Informed assessments: an introduction to information, entropy and statistics
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Horwood
1995
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 366 S. graph. Darst. |
| ISBN: | 0131092995 |
Internformat
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| 245 | 1 | 0 | |a Informed assessments |b an introduction to information, entropy and statistics |c Alan Jessop |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York [u.a.] |b Horwood |c 1995 | |
| 300 | |a XIII, 366 S. |b graph. Darst. | ||
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| 650 | 7 | |a Besliskunde |2 gtt | |
| 650 | 7 | |a Entropie (théorie de l'information) |2 ram | |
| 650 | 7 | |a Incertitude (théorie de l'information) |2 ram | |
| 650 | 7 | |a Informatietheorie |2 gtt | |
| 650 | 7 | |a Information, Théorie de l' |2 ram | |
| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 7 | |a Prise de décision (statistique) |2 ram | |
| 650 | 7 | |a Statistique bayésienne |2 ram | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Entropy (Information theory) | |
| 650 | 4 | |a Uncertainty (Information theory) | |
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Datensatz im Suchindex
| _version_ | 1804124747977457664 |
|---|---|
| adam_text | Contents
Preface xi
Acknowledgements xiii
Chapter 1 Probability
1.1 A little history 1
1.2 More than one event 4
1.3 Joint events 7
1.4 Distributions 10
1.5 Density functions 13
1.6 Summary measures 18
1.7 Expectation 24
1.8 Further reading 25
1.9 Examples 26
1.10 Exercises 35
Chapter 2 Information
2.1 Surprise 39
2.2 Searching 42
2.3 Signalling 45
2.4 Disorder 49
2.5 Drawing together 50
2.6 Redundancy 51
2.7 Further reading 52
2.8 Examples 53
2.9 Exercises 56
Chapter 3 Unbiased estimates
3.1 Jaynes criterion 58
3.2 Finding unbiased estimates 60
3.3 Assessment when the mean is known 63
3.4 Assessment when mean and variance are given 66
3.5 Further reading 69
3.6 Examples 70
3.7 Exercises 73
v
vi Contents
Chapter 4 More on unbiased estimates
4.1 Information change 75
4.2 Using an existing distribution 77
4.3 Using information about parts of the distribution 79
4.4 The answer! 82
4.5 Maximum entropy density functions 83
4.6 The negative exponential distribution 88
4.7 The Normal distribution 90
4.8 Bounded real variable: mean and variance given 92
4.9 Some practical considerations 93
4.10 Examples 95
4.11 Exercises 102
Chapter 5 Bayes Rule
5.1 Background and basic statement 105
5.2 Bayes1 Rule with a Binomial likelihood 109
5.3 Convenience priors: the Beta distribution 112
5.4 Poisson likelihood and Gamma prior 116
5.5 Normal likelihood and prior 120
5.6 Normal approximations 122
5.7 Fitting distributions 122
5.8 Bayesian learning 124
5.9 Further reading 127
5.10 Examples 128
5.11 Exercises 138
Chapter 6 Decision theory
6.1 Decisions 141
6.2 Utility 143
6.3 A decision rule 148
6.4 Loss 149
6.5 Further reading 150
6.6 Examples 151
6.7 Exercises 154
Contents vii
Chapter 7 Using probability estimates
7.1 Averages 158
7.2 Intervals 159
7.3 Estimating the population mean 163
7.4 Hypotheses 169
7.5 Discrimination 171
7.6 Further reading 177
7.7 Examples 177
7.8 Exercises 184
Chapter 8 Two dimensions
8.1 Structure in contingency tables 186
8.2 Correlation and independence 191
8.3 Testing for independence 193
8.4 Information transmission 196
8.5 Bayes Rule 198
8.6 Further reading 200
8.7 Examples 200
8.8 Exercises 208
Chapter 9 Least biased estimates of joint distributions
9.1 Marginal distributions as constraints 212
9.2 Using a previous estimate 214
9.3 Joint distribution with given mean 216
9.4 Modifying a previous estimate with a new mean 218
9.5 Estimating marginal distributions 219
9.6 The structural comparison of tables 220
9.7 Modelling two dimensional contingency tables 225
9.8 Modelling three dimensional contingency tables 228
9.9 Further reading 236
9.10 Examples 236
9.11 Exercises 245
Chapter 10 Correlation and regression
10.1 Covariance and correlation 250
10.2 Fitting a linear model 255
10.3 Model performance 258
10.4 Entropy reduction and correlation 260
viii Contents
10.5 Inference and forecast 261
10.6 Examples 263
10.7 Exercises 283
References 289
Answers to numerical exercises 305
Appendices
Al. The mathematics of entropy maximisation 311
Finding a simple maximum
Constrained optimisation
Maximising entropy
Minimising relative entropy
Joint distributions
Three dimensional tables and the log linear model
A2. Logarithms 319
A3. Numerical integration 322
The mid point rule
Simpson s Rule
Example
A4. The Binomial, Poisson and Normal distributions 326
The Binomial distribution
The Poisson distribution
The Normal distribution
A5. Statistical tables 331
A5.1 Binomial distribution 332
A5.2 Poisson distribution 341
A5.3 Normal distribution 346
A5.4 Beta distribution 348
A5.5 Gamma distribution 349
A5.6 x2 distribution 350
A5.7 The / distribution 353
A6. Measures of location and loss functions 355
Contents ix
A7. Conditions for a credible interval 357
A8. The regression model 358
Index 363
|
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| isbn | 0131092995 |
| language | English |
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| spelling | Jessop, Alan Verfasser aut Informed assessments an introduction to information, entropy and statistics Alan Jessop 1. publ. New York [u.a.] Horwood 1995 XIII, 366 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Besliskunde gtt Entropie (théorie de l'information) ram Incertitude (théorie de l'information) ram Informatietheorie gtt Information, Théorie de l' ram Methode van Bayes gtt Prise de décision (statistique) ram Statistique bayésienne ram Bayesian statistical decision theory Entropy (Information theory) Uncertainty (Information theory) Informationstheorie (DE-588)4026927-9 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Information (DE-588)4026899-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Entropie (DE-588)4014894-4 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s DE-604 Informationstheorie (DE-588)4026927-9 s Statistik (DE-588)4056995-0 s DE-188 Information (DE-588)4026899-8 s Entropie (DE-588)4014894-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006873145&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jessop, Alan Informed assessments an introduction to information, entropy and statistics Besliskunde gtt Entropie (théorie de l'information) ram Incertitude (théorie de l'information) ram Informatietheorie gtt Information, Théorie de l' ram Methode van Bayes gtt Prise de décision (statistique) ram Statistique bayésienne ram Bayesian statistical decision theory Entropy (Information theory) Uncertainty (Information theory) Informationstheorie (DE-588)4026927-9 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Information (DE-588)4026899-8 gnd Statistik (DE-588)4056995-0 gnd Entropie (DE-588)4014894-4 gnd |
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| title | Informed assessments an introduction to information, entropy and statistics |
| title_auth | Informed assessments an introduction to information, entropy and statistics |
| title_exact_search | Informed assessments an introduction to information, entropy and statistics |
| title_full | Informed assessments an introduction to information, entropy and statistics Alan Jessop |
| title_fullStr | Informed assessments an introduction to information, entropy and statistics Alan Jessop |
| title_full_unstemmed | Informed assessments an introduction to information, entropy and statistics Alan Jessop |
| title_short | Informed assessments |
| title_sort | informed assessments an introduction to information entropy and statistics |
| title_sub | an introduction to information, entropy and statistics |
| topic | Besliskunde gtt Entropie (théorie de l'information) ram Incertitude (théorie de l'information) ram Informatietheorie gtt Information, Théorie de l' ram Methode van Bayes gtt Prise de décision (statistique) ram Statistique bayésienne ram Bayesian statistical decision theory Entropy (Information theory) Uncertainty (Information theory) Informationstheorie (DE-588)4026927-9 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Information (DE-588)4026899-8 gnd Statistik (DE-588)4056995-0 gnd Entropie (DE-588)4014894-4 gnd |
| topic_facet | Besliskunde Entropie (théorie de l'information) Incertitude (théorie de l'information) Informatietheorie Information, Théorie de l' Methode van Bayes Prise de décision (statistique) Statistique bayésienne Bayesian statistical decision theory Entropy (Information theory) Uncertainty (Information theory) Informationstheorie Bayes-Entscheidungstheorie Information Statistik Entropie |
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