Bayesian computation with R:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Schriftenreihe: | Use R!
|
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2928497&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=015697606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 267 S. zahlr. graph. Darst. 235 mm x 155 mm |
| ISBN: | 9780387713854 9780387713847 0387713840 |
Internformat
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| 245 | 1 | 0 | |a Bayesian computation with R |c Jim Albert |
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Datensatz im Suchindex
| _version_ | 1819298538515857408 |
|---|---|
| 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
.................. 4
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
.............. 11
1.3.4
The Behavior of the True Significance Level Under
Different Assumptions
............................. 12
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
.............................................. 29
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
A Bayesian Test of the Fairness of a Coin
................... 50
3.6
Further Reading
......................................... 53
3.7
Summary of
R
Functions
................................. 53
3.8
Exercises
............................................... 54
Multiparameter Models
................................... 57
4.1
Introduction
............................................ 57
4.2
Normal Data with Both Parameters Unknown
.............. 57
4.3
A Multinomial Model
.................................... 60
4.4
A Bioassay Experiment
.................................. 60
4.5
Comparing Two Proportions
.............................. 65
4.6
Further Reading
......................................... 70
4.7
Summary of
R
Functions
................................. 70
4.8
Exercises
............................................... 71
Introduction to Bayesian Computation
.................... 75
5.1
Introduction
............................................ 75
5.2
Computing Integrals
..................................... 76
5.3
Setting Up a Problem on
R
............................... 77
5.4
A Beta-Binomial Model for Overdispersion
................. 78
5.5
Approximations Based on Posterior Modes
................. 80
5.6
The Example
........................................... 82
5.7
Monte Carlo Method for Computing Integrals
............... 84
5.8
Rejection Sampling
...................................... 85
5.9
Importance Sampling
.................................... 88
5.10
Sampling Importance Resampling
......................... 91
5.11
Further Reading
......................................... 94
5.12
Summary of
R
Functions
................................. 94
5.13
Exercises
............................................... 96
Markov Chain Monte Carlo Methods
......................101
6.1
Introduction
............................................101
6.2
Introduction to Discrete Markov Chains
....................101
6.3
Metropolis-Hasting Algorithms
............................104
6.4
Gibbs Sampling
.........................................106
6.5
MCMC Output Analysis
.................................106
6.6
A Strategy in Bayesian Computing
........................108
6.7
Learning About a Normal Population from Grouped Data
___108
6.8
Example of Output Analysis
..............................113
6.9
Modeling Data with Cauchy Errors
........................116
Contents ix
6.10
Analysis of the Stanford Heart Transplant Data
.............124
6.11
Further Reading
.........................................129
6.12
Summary of
R
Functions
.................................130
6.13
Exercises
...............................................131
Hierarchical Modeling
.....................................137
7.1
Introduction
............................................137
7.2
Introduction to Hierarchical Modeling
......................137
7.3
Individual and Combined Estimates
.......................139
7.4
Equal Mortality Rates?
..................................141
7.5
Modeling a Prior Belief of Exchangeability
..................145
7.6
Posterior Distribution
....................................147
7.7
Simulating from the Posterior
.............................147
7.8
Posterior Inferences
......................................151
7.8.1
Shrinkage
........................................152
7.8.2
Comparing Hospitals
..............................153
7.9
Posterior Predictive Model Checking
.......................155
7.10
Further Reading
.........................................157
7.11
Summary of
R
Functions
.................................158
7.12
Exercises
...............................................158
Model Comparison
........................................163
8.1
Introduction
............................................163
8.2
Comparison of Hypotheses
................................163
8.3
A One-Sided Test of a Normal Mean
.......................164
8.4
A Two-Sided Test of a Normal Mean
......................167
8.5
Comparing Two Models
..................................168
8.6
Models for Soccer Goals
..................................169
8.7
Is a Baseball Hitter Really Streaky?
.......................172
8.8
A Test of Independence in a Two-Way Contingency Table
.... 176
8.9
Further Reading
.........................................180
8.10
Summary of
R
Functions
.................................181
8.11
Exercises
...............................................183
Regression Models
.........................................187
9.1
Introduction
............................................187
9.2
Normal Linear Regression
................................187
9.2.1
The Model
.......................................187
9.2.2
The Posterior Distribution
..........................188
9.2.3
Prediction of Future Observations
...................188
9.2.4
Computation
.....................................189
9.2.5
Model Checking
...................................189
9.2.6
An Example
......................................190
9.3
Survival Modeling
.......................................199
9.4
Further Reading
.........................................204
χ
Contents
9.5
Summary of
R
Functions
.................................205
9.6
Exercises
...............................................206
10
Gibbs Sampling
............................................211
10.1
Introduction
............................................211
10.2
Robust Modeling
........................................212
10.3
Binary Response Regression with
a
Probit Link.............216
10.4
Estimating a Table of Means
..............................219
10.4.1
Introduction
......................................219
10.4.2
A Flat Prior Over the Restricted Space
..............223
10.4.3
A Hierarchical Regression Prior
.....................227
10.4.4
Predicting the Success of Future Students
............232
10.5
Further Reading
.........................................233
10.6
Summary of
R
Functions
.................................233
10.7
Exercises
...............................................234
11
Using
R
to Interface with WinBUGS
......................237
11.1
Introduction to WinBUGS
................................237
11.2
An
R
Interface to WinBUGS
..............................238
11.3
MCMC Diagnostics Using the boa Package
.................239
11.4
A Change-Point Model
...................................240
11.5
A Robust Regression Model
..............................243
11.6
Estimating Career Trajectories
............................247
11.7
Further Reading
.........................................253
11.8
Exercises
...............................................254
References
.....................................................259
Index
.........................................................263
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| id | DE-604.BV022490385 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:56:33Z |
| institution | BVB |
| isbn | 9780387713854 9780387713847 0387713840 |
| language | English |
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| physical | X, 267 S. zahlr. graph. Darst. 235 mm x 155 mm |
| publishDate | 2007 |
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| series2 | Use R! |
| spellingShingle | Albert, Jim 1953- Bayesian computation with R Datenverarbeitung Bayesian statistical decision theory Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Bayes-Inferenz (DE-588)4648118-7 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4648118-7 |
| 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 | Datenverarbeitung Bayesian statistical decision theory Data processing R (Computer program language) R Programm (DE-588)4705956-4 gnd Bayes-Inferenz (DE-588)4648118-7 gnd |
| topic_facet | Datenverarbeitung Bayesian statistical decision theory Data processing R (Computer program language) R Programm Bayes-Inferenz |
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