Statistical inference: an integrated Bayesian/likelihood approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2010
|
| Series: | Monographs on statistics and applied probability
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 236 S. Ill., graph. Darst. |
| ISBN: | 9781420093438 1420093436 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface
.................................................................xiii
1.
Theories of Statistical Inference
....................................1
1.1
Example
........................................................1
1.2
Statistical models
...............................................1
1.3
The likelihood function
.........................................2
1.4
Theories
........................................................3
1.4.1
Pure likelihood theory
...................................3
1.4.2
Bayesian theory
..........................................5
1.4.3
Likelihood-based repeated sampling theory
.............10
1.4.4
Model-guided survey sampling theory
...............12
1.5
Nonmodel-based repeated sampling
...........................18
1.6
Conclusion
....................................................19
2.
The Integrated Bayes/Likelihood Approach
.......................21
2.1
Introduction
...................................................21
2.2
Probability
....................................................21
2.3
Prior ignorance
................................................23
2.4
The importance of parametrization
............................24
2.4.1
Inference about the Binomial
N.........................25
2.4.1.1
Profiling
.......................................26
2.4.1.2
Conditioning
..................................26
2.4.2
The effect size
..........................................31
2.5
The simple/simple hypothesis testing problem
................34
2.5.1
Bayes
calibration
.......................................35
2.5.2
Frequentisi
calibration (fixed sample size)
...............36
2.5.3
Nonfixed error probabilities
.............................37
2.5.4
Frequentisi test
(sequential sampling)
...................38
2.5.5
Bayesian interpretation of type I error probabilities
......39
2.6
The simple/composite hypothesis testing problem
.............40
2.6.1
Fixed-sample
frequentisi
analysis
.......................40
2.6.2
Sequential sampling approach
..........................41
2.7
Posterior likelihood approach
.................................41
2.7.1
Large-sample result
.....................................43
2.7.2
Strength of support for the null hypothesis
..............44
2.7.3
Credible intervals for the deviance difference
............44
IX
.с
Contents
2.8
Bayes
factors
..................................................45
2.8.1
Difficulties with the
Bayes
factor
........................47
2.8.2
Conjugate prior difficulties
..............................50
2.8.3
Stone example
..........................................51
2.9
The comparison of unrelated models
..........................53
2.9.1
Large-sample result
.....................................53
2.9.2
Bayes
factor
............................................54
2.9.3
Example
................................................55
2.9.4
Misleading conclusions from
Bayes
factors
..............58
2.9.5
Modified
Bayes
factors
..................................63
2.10
Example
-
GHQ score and psychiatric diagnosis
..............64
3.
ŕ-Tests
and Normal Variance Tests
.................................69
3.1
One-sample
ŕ-test
.............................................69
3.1.1
Credible interval
........................................69
3.1.2
Model comparisons
.....................................70
3.1.3
Example
................................................71
3.2
Two samples: equal variances
..................................72
3.2.1
Credible interval
........................................72
3.2.2
Model comparisons
.....................................73
3.2.3
Example
................................................74
3.3
The two-sample test
...........................................76
3.3.1
Informative prior for the effect size
......................76
3.4
Two samples: different variances
..............................77
ЗАЛ
Credible interval
........................................77
3.4.2
Model comparison
......................................78
3.4.3
Example
................................................79
3.5
The normal model variance
....................................81
3.5.1
Credible interval
........................................81
3.5.2
Model comparisons
.....................................81
3.5.3
Example
................................................82
3.5.4
Marginal and full likelihoods
...........................83
3.6
Variance heterogeneity test
....................................85
3.6.1
Nonrobustness of variance tests
.........................87
4.
Unified Analysis of Finite Populations
............................91
4.1
Sample selection indicators
....................................92
4.2
The Bayesian bootstrap
........................................95
4.2.1
Multinomial model
.....................................96
4.2.2
Dirichlet prior
..........................................97
4.2.3
Confidence coverage of credible intervals
...............98
4.2.4
Example
-
income population
...........................99
4.2.5
Simulation study
......................................105
4.2.6
Extensions of the Bayesian bootstrap
...................107
Contents xi
4.3
Sampling without replacement
...............................107
4.3.1
Simulation study
......................................109
4.4
Regression models
...........................................110
4.4.1
Design-based approach
................................112
4.4.2
Bayesian bootstrap approach
...........................112
4.4.3
Simulation study
......................................113
4.4.4
Ancillary information
..................................116
4.4.5
Sampling without replacement
.........................116
4.4.6
Simulation study
......................................118
4.5
More general regression models
..............................118
4.6
The multinomial model for multiple populations
.............119
4.7
Complex sample designs
.....................................120
4.7.1
Stratified sampling
....................................120
4.7.2
Cluster sampling
......................................121
4.7.3
Shrinkage estimation
..................................125
4.8
A complex example
..........................................127
4.9
Discussion
...................................................130
5.
Regression and Analysis of Variance
.............................133
5.1
Multiple regression
...........................................133
5.2
Nonnested models
...........................................137
6.
Binomial and Multinomial Data
..................................143
6.1
Single binomial samples
......................................143
6.1.1
Bayes
factor
...........................................144
6.1.2
Example
...............................................144
6.2
Single multinomial samples
..................................146
6.3
Two-way tables for correlated proportions
....................147
6.3.1
Likelihood
.............................................147
6.3.2
Bayes
factor
...........................................148
6.3.3
Posterior likelihood ratio
..............................148
6.4
Multiple binomial samples
...................................150
6.4.1
A social network table
.................................150
6.4.2
Network model
........................................150
6.4.3
Frequentist analysis
...................................152
6.4.4
Choice of alternative model prior
......................152
6.4.5
Simulations
............................................153
6.5
Two-way tables for categorical responses
-
no fixed
margins
......................................................154
6.5.1
The ECMO study
......................................155
6.5.2
Bayes
analysis
.........................................155
6.5.3
Multinomial likelihoods
...............................156
6.5.4
Dirichlet prior
.........................................156
6.5.5
Simulations
............................................157
xii
Contents
6.6
Two-way tables for categorical responses
-
one fixed
margin
.......................................................160
6.7
Multinomial nonparametric analysis
.......................164
7.
Goodness of Fit and Model Diagnostics
..........................169
7.1
Frequentist model diagnostics
................................169
7.2
Bayesian model diagnostics
..................................171
7.3
The posterior predictive distribution
..........................172
7.3.1
Marginalization and model diagnostics
................174
7.4
Multinomial deviance computation
...........................179
7.5
Model comparison through posterior
déviances
..............181
7.6
Examples
....................................................182
7.6.1
Three binomial models
................................182
7.6.2
Poisson
model
.........................................186
7.7
Simulation study
.............................................188
7.8
Discussion
...................................................194
8.
Complex Models
.................................................197
8.1
The data augmentation algorithm
............................197
8.2
Two-level variance component models
.......................198
8.2.1
Two-level fixed effects model
..........................199
8.2.2
Two-level random effects model
.......................199
8.2.3
Posterior inference
.....................................200
8.2.4
Likelihood
.............................................200
8.2.5
Maximum likelihood estimates
........................201
8.2.6
Posteriors
.............................................201
8.2.7
Box-Tiao example
......................................202
8.3
Test for a zero variance component
...........................208
8.3.1
Alternative tests
.......................................209
8.3.2
Generalized linear mixed models
......................210
8.4
Finite mixtures
...............................................210
8.4.1
Example
-
the galaxy velocity study
...................211
8.4.2
Data examination
......................................211
8.4.3
Maximum likelihood estimates
........................212
8.4.4
Bayes
analysis
.........................................213
8.4.5
Posterior likelihood analysis
...........................215
8.4.6
Simulation studies
.....................................221
References
.............................................................223
Author Index
..........................................................229
Subject Index
..........................................................233
|
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| id | DE-604.BV036895349 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:50:23Z |
| institution | BVB |
| isbn | 9781420093438 1420093436 |
| language | English |
| lccn | 2010008250 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020810455 |
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| physical | XVII, 236 S. Ill., graph. Darst. |
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| publisher | CRC Press |
| record_format | marc |
| series | Monographs on statistics and applied probability |
| series2 | Monographs on statistics and applied probability A Chapman & Hall book |
| spelling | Aitkin, Murray Verfasser aut Statistical inference an integrated Bayesian/likelihood approach Murray Aitkin Boca Raton [u.a.] CRC Press 2010 XVII, 236 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 116 A Chapman & Hall book Statistischer Test (DE-588)4077852-6 gnd rswk-swf Statistische Hypothese (DE-588)4182959-1 gnd rswk-swf Bayes-Inferenz (DE-588)4648118-7 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Bayes-Inferenz (DE-588)4648118-7 s Statistische Schlussweise (DE-588)4182963-3 s Statistische Hypothese (DE-588)4182959-1 s Statistischer Test (DE-588)4077852-6 s DE-604 Monographs on statistics and applied probability 116 (DE-604)BV002494005 116 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020810455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aitkin, Murray Statistical inference an integrated Bayesian/likelihood approach Monographs on statistics and applied probability Statistischer Test (DE-588)4077852-6 gnd Statistische Hypothese (DE-588)4182959-1 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4077852-6 (DE-588)4182959-1 (DE-588)4648118-7 (DE-588)4182963-3 |
| title | Statistical inference an integrated Bayesian/likelihood approach |
| title_auth | Statistical inference an integrated Bayesian/likelihood approach |
| title_exact_search | Statistical inference an integrated Bayesian/likelihood approach |
| title_full | Statistical inference an integrated Bayesian/likelihood approach Murray Aitkin |
| title_fullStr | Statistical inference an integrated Bayesian/likelihood approach Murray Aitkin |
| title_full_unstemmed | Statistical inference an integrated Bayesian/likelihood approach Murray Aitkin |
| title_short | Statistical inference |
| title_sort | statistical inference an integrated bayesian likelihood approach |
| title_sub | an integrated Bayesian/likelihood approach |
| topic | Statistischer Test (DE-588)4077852-6 gnd Statistische Hypothese (DE-588)4182959-1 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Statistischer Test Statistische Hypothese Bayes-Inferenz Statistische Schlussweise |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020810455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002494005 |
| work_keys_str_mv | AT aitkinmurray statisticalinferenceanintegratedbayesianlikelihoodapproach |