Bayesian spectrum analysis and parameter estimation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1988
|
| Schriftenreihe: | Lecture notes in statistics
48 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 209 S. |
| ISBN: | 0387968717 3540968717 |
Internformat
MARC
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| 100 | 1 | |a Bretthorst, G. Larry |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bayesian spectrum analysis and parameter estimation |c G. Larry Bretthorst |
| 264 | 1 | |a New York u.a. |b Springer |c 1988 | |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Lecture notes in statistics |v 48 | |
| 502 | |a Zugl.: Washington Univ., Diss., 1987 | ||
| 650 | 4 | |a Analyse multivariée | |
| 650 | 4 | |a Statistique bayésienne | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Multivariate analysis | |
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Datensatz im Suchindex
| _version_ | 1810361705629220864 |
|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 1
1.1 HISTORICAL PERSPECTIVE. 5
1.2 METHOD OF CALCULATION. 8
2 SINGLE STATIONARY SINUSOID PLUS NOISE 13
2.1 THE MODEL. 13
2.2 THE LIKELIHOOD FUNCTION. 14
2.3 ELIMINATION OF NUISANCE PARAMETERS. 18
2.4 RESOLVING POWER. 20
2.5 THE POWER SPECTRAL DENSITY P. 25
2.6 WOLF'S RELATIVE SUNSPOT NUMBERS. 27
3 THE GENERAL MODEL EQUATION PLUS NOISE 31
3.1 THE LIKELIHOOD FUNCTION. 31
3.2 THE ORTHONORMAL MODEL EQUATIONS. 32
3.3 ELIMINATION OF THE NUISANCE PARAMETERS . 34
3.4 THE BESSEL INEQUALITY. 35
3.5 AN INTUITIVE PICTURE. 36
3.6 A SIMPLE DIAGNOSTIC TEST. 38
4 ESTIMATING THE PARAMETERS 43
4.1 THE EXPECTED AMPLITUDES (A,). 43
4.2 THE SECOND POSTERIOR MOMENTS {A,A*). 45
4.3 THE ESTIMATED NOISE VARIANCE (A2). 46
4.4 THE SIGNAL-TO-NOISE RATIO. 47
4.5 ESTIMATING THE {W PARAMETERS. 48
4.6 THE POWER SPECTRAL DENSITY. 51
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/890214239
VIII
5 MODEL SELECTION 55
5.1 WHAT ABOUT "SOMETHING ELSE?". 55
5.2 THE RELATIVE PROBABILITY OF MODEL /;. 57
5.3 ONE MORE PARAMETER. 63
5.4 WHAT IS A GOOD MODEL?. 65
8 SPECTRAL ESTIMATION 68
6.1 THE SPECTRUM OF A SINGLE FREQUENCY . 70
6.1.1 THE "STUDENT T-DISTRIBUTION" . 70
6.1.2 EXAMPLE - SINGLE HARMONIC FREQUENCY. 71
6.1.3 THE SAMPLING DISTRIBUTION OF THE ESTIMATES. 74
6.1.4 VIOLATING THE ASSUMPTIONS - ROBUSTNESS. 74
6.1.5 NONUNIFORM SAMPLING . 81
6.2 A FREQUENCY WITH LORENTZIAN DECAY. 86
6.2.1 THE "STUDENT T-DISTRIBUTION" . 87
6.2.2 ACCURACY ESTIMATES. 88
6.2.3 EXAMPLE - ONE FREQUENCY WITH DECAY. 90
6.3 TWO HARMONIC FREQUENCIES. 94
6.3.1 THE "STUDENT T-DISTRIBUTION" . 94
6.3.2 ACCURACY ESTIMATES. 98
6.3.3 MORE ACCURACY ESTIMATES . 101
6.3.4 THE POWER SPECTRAL DENSITY. 103
6.3.5 EXAMPLE - TWO HARMONIC FREQUENCIES. 105
6.4 ESTIMATION OF MULTIPLE
STATIONARY FREQUENCIES.108
6.5 THE "STUDENT T-DISTRIBUTION" . 109
6.5.1 EXAMPLE - MULTIPLE STATIONARY FREQUENCIES. HI
6.5.2 THE POWER SPECTRAL DENSITY. H2
6.5.3 THE LINE POWER SPECTRAL DENSITY. H4
6.6 MULTIPLE NONSTATIONARY FREQUENCY ESTIMATION. 115
7 APPLICATIONS 117
7.1 NMR TIME SERIES. 117
7.2 CORN CROP YIELDS. I34
7.3 ANOTHER NMR EXAMPLE . I44
7.4 WOLF'S RELATIVE SUNSPOT NUMBERS. 14G
IX
7.4.1 ORTHOGONAL EXPANSION OF THE RELATIVE SUNSPOT
NUMBERS. 148
7.4.2 HARMONIC ANALYSIS OF THE
RELATIVE SUNSPOT NUMBERS. 151
7.4.3 THE SUNSPOT NUMBERS IN TERMS OF
HARMONICALLY RELATED FREQUENCIES. 157
7.4.4 CHIRP IN THE SUNSPOT NUMBERS . 158
7.5 MULTIPLE MEASUREMENTS. 161
7.5.1 THE AVERAGING RULE. 163
7.5.2 THE RESOLUTION IMPROVEMENT . 166
7.5.3 SIGNAL DETECTION . 167
7.5.4 THE DISTRIBUTION OF THE SAMPLE ESTIMATES. 169
7.5.5 EXAMPLE - MULTIPLE MEASUREMENTS. 173
8 SUMMARY AND CONCLUSIONS 179
8.1 SUMMARY. 179
8.2 CONCLUSIONS. 180
A CHOOSING A PRIOR PROBABILITY 183
B IMPROPER PRIORS AS LIMITS 189
C REMOVING NUISANCE PARAMETERS 193
D UNINFORMATIVE PRIOR PROBABILITIES 195
E COMPUTING THE
"STUDENT T-DISTRIBUTION" 197 |
| any_adam_object | 1 |
| author | Bretthorst, G. Larry |
| author_facet | Bretthorst, G. Larry |
| author_role | aut |
| author_sort | Bretthorst, G. Larry |
| author_variant | g l b gl glb |
| building | Verbundindex |
| bvnumber | BV001638231 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279.5.B74 1988 |
| callnumber-search | QA279.5.B74 1988 |
| callnumber-sort | QA 3279.5 B74 41988 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 237 SI 856 SK 830 |
| ctrlnum | (OCoLC)18938743 (DE-599)BVBBV001638231 |
| dewey-full | 519.5/42 519.5/4220 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 519.5/42 20 |
| dewey-search | 519.5/42 519.5/42 20 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Thesis Book |
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| id | DE-604.BV001638231 |
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| indexdate | 2024-09-16T14:04:19Z |
| institution | BVB |
| isbn | 0387968717 3540968717 |
| language | English |
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| physical | XII, 209 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Bretthorst, G. Larry Verfasser aut Bayesian spectrum analysis and parameter estimation G. Larry Bretthorst New York u.a. Springer 1988 XII, 209 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 48 Zugl.: Washington Univ., Diss., 1987 Analyse multivariée Statistique bayésienne Bayesian statistical decision theory Multivariate analysis Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Spektralanalyse Stochastik (DE-588)4056125-2 gnd rswk-swf Parameterschätzung (DE-588)4044614-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Parameterschätzung (DE-588)4044614-1 s Bayes-Verfahren (DE-588)4204326-8 s DE-604 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Spektralanalyse Stochastik (DE-588)4056125-2 s 1\p DE-604 Bayes-Entscheidungstheorie (DE-588)4144220-9 s 2\p DE-604 Lecture notes in statistics 48 (DE-604)BV002447846 48 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001073489&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bretthorst, G. Larry Bayesian spectrum analysis and parameter estimation Lecture notes in statistics Analyse multivariée Statistique bayésienne Bayesian statistical decision theory Multivariate analysis Bayes-Verfahren (DE-588)4204326-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4064324-4 (DE-588)4144220-9 (DE-588)4056125-2 (DE-588)4044614-1 (DE-588)4113937-9 |
| title | Bayesian spectrum analysis and parameter estimation |
| title_auth | Bayesian spectrum analysis and parameter estimation |
| title_exact_search | Bayesian spectrum analysis and parameter estimation |
| title_full | Bayesian spectrum analysis and parameter estimation G. Larry Bretthorst |
| title_fullStr | Bayesian spectrum analysis and parameter estimation G. Larry Bretthorst |
| title_full_unstemmed | Bayesian spectrum analysis and parameter estimation G. Larry Bretthorst |
| title_short | Bayesian spectrum analysis and parameter estimation |
| title_sort | bayesian spectrum analysis and parameter estimation |
| topic | Analyse multivariée Statistique bayésienne Bayesian statistical decision theory Multivariate analysis Bayes-Verfahren (DE-588)4204326-8 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Spektralanalyse Stochastik (DE-588)4056125-2 gnd Parameterschätzung (DE-588)4044614-1 gnd |
| topic_facet | Analyse multivariée Statistique bayésienne Bayesian statistical decision theory Multivariate analysis Bayes-Verfahren Wahrscheinlichkeitsrechnung Bayes-Entscheidungstheorie Spektralanalyse Stochastik Parameterschätzung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001073489&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
| work_keys_str_mv | AT bretthorstglarry bayesianspectrumanalysisandparameterestimation |