A first course in Bayesian statistical methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Springer
2009
|
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 270 S. Ill., graph. Darst. |
| ISBN: | 9780387922997 9780387924076 |
Staff View
MARC
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| 100 | 1 | |a Hoff, Peter D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first course in Bayesian statistical methods |c Peter D. Hoff |
| 264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2009 | |
| 300 | |a IX, 270 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 4 | |a Statistique bayésienne | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Social sciences |x Statistical methods | |
| 650 | 0 | 7 | |a Bayes-Verfahren |0 (DE-588)4204326-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
Contents
1
Introduction
and examples
. 1
1.1
Introduction
. 1
1.2
Why
Bayes?
. 2
1.2.1
Estimating the probability of a rare event
. 3
1.2.2
Building a predictive model
. 8
1.3
Where we are going
. 11
1.4
Discussion and further references
. 12
2
Belief, probability and exchangeability
. 13
2.1
Belief functions and probabilities
. 13
2.2
Events, partitions and
Bayes'
rule
. 14
2.3
Independence
. 17
2.4
Random variables
. 17
2.4.1
Discrete random variables
. 18
2.4.2
Continuous random variables
. 19
2.4.3
Descriptions of distributions
. 21
2.5
Joint distributions
. 23
2.6
Independent random variables
. 26
2.7
Exchangeability
. 27
2.8
de Finetti's
theorem
. 29
2.9
Discussion and further references
. 30
3
One-parameter models
. 31
3.1
The binomial model
. 31
3.1.1
Inference for exchangeable binary data
. 35
3.1.2
Confidence regions
. 41
3.2
The
Poisson
model
. 43
3.2.1
Posterior inference
. 45
3.2.2
Example: Birth rates
. 48
3.3
Exponential families and conjugate priors
. 51
3.4
Discussion and further references
. 52
VIII Contents
4
Monte
Carlo approximation
. 53
4.1
The Monte Carlo
method.
53
4.2
Posterior inference for arbitrary functions
. 57
4.3
Sampling from predictive distributions
. 60
4.4
Posterior predictive model checking
. 62
4.5
Discussion and further references
. 65
5
The normal model
. 67
5.1
The normal model
. 67
5.2
Inference for the mean, conditional on the variance
. 69
5.3
Joint inference for the mean and variance
. 73
5.4
Bias, variance and mean squared error
. 79
5.5
Prior specification based on expectations
. 83
5.6
The normal model for non-normal data
. 84
5.7
Discussion and further references
. 86
6
Posterior approximation with the Gibbs sampler
. 89
6.1
A semiconjugate prior distribution
. 89
6.2
Discrete approximations
. 90
6.3
Sampling from the conditional distributions
. 92
6.4
Gibbs sampling
. 93
6.5
General properties of the Gibbs sampler
. 96
6.6
Introduction to MCMC diagnostics
. 98
6.7
Discussion and further references
. 104
7
The multivariate normal model
.105
7.1
The multivariate normal density
.105
7.2
A semiconjugate prior distribution for the mean
.107
7.3
The inverse-
Wishart
distribution
.109
7.4
Gibbs sampling of the mean and covariance
.112
7.5
Missing data and imputation
.115
7.6
Discussion and further references
.123
8
Group comparisons and hierarchical modeling
.125
8.1
Comparing two groups
.125
8.2
Comparing multiple groups
.130
8.2.1
Exchangeability and hierarchical models
.131
8.3
The hierarchical normal model
.132
8.3.1
Posterior inference
.133
8.4
Example: Math scores in U.S. public schools
.135
8.4.1
Prior distributions and posterior approximation
.137
8.4.2
Posterior summaries and shrinkage
.140
8.5
Hierarchical modeling of means and variances
.143
8.5.1
Analysis of math score data
.145
8.6
Discussion and further references
.146
Contents
IX
9 Linear
regression.
149
9.1 The linear
regression model
.149
9.1.1
Least squares estimation for the oxygen uptake data
. . . 153
9.2
Bayesian estimation for a regression model
.154
9.2.1
A semiconjugate prior distribution
.154
9.2.2
Default and weakly informative prior distributions
.155
9.3
Model selection
.160
9.3.1
Bayesian model comparison
.163
9.3.2
Gibbs sampling and model averaging
.167
9.4
Discussion and further references
.170
10
Nonconjugate priors and Metropolis-Hastings algorithms
. . 171
10.1
Generalized linear models
.171
10.2
The Metropolis algorithm
.173
10.3
The Metropolis algorithm for
Poisson
regression
.179
10.4
Metropolis, Metropolis-Hastings and Gibbs
.181
10.4.1
The Metropolis-Hastings algorithm
.182
10.4.2
Why does the Metropolis-Hastings algorithm work?
. 184
10.5
Combining the Metropolis and Gibbs algorithms
.187
10.5.1
A regression model with correlated errors
.188
10.5.2
Analysis of the ice core data
.191
10.6
Discussion and further references
.192
11
Linear and generalized linear mixed effects models
.195
11.1
A hierarchical regression model
.195
11.2
Full conditional distributions
.198
11.3
Posterior analysis of the math score data
.200
11.4
Generalized linear mixed effects models
.201
11.4.1
A Metropolis-Gibbs algorithm for posterior
approximation
.202
11.4.2
Analysis of tumor location data
.203
11.5
Discussion and further references
.207
12
Latent variable methods for ordinal data
.209
12.1
Ordered
probit
regression and the rank likelihood
.209
12.1.1
Probit
regression
.211
12.1.2
Transformation models and the rank likelihood
.214
12.2
The Gaussian copula model
.217
12.2.1
Rank likelihood for copula estimation
.218
12.3
Discussion and further references
.223
Exercises
.225
Common distributions
.253
References
.259
Index
.267 |
| any_adam_object | 1 |
| author | Hoff, Peter D. |
| author_facet | Hoff, Peter D. |
| author_role | aut |
| author_sort | Hoff, Peter D. |
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| ctrlnum | (OCoLC)551817045 (DE-599)DNB992520940 |
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| dewey-tens | 300 - Social sciences |
| discipline | Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| institution | BVB |
| isbn | 9780387922997 9780387924076 |
| language | English |
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| spelling | Hoff, Peter D. Verfasser aut A first course in Bayesian statistical methods Peter D. Hoff Dordrecht [u.a.] Springer 2009 IX, 270 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Methode van Bayes gtt Statistique bayésienne Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Bayes-Verfahren (DE-588)4204326-8 s Datenanalyse (DE-588)4123037-1 s DE-604 Erscheint auch als Online-Ausgabe 10.1007/978-0-387-92407-6 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017329585&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoff, Peter D. A first course in Bayesian statistical methods Methode van Bayes gtt Statistique bayésienne Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4123037-1 (DE-588)4144220-9 |
| title | A first course in Bayesian statistical methods |
| title_auth | A first course in Bayesian statistical methods |
| title_exact_search | A first course in Bayesian statistical methods |
| title_full | A first course in Bayesian statistical methods Peter D. Hoff |
| title_fullStr | A first course in Bayesian statistical methods Peter D. Hoff |
| title_full_unstemmed | A first course in Bayesian statistical methods Peter D. Hoff |
| title_short | A first course in Bayesian statistical methods |
| title_sort | a first course in bayesian statistical methods |
| topic | Methode van Bayes gtt Statistique bayésienne Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Methode van Bayes Statistique bayésienne Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren Datenanalyse Bayes-Entscheidungstheorie |
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