Applied Bayesian modelling
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2014
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and statistics
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
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Datensatz im Suchindex
| _version_ | 1804152336600268800 |
|---|---|
| adam_text | Contents
Preface
χι
Bayesian methods and Bayesian estimation
1
1.1
Introduction
1
1.1.1
Summarising existing knowledge: Prior densities for parameters
2
1.1.2
Updating information: Prior, likelihood and posterior densities
3
1.1.3
Predictions and assessment
5
1.1.4
Sampling parameters
6
1.2
MCMC techniques: The Metropolis-Hastings algorithm
7
1.2.1
Gibbs sampling
8
1.2.2
Other MCMC algorithms
9
1.2.3
INLA approximations
10
1.3
Software for MCMC: BUGS, JAGS and R-INLA
11
1.4
Monitoring MCMC chains and assessing convergence
19
1.4.1
Convergence diagnostics
20
1.4.2
Model identirmbility
21
1.5
Model assessment
23
1.5.1
Sensitivity to priors
23
1.5.2
Model checks
24
1.5.3
Model choice
25
References
28
Hierarchical models for related units
34
2.1
Introduction: Smoothing to the hyper population
34
2.2
Approaches to model assessment: Penalised fit criteria, marginal likelihood
and predictive methods
35
2.2.1
Penalised fit criteria
36
2.2.2
Formal model selection using marginal likelihoods
37
2.2.3
Estimating model probabilities or marginal likelihoods in practice
38
2.2.4
Approximating the posterior density
40
2.2.5
Modei
averaging from MCMC samples
42
2.2.6
Predictive criteria for model checking and selection:
Cross-validation
46
vi
CONTENTS
2.2.7
Predictive checks and model choice using complete data replicate
sampling
50
2.3
Ensemble estimates:
Poisson
-gamma and Beta-binomial
hierarchical models
53
2.3.1
Hierarchical mixtures for
poisson
and binomial data
54
2.4
Hierarchical smoothing methods for continuous data
61
2.4.1
Priors on hyperparameters
62
2.4.2
Relaxing normality assumptions
63
2.4.3
Multivariate borrowing of strength
65
2.5
Discrete mixtures and dirichlet processes
69
2.5.1
Finite mixture models
69
2.5.2
Dirichlet process priors
72
2.6
General additive and histogram smoothing priors
78
2.6.1
Smoothness priors
79
2.6.2
Histogram smoothing
80
Exercises
83
Notes
86
References
89
3
Regression techniques
97
3.1
Introduction: Bayesian regression
97
3.2
Normal linear regression
98
3.2.1
Linear regression model checking
99
3.3
Simple generalized linear models: Binomial, binary and
Poisson
regression
102
3.3.1
Binary and binomial regression
102
3.3.2
Poisson
regression
105
3.4
Augmented data regression
107
3.5
Predictor subset choice
110
3.5.1
The ¿»-prior approach
114
3.5.2
Hierarchical lasso prior methods
116
3.6
Multinomial, nested and ordinal regression
126
3.6.1
Nested logit specification
128
3.6.2
Ordinal outcomes
130
Exercises
136
Notes
138
References
144
4
More advanced regression techniques
149
4.1
Introduction
149
4.2
Departures from linear model assumptions and robust alternatives
149
4.3
Regression for overdispersed discrete outcomes
154
4.3.1
Excess zeroes
157
4.4
Link selection
160
4.5
Discrete mixture regressions for regression and outlier status
161
4.5.1
Outlier accommodation
163
4.6
Modelling non-linear regression effects
167
4.6.1
Smoothness priors for non-linear regression
167
CONTENTS
vii
4.6.2
Spline regression and other basis functions
169
4.6.3
Priors on basis coefficients
171
4.7
Quanti le
regression
175
Exercises
177
Notes
177
References
179
5
Meta-analysis and multilevel models
183
5.1
Introduction
183
5.2
Meta-analysis; Bayesian evidence synthesis
184
5.2.1
Common forms of meta-analysis
185
5.2.2
Priors for stage
2
variation in meta-analysis
188
5.2.3
Multi variate meta-analysis
193
5.3
Multilevel models: Univariate continuous outcomes
195
5.4
Multilevel discrete responses
201
5.5
Modelling heteroscedasticity
204
5.6
Multilevel data on
multi variate
indices
206
Exercises
208
Notes
210
References
211
6
Models for time series
215
6.1
Introduction
215
6.2
Autoregressive
and moving average models
216
6.2.1
Depende ni
errors
218
6.2.2
Bayesian priors
în
ARMA
models
218
6.2.3
Further types of time dependence
222
6.3
Discrete outcomes
229
6.3.1
IN
AR
models for counts
231
6.3.2
Evolution in conjugate process parameters
232
6.4
Dynamic linear and general linear models
235
6.4.1
Further forma of dynamic models
238
6.5
Stochastic variances and stochastic volatility
244
6.5.1
ARCH and GARCH models
244
6.5.2
State space stochastic volatility models
245
6.6
Modelling structural shifts
248
6.6.1
Level, trend and variance shifts
249
6.6.2
Latent state models including historic dependence
250
6.6.3
Switching regressions and autoregressions
251
Exercises
258
Notes
261
References
265
7
Analysis of
panei
data
273
7.1
Introduction
273
7.2
Hierarchical longitudinal models for metric data
274
7.2.1
Autoregressive
errors
275
viii CONTENTS
7.2.2 Dynamic
linear
models
276
7.2.3
Extended time dependence
276
7.3
Normal linear panel models and normal linear growth curves
278
7.3.1
Growth curves
280
7.3.2
Subject level
autoregressive
parameters
283
7.4
Longitudinal discrete data: Binary, categorical and
Poisson
panel data
285
7.4.1
Binary panel data
285
7.4.2
Ordinai
panel data
288
7.4.3
Panel data for counts
292
7.5
Random effects selection
295
7.6
Missing data in longitudinal studies
297
Exercises
302
Notes
303
References
306
8
Models for spatial outcomes and geographical association
312
8.1
Introduction
312
8.2
Spatial regressions and simultaneous dependence
313
8.2.
ł
Regression with localised dependence
316
8.2.2
Binary outcomes
317
8.3
Conditional prior models
321
8.3.1
Ecological analysis involving count data
324
8.4
Spatial covariation and interpolation in continuous space
329
8.4.1
Discrete convolution processes
332
8.5
Spatial heterogeneity and spatially varying coefficient priors
337
8.5.1
Spatial expansion and geographically weighted regression
338
8.5.2
Spatially varying coefficients via multivariate priors
339
8.6
Spatio-temporal models
343
8.6.1
Conditional prior representations
345
8.7
Clustering in relation to known centres
348
8.7.1
Areas or cases as data
350
8.7.2
Multiple sources
350
Exercises
352
Notes
354
References
355
9
Latent variable and structural equation models
364
9.1
Introduction
364
9.2
Normal linear structural equation models
365
9.2.1
Cross-sectional normal SEMs
365
9.2.2
Identifiability constraints
367
9.3
Dynamic factor models, panel data factor models and spatial factor
models
372
9.3.1
Dynamic factor models
372
9.3.2
Linear SEMs for panel data
374
9.3.3
Spatial factor models
378
CONTENTS ix
9.4 Latent
trait and
latent
class analysis for discrete outcomes
381
9.4.1
Latent trait models
381
9.4.2
Latent class models
382
9.5
Latent trait models for multilevel data
387
9.6
Structural equation models for missing data
389
Exercises
392
Notes
394
References
397
10
Survival and event history models
402
10.1
Introduction
402
10.2
Continuous time functions for survival
403
10.2.1
Parametric hazard models
405
10.2.2
Se mi-
parametric hazards
408
10.3
Accelerated hazards
411
10.4
Discrete time approximations
413
10.4.1
Discrete time hazards regression
415
10.5
Accounting for frailty in event history and survival models
417
10.6
Further applications of frailty models
421
10.7
Competing risks
423
Exercises
425
References
426
Index
431
Applied
Bayesian Modelling
Second Edition
Peter Congdon
Centre for Statistics and Department of Geography, Queen Mary, University of
London, UK
Application settings for Bayesian methods have widened considerably in the last
decade, and Bayesian inference and estimation is now a popular choice for routine
data analysis. This second edition of Applied Bayesian Modelling reviews a range of
major statistical models from a Bayesian perspective, and focuses on the practical
implementation of Bayesian techniques using real-life examples. The main focus for
implementation is BUGS, encompassing the WinBUGS, OpenBUGS and JAGS freeware
packages that offer a simplified and flexible approach to Bayesian statistical modelling.
However, also included are analyses in
R
which is increasingly used as a standalone
option or as platform for interface with BUGS. The book gives a detailed explanation of
each example
-
explaining fully the choice of model for each particular problem.
Key Features:
•
Provides a broad and comprehensive account of applied Bayesian modelling.
•
Describes a variety of model assessment methods and the flexibility of Bayesian
prior specifications.
•
Covers many application areas, including panel data models, structural equation
and other multivariate structure models, spatial analysis, and survival analysis.
•
Provides detailed and updated worked examples in BUGS and
R
to illustrate the
practical application of the techniques described.
•
All BUGS and
R
programs are available from an ftp site.
Applied Bayesian Modelling provides a good introduction to Bayesian modelling and
data analysis for a wide range of people involved in applied statistical analysis, including
researchers and students from statistics and the health and social sciences. The wealth
of examples makes this book an ideal reference for anyone involved in statistical
modelling and analysis.
Front cover graphic depicts modelled monthly Arctic sea ice extents.
1979-2011,
R-INLA estimates
|
| any_adam_object | 1 |
| author | Congdon, Peter 1949- |
| author_GND | (DE-588)170438783 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 830 |
| ctrlnum | (OCoLC)879620479 (DE-599)GBV782724655 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041953769 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:09:06Z |
| institution | BVB |
| isbn | 9781119951513 |
| language | English |
| lccn | 2014004862 |
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| owner_facet | DE-19 DE-BY-UBM DE-29T DE-11 DE-1049 DE-703 DE-824 |
| physical | IX, 437 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Congdon, Peter 1949- Verfasser (DE-588)170438783 aut Applied Bayesian modelling Peter Congdon 2. ed. Chichester Wiley 2014 IX, 437 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Literaturangaben Bayesian statistical decision theory Mathematical statistics Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s DE-604 Bayes-Verfahren (DE-588)4204326-8 s 1\p DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027396685&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027396685&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Congdon, Peter 1949- Applied Bayesian modelling Bayesian statistical decision theory Mathematical statistics Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4144220-9 |
| title | Applied Bayesian modelling |
| title_auth | Applied Bayesian modelling |
| title_exact_search | Applied Bayesian modelling |
| title_full | Applied Bayesian modelling Peter Congdon |
| title_fullStr | Applied Bayesian modelling Peter Congdon |
| title_full_unstemmed | Applied Bayesian modelling Peter Congdon |
| title_short | Applied Bayesian modelling |
| title_sort | applied bayesian modelling |
| topic | Bayesian statistical decision theory Mathematical statistics Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayesian statistical decision theory Mathematical statistics Bayes-Verfahren Bayes-Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027396685&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027396685&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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