Recursive nonlinear estimation: a geometric approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
London [u.a.]
Springer
1996
|
| Series: | Lecture notes in control and information sciences
216 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 224 S. Ill., graph. Darst. |
| ISBN: | 3540760636 |
Staff View
MARC
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| 100 | 1 | |a Kulhavý, Rudolf |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Recursive nonlinear estimation |b a geometric approach |c Rudolf Kulhavý |
| 264 | 1 | |a London [u.a.] |b Springer |c 1996 | |
| 300 | |a XVI, 224 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in control and information sciences |v 216 | |
| 650 | 7 | |a ESTIMATION OPTIMALE |2 inriac | |
| 650 | 7 | |a Estimation de paramètres |2 ram | |
| 650 | 7 | |a Schattingstheorie |2 gtt | |
| 650 | 7 | |a Statistique bayésienne |2 ram | |
| 650 | 7 | |a Systèmes, identification des |2 ram | |
| 650 | 7 | |a estimation paramètre |2 inriac | |
| 650 | 7 | |a théorie estimation |2 inriac | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Parameter estimation | |
| 650 | 4 | |a System identification | |
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Record in the Search Index
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Table of Contents
1 Inference Under Constraints 1
1.1 The Bayesian Paradigm 1
1.2 Recursive Estimation 2
1.3 Admissible Complexity 3
1.4 Common Approaches to Approximation 5
1.5 Why the Geometric Approach? 10
2 From Matching Data to Matching Probabilities 13
2.1 Data Matching in Euclidean Space 13
2.2 Probability based Estimation 17
2.3 Estimation via Inaccuracy 25
2.4 Maximum Likelihood versus Bayesian Estimation 34
2.5 Inaccuracy for Discrete Data 38
2.6 Examples: Probability Matching 47
2.7 Historical Notes 61
3 Optimal Estimation with Compressed Data 63
3.1 Data Compression in Euclidean Space 63
3.2 Kullback Leibler Distance 70
3.3 Pythagorean View of Statistical Estimation 77
3.4 Examples: Normal and Linear Models 104
3.5 Data Compression 110
3.6 Historical Notes 126
4 Approximate Estimation with Compressed Data 129
4.1 Further Compressing Data: Euclidean Case 129
4.2 Idea of Approximate Estimation 132
4.3 Key Properties of Approximation 141
4.4 Relation to Large Deviation Theory 147
4.5 Choice of Statistic 151
4.6 Examples: Models and Statistics 159
4.7 Approximation of Empirical Expectation 171
4.8 Historical Notes 176
XII Table of Contents
5 Numerical Implementation 179
5.1 Direct Optimization 179
5.2 Prior Approximation of Critical Maps 183
5.3 Parameter Tracking via Forgetting 186
5.4 Historical Notes 190
6 Concluding Remarks 191
6.1 Summary of Key Points 191
6.2 Open Problems 195
6.3 Outlook 197
A Selected Topics from Probability Theory 199
A.I Probability Spaces 199
A.2 Discrete Random Variables 202
A.3 Continuous Random Variables 204
A.4 Normal Distribution 207
A.5 Holder Inequality 207
B Selected Topics from Convex Optimization 209
B.I Convex Sets and Functions 209
B.2 Minimization of Convex Functions 210
B.3 Jensen's Inequality 210
B.4 Legendre Fenchel Transform 210
References 213
Index 223 |
| any_adam_object | 1 |
| author | Kulhavý, Rudolf |
| author_facet | Kulhavý, Rudolf |
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| author_sort | Kulhavý, Rudolf |
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| bvnumber | BV010821769 |
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| dewey-full | 519.5/44 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/44 |
| dewey-search | 519.5/44 |
| dewey-sort | 3519.5 244 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010821769 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:16Z |
| institution | BVB |
| isbn | 3540760636 |
| language | German |
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| physical | XVI, 224 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
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| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spelling | Kulhavý, Rudolf Verfasser aut Recursive nonlinear estimation a geometric approach Rudolf Kulhavý London [u.a.] Springer 1996 XVI, 224 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in control and information sciences 216 ESTIMATION OPTIMALE inriac Estimation de paramètres ram Schattingstheorie gtt Statistique bayésienne ram Systèmes, identification des ram estimation paramètre inriac théorie estimation inriac Bayesian statistical decision theory Parameter estimation System identification Nichtlineare Schätzung (DE-588)4248209-4 gnd rswk-swf Rekursive Parameterschätzung (DE-588)4199569-7 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 s Nichtlineare Schätzung (DE-588)4248209-4 s DE-604 Rekursive Parameterschätzung (DE-588)4199569-7 s Lecture notes in control and information sciences 216 (DE-604)BV005848579 216 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007232254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kulhavý, Rudolf Recursive nonlinear estimation a geometric approach Lecture notes in control and information sciences ESTIMATION OPTIMALE inriac Estimation de paramètres ram Schattingstheorie gtt Statistique bayésienne ram Systèmes, identification des ram estimation paramètre inriac théorie estimation inriac Bayesian statistical decision theory Parameter estimation System identification Nichtlineare Schätzung (DE-588)4248209-4 gnd Rekursive Parameterschätzung (DE-588)4199569-7 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4248209-4 (DE-588)4199569-7 (DE-588)4044614-1 |
| title | Recursive nonlinear estimation a geometric approach |
| title_auth | Recursive nonlinear estimation a geometric approach |
| title_exact_search | Recursive nonlinear estimation a geometric approach |
| title_full | Recursive nonlinear estimation a geometric approach Rudolf Kulhavý |
| title_fullStr | Recursive nonlinear estimation a geometric approach Rudolf Kulhavý |
| title_full_unstemmed | Recursive nonlinear estimation a geometric approach Rudolf Kulhavý |
| title_short | Recursive nonlinear estimation |
| title_sort | recursive nonlinear estimation a geometric approach |
| title_sub | a geometric approach |
| topic | ESTIMATION OPTIMALE inriac Estimation de paramètres ram Schattingstheorie gtt Statistique bayésienne ram Systèmes, identification des ram estimation paramètre inriac théorie estimation inriac Bayesian statistical decision theory Parameter estimation System identification Nichtlineare Schätzung (DE-588)4248209-4 gnd Rekursive Parameterschätzung (DE-588)4199569-7 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | ESTIMATION OPTIMALE Estimation de paramètres Schattingstheorie Statistique bayésienne Systèmes, identification des estimation paramètre théorie estimation Bayesian statistical decision theory Parameter estimation System identification Nichtlineare Schätzung Rekursive Parameterschätzung Parameterschätzung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007232254&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
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