Bayesian model selection and statistical modeling:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, FL [u.a.]
CRC Press
2010
|
| Schriftenreihe: | Statistics
A Chapman & Hall book |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 286 S. Ill., graph. Darst. 25 cm |
| ISBN: | 9781439836149 1439836140 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV036610519 | ||
| 003 | DE-604 | ||
| 005 | 20120918 | ||
| 007 | t| | ||
| 008 | 100810s2010 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9781439836149 |9 978-1-4398-3614-9 | ||
| 020 | |a 1439836140 |9 1-4398-3614-0 | ||
| 035 | |a (OCoLC)466360865 | ||
| 035 | |a (DE-599)BVBBV036610519 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-634 |a DE-91G |a DE-473 |a DE-824 | ||
| 082 | 0 | |a 519.5/42 |2 22 | |
| 084 | |a QH 233 |0 (DE-625)141548: |2 rvk | ||
| 084 | |a SK 830 |0 (DE-625)143259: |2 rvk | ||
| 084 | |a MAT 624f |2 stub | ||
| 084 | |a MAT 622f |2 stub | ||
| 100 | 1 | |a Ando, Tomohiro |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bayesian model selection and statistical modeling |c Tomohiro Ando |
| 264 | 1 | |a Boca Raton, FL [u.a.] |b CRC Press |c 2010 | |
| 300 | |a XIV, 286 S. |b Ill., graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics | |
| 490 | 0 | |a A Chapman & Hall book | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Mathematical models | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 0 | 7 | |a Statistisches Modell |0 (DE-588)4121722-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Bayes-Entscheidungstheorie |0 (DE-588)4144220-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Bayes-Entscheidungstheorie |0 (DE-588)4144220-9 |D s |
| 689 | 0 | 1 | |a Statistisches Modell |0 (DE-588)4121722-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-020530788 | |
Datensatz im Suchindex
| _version_ | 1817681160136818688 |
|---|---|
| adam_text |
Contents
Preface
ИИ
1
Introduction
1
1.1
Statistical models
. 1
1.2
Bayesian statistical modeling
. 6
1.3
Book organization
. 8
2
Introduction to Bayesian analysis
13
2.1
Probability and
Bayes'
theorem
. 13
2.2
Introduction to Bayesian analysis
. 15
2.3
Bayesian inference on statistical models
. 17
2.4
Sampling density specification
. 19
2.4.1
Probability density specification
. 19
2.4.2
Econometrics: Quantifying price elasticity of demand
. 20
2.4.3
Financial econometrics: Describing a stock market
behavior
. 21
2.4.4
Bioinformatics: Tumor classification with gene
expression data
. 22
2.4.5
Psychometrics: Factor analysis model
. 23
2.4.6
Marketing: Survival analysis model for quantifying
customer lifetime value
. 24
2.4.7
Medical science: Nonlinear logistic regression models
. 25
2.4.8
Under the limited computer resources
. 26
2.5
Prior distribution
. 26
2.5.1
Diffuse priors
. 26
2.5.2
The Jeffreys' prior
. 27
2.5.3
Conjugate priors
. 27
2.5.4
Informative priors
. 27
2.5.5
Other priors
. 28
2.6
Summarizing the posterior inference
. 28
2.6.1
Point estimates
. 28
2.6.2
Interval estimates
. 29
2.6.3
Densities
. 29
2.6.4
Predictive distributions
. 30
2.7
Bayesian inference on linear regression models
. 30
2.8
Bayesian model selection problems
. 33
vn
Vlil
2.8.1
Example: Subset variable selection problem
. 33
2.8.2
Example: Smoothing parameter selection problem
. . 35
2.8.3
Summary
. 37
Asymptotic approach for Bayesian inference
43
3.1
Asymptotic properties of the posterior distribution
. 43
3.1.1
Consistency
. 43
3.1.2
Asymptotic normality of the posterior mode
. 44
3.1.3
Example: Asymptotic normality of the posterior mode
of logistic regression
. 45
3.2
Bayesian central limit theorem
. 46
3.2.1
Bayesian central limit theorem
. 47
3.2.2
Example:
Poisson
distribution with conjugate prior
. . 49
3.2.3
Example: Confidence intervals
. 50
3.3
Laplace method
. 51
3.3.1
Laplace method for integral
. 51
3.3.2
Posterior expectation of a function of parameter
. 53
3.3.3
Example: Bernoulli distribution with a uniform prior
. 55
3.3.4
Asymptotic approximation of the Bayesian predictive
distribution
. 57
3.3.5
Laplace method for approximating marginal posterior
distribution
. 58
Computational approach for Bayesian inference
63
4.1
Monte Carlo integration
. 63
4.2
Markov chain Monte Carlo methods for Bayesian
inference
. 64
4.2.1
Gibbs sampler
. 65
4.2.2
Metropolis-Hastings sampler
. 65
4.2.3
Convergence check
. 67
4.2.4
Example: Gibbs sampling for seemingly unrelated
regression model
. 68
4.2.5
Example: Gibbs sampling for auto-correlated errors
. . 73
4.3
Data augmentation
. 76
4.3.1
Probit
model
. 76
4.3.2
Generating random samples from the truncated
normal density
. 78
4.3.3
Ordered
probit
model
. 79
4.4
Hierarchical modeling
. 81
4.4.1
Lasso
. 81
4.4.2
Gibbs sampling for Bayesian Lasso
. 82
4.5
MCMC studies for the Bayesian inference on various types of
models
. 83
4.5.1
Volatility time series models
. 83
4.5.2
Simultaneous equation model
. 84
їх
4.5.3
Quantile regression
. 86
4.5.4
Graphical models
. 88
4.5.5
Multinomial
probit
models
. 88
4.5.6
Markov switching models
. 90
4.6
Noniterative
computation methods for Bayesian
inference
. 93
4.6.1
The direct Monte Carlo
. 93
4.6.2
Importance sampling
. 94
4.6.3
Rejection sampling
. 95
4.6.4
Weighted bootstrap
. 96
Bayesian approach for model selection
101
5.1
General framework
. 101
5.2
Definition of the
Bayes
factor
. 103
5.2.1
Example: Hypothesis testing
1 . 104
5.2.2
Example: Hypothesis testing
2 . 105
5.2.3
Example:
Poisson
models with conjugate priors
. . . 106
5.3
Exact calculation of the marginal likelihood
. 108
5.3.1
Example: Binomial model with conjugate prior
. 108
5.3.2
Example: Normal regression model with conjugate prior
and Zellner's g-prior
. 109
5.3.3
Example: Multi-response normal regression model
. .
Ill
5.4
Laplace's method and asymptotic approach for computing the
marginal likelihood
. 113
5.5
Definition of the Bayesian information criterion
. 115
5.5.1
Example: Evaluation of the approximation error
. 116
5.5.2
Example: Link function selection for binomial
regression
. 116
5.5.3
Example: Selecting the number of factors in factor
analysis model
. 118
5.5.4
Example: Survival analysis
. 121
5.5.5
Consistency of the Bayesian information criteria
. . . 124
5.6
Definition of the generalized Bayesian information criterion
. 125
5.6.1
Example: Nonlinear regression models using basis
expansion predictors
. 126
5.6.2
Example: Multinomial logistic model with basis
expansion predictors
. 132
5.7
Bayes
factor with improper prior
. 141
5.7.1
Intrinsic
Bayes
factors
. 142
5.7.2
Partial
Bayes
factor and fractional
Bayes
factor
. 146
5.7.3
Posterior
Bayes
factors
. 147
5.7.4
Pseudo
Bayes
factors based on cross validation
. 148
5.7.4.1
Example: Bayesian linear regression model
with improper prior
. 148
5.8
Expected predictive likelihood approach for Bayesian model
selection
. 149
5.8.1
Predictive likelihood for model selection
. 150
5.8.2
Example: Normal model with conjugate prior
. 152
5.8.3
Example: Bayesian spatial modeling
. 152
5.9
Other related topics
. 155
5.9.1
Bayes
factors when model dimension grows
. 155
5.9.2
Bayesian p-values
. 156
5.9.3
Bayesian sensitivity analysis
. 157
5.9.3.1
Example: Sensitivity analysis of Value at Risk
158
5.9.3.2
Example: Bayesian change point analysis
. . 160
6
Simulation approach for computing the marginal likelihood
169
6.1
Laplace-Metropolis approximation
. 169
6.1.1
Example: Multinomial
probit
models
. 170
6.2
Gelfand-Day's approximation and the harmonic mean estima¬
tor
. 172
6.2.1
Example: Bayesian analysis of the ordered
probit
model
172
6.3
Chib's estimator from Gibb's sampling
. 174
6.3.1
Example: Seemingly unrelated regression model with
informative prior
. 176
6.3.1.1
Calculation of the marginal likelihood
. 177
6.4
Chib's estimator from MH sampling
. 179
6.5
Bridge sampling methods
. 181
6.6
The Savage-Dickey density ratio approach
. 182
6.6.1
Example: Bayesian linear regression model
. 182
6.7
Kernel density approach
. 185
6.7.1
Example: Bayesian analysis of the
probit
model
. . . 185
6.8
Direct computation of the posterior model probabilities
. . . 187
6.8.1
Reversible jump MCMC
. 187
6.8.2
Example: Reversible jump MCMC for seemingly
unrelated regression model with informative prior
. . . 188
6.8.3
Product space search and metropolized product space
search
. 190
6.8.4
Bayesian variable selection for large model space
. . . 192
7
Various Bayesian model selection criteria
199
7.1
Bayesian predictive information criterion
. 199
7.1.1
The posterior mean of the log-likelihood and the
expected log-likelihood
. 199
7.1.2
Bias correction for the posterior mean of the log-
likelihood
. 201
7.1.3
Definition of the Bayesian predictive information
criterion
. 201
7.1.4
Example: Bayesian generalized state space modeling
. 204
Xl
7.2
Deviance information criterion
. 214
7.2.1
Example: Hierarchical Bayesian modeling for logistic
regression
. 215
7.3
A minimum posterior predictive loss approach
. 216
7.4
Modified Bayesian information criterion
. 218
7.4.1
Example: P-spline regression model with Gaussian
noise
. 220
7.4.2
Example: P-spline logistic regression
. 221
7.5
Generalized information criterion
. 222
7.5.1
Example: Heterogeneous error model for the analysis
motorcycle impact data
. 226
7.5.2
Example: Microarray data analysis
. 227
8
Theoretical development and comparisons
235
8.1
Derivation of Bayesian information criteria
. 235
8.2
Derivation of generalized Bayesian information criteria
. . . 237
8.3
Derivation of Bayesian predictive information criterion
. . . 238
8.3.1
Derivation of
ВРІС
. 239
8.3.2
Further simplification of
ВРІС
. 243
8.4
Derivation of generalized information criterion
. 245
8.4.1
Information theoretic approach
. 245
8.4.2
Derivation of GIC
. 248
8.5
Comparison of various Bayesian model selection criteria
. . . 250
8.5.1
Utility function
. 250
8.5.2
Robustness to the improper prior
. 252
8.5.3
Computational cost
. 252
8.5.4
Estimation methods
. 253
8.5.5
Misspecified models
. 253
8.5.6
Consistency
. 253
9
Bayesian model averaging
257
9.1
Definition of Bayesian model averaging
. 257
9.2
Occam's window method
. 259
9.3
Bayesian model averaging for linear regression models
. 260
9.4
Other model averaging methods
. 261
9.4.1
Model averaging with AIC
. 262
9.4.2
Model averaging with predictive likelihood
. 262
Bibliography
265
Index
285 |
| any_adam_object | 1 |
| author | Ando, Tomohiro |
| author_facet | Ando, Tomohiro |
| author_role | aut |
| author_sort | Ando, Tomohiro |
| author_variant | t a ta |
| building | Verbundindex |
| bvnumber | BV036610519 |
| classification_rvk | QH 233 SK 830 |
| classification_tum | MAT 624f MAT 622f |
| ctrlnum | (OCoLC)466360865 (DE-599)BVBBV036610519 |
| dewey-full | 519.5/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 |
| dewey-search | 519.5/42 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV036610519</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20120918</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">100810s2010 xx ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781439836149</subfield><subfield code="9">978-1-4398-3614-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1439836140</subfield><subfield code="9">1-4398-3614-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)466360865</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV036610519</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-634</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-473</subfield><subfield code="a">DE-824</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5/42</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">QH 233</subfield><subfield code="0">(DE-625)141548:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 830</subfield><subfield code="0">(DE-625)143259:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 624f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 622f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ando, Tomohiro</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Bayesian model selection and statistical modeling</subfield><subfield code="c">Tomohiro Ando</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton, FL [u.a.]</subfield><subfield code="b">CRC Press</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 286 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield><subfield code="c">25 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Statistics</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">A Chapman & Hall book</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bayesian statistical decision theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical statistics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematical models</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematisches Modell</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Statistisches Modell</subfield><subfield code="0">(DE-588)4121722-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Bayes-Entscheidungstheorie</subfield><subfield code="0">(DE-588)4144220-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Bayes-Entscheidungstheorie</subfield><subfield code="0">(DE-588)4144220-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Statistisches Modell</subfield><subfield code="0">(DE-588)4121722-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bamberg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-020530788</subfield></datafield></record></collection> |
| id | DE-604.BV036610519 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:57Z |
| institution | BVB |
| isbn | 9781439836149 1439836140 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020530788 |
| oclc_num | 466360865 |
| open_access_boolean | |
| owner | DE-634 DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-824 |
| owner_facet | DE-634 DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-824 |
| physical | XIV, 286 S. Ill., graph. Darst. 25 cm |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Statistics A Chapman & Hall book |
| spelling | Ando, Tomohiro Verfasser aut Bayesian model selection and statistical modeling Tomohiro Ando Boca Raton, FL [u.a.] CRC Press 2010 XIV, 286 S. Ill., graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Statistics A Chapman & Hall book Bayesian statistical decision theory Mathematical statistics Mathematical models Mathematisches Modell Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Statistisches Modell (DE-588)4121722-6 s DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ando, Tomohiro Bayesian model selection and statistical modeling Bayesian statistical decision theory Mathematical statistics Mathematical models Mathematisches Modell Statistisches Modell (DE-588)4121722-6 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4121722-6 (DE-588)4144220-9 |
| title | Bayesian model selection and statistical modeling |
| title_auth | Bayesian model selection and statistical modeling |
| title_exact_search | Bayesian model selection and statistical modeling |
| title_full | Bayesian model selection and statistical modeling Tomohiro Ando |
| title_fullStr | Bayesian model selection and statistical modeling Tomohiro Ando |
| title_full_unstemmed | Bayesian model selection and statistical modeling Tomohiro Ando |
| title_short | Bayesian model selection and statistical modeling |
| title_sort | bayesian model selection and statistical modeling |
| topic | Bayesian statistical decision theory Mathematical statistics Mathematical models Mathematisches Modell Statistisches Modell (DE-588)4121722-6 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayesian statistical decision theory Mathematical statistics Mathematical models Mathematisches Modell Statistisches Modell Bayes-Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020530788&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT andotomohiro bayesianmodelselectionandstatisticalmodeling |