480 aut Erscheint auch als Online-Ausgabe 978-3-031-01440-6 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034066970&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Visser, Ingmar 19XX- Speekenbrink, Maarten 19XX- Mixture and Hidden Markov Models with R R Programm (DE-588)4705956-4 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4352479-5 |
| title | Mixture and Hidden Markov Models with R |
| title_auth | Mixture and Hidden Markov Models with R |
| title_exact_search | Mixture and Hidden Markov Models with R |
| title_exact_search_txtP | Mixture and Hidden Markov Models with R |
| title_full | Mixture and Hidden Markov Models with R Ingmar Visser, Maarten Speekenbrink |
| title_fullStr | Mixture and Hidden Markov Models with R Ingmar Visser, Maarten Speekenbrink |
| title_full_unstemmed | Mixture and Hidden Markov Models with R Ingmar Visser, Maarten Speekenbrink |
| title_short | Mixture and Hidden Markov Models with R |
| title_sort | mixture and hidden markov models with r |
| topic | R Programm (DE-588)4705956-4 gnd Hidden-Markov-Modell (DE-588)4352479-5 gnd |
| topic_facet | R Programm Hidden-Markov-Modell |
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