Bayesian computation with R:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht [u.a.]
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Use R!
|
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=3179418&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017076773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 298 S. graph. Darst. |
| ISBN: | 9780387922973 |
Internformat
MARC
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| 100 | 1 | |a Albert, Jim |d 1953- |e Verfasser |0 (DE-588)133457834 |4 aut | |
| 245 | 1 | 0 | |a Bayesian computation with R |c Jim Albert |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Dordrecht [u.a.] |b Springer |c 2009 | |
| 300 | |a XII, 298 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Bayes-Inferenz |0 (DE-588)4648118-7 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017076773 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0002 MAT 620f 2009 A 4710(2) 0041 MAT 620f 2009 A 4578 0102 MAT 620f 2010 A 1663(2) |
|---|---|
| DE-BY-TUM_katkey | 1664692 |
| DE-BY-TUM_location | 00 LSB 01 |
| DE-BY-TUM_media_number | 040090452365 040090451897 040010225760 |
| _version_ | 1821933532571762688 |
| adam_text | Contents
An
Introduction
to R
...................................... 1
1.1
Overview
............................................... 1
1.2
Exploring a Student
Dataset
.............................. 1
1.2.1
Introduction to the
Dataset
......................... 1
1.2.2
Reading the Data into
R
........................... 2
1.2.3
R
Commands to Summarize and Graph
a Single Batch
.................................... 2
1.2.4
R
Commands to Compare Batches
.................. 5
1.2.5
R
Commands for Studying Relationships
............. 6
1.3
Exploring the Robustness of the
t
Statistic
................. 8
1.3.1
Introduction
...................................... 8
1.3.2
Writing a Function to Compute the
t
Statistic
........ 9
1.3.3
Programming a Monte Carlo Simulation
.............. 10
1.3.4
The Behavior of the True Significance Level Under
Different Assumptions
............................. 11
1.4
Further Reading
......................................... 13
1.5
Summary of
R
Functions
................................. 14
1.6
Exercises
............................................... 15
Introduction to Bayesian Thinking
......................... 19
2.1
Introduction
............................................ 19
2.2
Learning About the Proportion of Heavy Sleepers
........... 19
2.3
Using a Discrete Prior
................................... 20
2.4
Using a Beta Prior
...................................... 22
2.5
Using a Histogram Prior
................................. 26
2.6
Prediction
.............................................. 28
2.7
Further Reading
......................................... 34
2.8
Summary of
R
Functions
................................. 34
2.9
Exercises
............................................... 35
Contents
Single-Parameter Models.................................. 39
3.1
Introduction
............................................ 39
3.2 Normal Distribution
with Known Mean but Unknown
Variance
............................................... 39
3.3
Estimating a Heart Transplant Mortality Rate
.............. 41
3.4
An Illustration of Bayesian Robustness
..................... 44
3.5
Mixtures of Conjugate Priors
............................. 49
3.6
A Bayesian Test of the Fairness of a Coin
................... 52
3.7
Further Reading
......................................... 57
3.8
Summary of
R
Functions
................................. 57
3.9
Exercises
............................................... 58
Multiparameter Models
................................... 63
4.1
Introduction
............................................ 63
4.2
Normal Data with Both Parameters Unknown
.............. 63
4.3
A Multinomial Model
.................................... 66
4.4
A Bioassay Experiment
.................................. 69
4.5
Comparing Two Proportions
.............................. 75
4.6
Further Reading
......................................... 80
4.7
Summary of
R
Functions
................................. 80
4.8
Exercises
............................................... 81
Introduction to Bayesian Computation
.................... 87
5.1
Introduction
............................................ 87
5.2
Computing Integrals
..................................... 88
5.3
Setting Up a Problem in
R
............................... 89
5.4
A Beta-Binomial Model for Overdispersion
................. 90
5.5
Approximations Based on Posterior Modes
................. 94
5.6
The Example
........................................... 95
5.7
Monte Carlo Method for Computing Integrals
............... 97
5.8
Rejection Sampling
...................................... 98
5.9
Importance Sampling
.................................... 101
5.9.1
Introduction
......................................101
5.9.2
Using
a Multi
variate
t
as a Proposal Density
..........103
5.10
Sampling Importance Resampling
.........................105
5.11
Further Reading
.........................................108
5.12
Summary of
R
Functions
.................................109
5.13
Exercises
...............................................110
Markov Chain Monte Carlo Methods
......................117
6.1
Introduction
............................................117
6.2
Introduction to Discrete Markov Chains
....................117
6.3
Metropolis-Hastings Algorithms
...........................120
6.4
Gibbs Sampling
.........................................122
6.5
MCMC Output Analysis
.................................122
Contents xi
6.6
A Strategy in Bayesian Computing
........................124
6.7
Learning About a Normal Population from Grouped Data
.... 124
6.8
Example of Output Analysis
..............................129
6.9
Modeling Data with Cauchy Errors
........................131
6.10
Analysis of the Stanford Heart Transplant Data
.............140
6.11
Further Reading
.........................................145
6.12
Summary of
R
Functions
.................................146
6.13
Exercises
...............................................147
Hierarchical Modeling
.....................................153
7.1
Introduction
............................................153
7.2
Three Examples
.........................................153
7.3
Individual and Combined Estimates
.......................155
7.4
Equal Mortality Rates?
..................................157
7.5
Modeling a Prior Belief of Exchangeability
..................161
7.6
Posterior Distribution
....................................163
7.7
Simulating from the Posterior
.............................163
7.8
Posterior Inferences
......................................168
7.8.1
Shrinkage
........................................168
7.8.2
Comparing Hospitals
..............................169
7.9
Bayesian Sensitivity Analysis
.............................171
7.10
Posterior Predictive Model Checking
.......................173
7.11
Further Reading
.........................................175
7.12
Summary of
R
Functions
.................................175
7.13
Exercises
...............................................176
Model Comparison
........................................181
8.1
Introduction
............................................181
8.2
Comparison of Hypotheses
................................181
8.3
A One-Sided Test of a Normal Mean
.......................182
8.4
A Two-Sided Test of a Normal Mean
......................185
8.5
Comparing Two Models
..................................186
8.6
Models for Soccer Goals
..................................187
8.7
Is a Baseball Hitter Really Streaky?
.......................190
8.8
A Test of Independence in a Two-Way Contingency Table
.... 194
8.9
Further Reading
.........................................199
8.10
Summary of
R
Functions
.................................199
8.11
Exercises
...............................................201
Regression Models
.........................................205
9.1
Introduction
............................................205
9.2
Normal Linear Regression
................................205
9.2.1
The Model
.......................................205
9.2.2
The Posterior Distribution
..........................206
9.2.3
Prediction of Future Observations
...................206
xii Contents
9.2.4
Computation
.....................................207
9.2.5 Model
Checking
...................................207
9.2.6 An
Example
......................................208
9.3 Model
Selection Using Zellner s
g
Prior
.....................217
9.4
Survival Modeling
.......................................222
9.5
Further Reading
.........................................227
9.6
Summary of
R
Functions
.................................227
9.7
Exercises
...............................................229
10
Gibbs Sampling
............................................235
10.1
Introduction
............................................235
10.2
Robust Modeling
........................................236
10.3
Binary Response Regression with
a
Probit Link.............240
10.3.1
Missing Data and Gibbs Sampling
...................240
10.3.2
Proper Priors and Model Selection
..................243
10.4
Estimating a Table of Means
..............................248
10.4.1
Introduction
......................................248
10.4.2
A Flat Prior Over the Restricted Space
..............250
10.4.3
A Hierarchical Regression Prior
.....................254
10.4.4
Predicting the Success of Future Students
............259
10.5
Further Reading
.........................................260
10.6
Summary of
R
Functions
.................................260
10.7
Exercises
...............................................261
11
Using
R
to Interface with WinBUGS
......................265
11.1
Introduction to WinBUGS
................................265
11.2
An
R
Interface to WinBUGS
..............................266
11.3
MCMC Diagnostics Using the coda Package
................267
11.4
A Change-Point Model
...................................268
11.5
A Robust Regression Model
..............................272
11.6
Estimating Career Trajectories
............................276
11.7
Further Reading
.........................................281
11.8
Exercises
...............................................282
References
.....................................................287
Index
....................................... ..............293
|
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| discipline | Informatik Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035271411 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:27:20Z |
| institution | BVB |
| isbn | 9780387922973 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017076773 |
| oclc_num | 495065906 |
| open_access_boolean | |
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| physical | XII, 298 S. graph. Darst. |
| publishDate | 2009 |
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| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Use R! |
| spellingShingle | Albert, Jim 1953- Bayesian computation with R Bayes-Inferenz (DE-588)4648118-7 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4648118-7 (DE-588)4705956-4 |
| title | Bayesian computation with R |
| title_auth | Bayesian computation with R |
| title_exact_search | Bayesian computation with R |
| title_full | Bayesian computation with R Jim Albert |
| title_fullStr | Bayesian computation with R Jim Albert |
| title_full_unstemmed | Bayesian computation with R Jim Albert |
| title_short | Bayesian computation with R |
| title_sort | bayesian computation with r |
| topic | Bayes-Inferenz (DE-588)4648118-7 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Bayes-Inferenz R Programm |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3179418&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017076773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT albertjim bayesiancomputationwithr |
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Teilbibliothek Stammgelände
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Teilbibliothek Mathematik & Informatik
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