Nonlinear mixture models: a Bayesian approach
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College press
[2015]
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxv, 269 Seiten Diagramme |
| ISBN: | 9781848167568 |
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MARC
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| 245 | 1 | 0 | |a Nonlinear mixture models |b a Bayesian approach |c Tatiana Tatarinova, University of California, USA; Alan Schumitzky, University of California, USA |
| 264 | 1 | |a London |b Imperial College press |c [2015] | |
| 264 | 4 | |c © 2015 | |
| 300 | |a xxv, 269 Seiten |b Diagramme | ||
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Record in the Search Index
| _version_ | 1804152159300747264 |
|---|---|
| adam_text | Contents
List of Tables
xiii
l.tsf of Fiyuivs
xvii
Λ
(
kno wlvdgmv
л
t s
xxv
1.
Introduction
1
1.1
Bayesian Approach
...................... 3
1.2
Review of Applications of
Mixturo
Models in Population
Pharniacokiiiot
ics
....................... 1
1.3
Review of Applications of Mixture Models to Problems in
Computational Biology
.................... (>
I .. J.I Problems with mixture models
...........
II
I.I Outline of the Book
..................... 11
2.
Mathematical
Descript
ion of Nonlinear Mixture Models
15
2.1
Fundamental Notions of Markov chain Monte Carlo
. . . . 15
2.2
Nonlinear Hierarchical Models
................
li)
2.2.1
()ne-<-om|H)iient model
................
li)
2.2.2
Mixture models
................... 21
2.2.Л
Normal mixture models
............... 23
2.2.1
Nonlinear normal mixture models and
phanuacokinctic examples
............. 21
2.2.5
Linear normal mixture models and Kves example
.
2(>
2-2.fi Allocation formulation
...............
2Í)
Ί. λ
Gihlïs
Sampling
........................
Лі)
2.3.1
Theoretical convergence of the
С
Y h ìs
sainplfT
. . . 32
V
Η
vUi Nonhnrar Kftxtuiv
Models: A Bayesian Approach
2.3.2
ImKlucibility
and aperiodicity of the hybrid Gibbs-
Metropolis chain
...................
2.3.3
WiuBUGS and JAGS
................
35
2.4
Prior Distributions: Linear and Nonlinear Cases
...... 38
3.
Lalx-l Switching and Trapping 43
3.1
LnU l Switching and Permutation
Invariance
........ 43
3.
1
.1
Label switching
................... 43
3.
1
.2
Porimitation
invariance
............... 44
3.1.3
Allocation variables
{Z¿}
.............. 46
Λ.
І
A An example of label switching
........... 47
3.2
Markov Chain Convergence
................. 48
3.2.1
Trupping
states and convergence
.......... 54
3.3
Random Permutation Sampler
................ 59
3.3.1
RPS post processing
................. 63
3.4
Hł^parainetrization
...................... 65
З··1»
Stephens* Approach: Relabeling Strategies
......... 67
3.5.
1 Linear normal mixture: Eyes problem
....... 70
•1.
Trrntinent
of Mixture Models with an Unknown Number
of Coinjxments
73
1.1
Introduction
.......................... 73
1.2
Finding the Optimal Number of Components Using
Weighted Kullhnck Leibler Distance
............ 74
4.2.1
Distance between K-component model and
collapsed (K-O-component model
......... 75
1.2.2
Weighted Kullback Leibler distance for the
mixture of multivariate normals
.......... 76
4.2.3
Weighted
КиНЫск
Leibler distance for the
mult
і
variate
normal mixture model with diagonal
covariance matrix
.................. 78
4.2.4
Weighted Kullback-Leibler distance for the
oiKsdiniensional mixture of normals
........ 78
4.2.5
Comparison of weighted and un-weighted
К
iillback Leibler distances for one-dimensional
mixture of normals
............ 79
4.2.6
Weighted Kullback Leibler distance for a mixture
of binomial distributions
.............. 80
( otltrnts
ix
4.2.7
Weighted
K ull
back Loibler
distanco
for a mixture
of
Poisson
distributions
...............
HI
4.2.8
Mot
rit·
and
sémimet
ric
................ 82
4.2.9
Determinat
Urn of
tlu*
number of components in the
Bavesian
framework
................. 85
4.3
Stephens Approach: Birth Death Markov Chain Monte
Carlo
.............................. 80
4.3.1
Treatment of the Kyes model
............
8Í)
4.3.2
Treatment of nonlinear normal mixture models
. . 91
4.4 Kuliback Leibler
Markov Chain Monte Carlo A Now
Algorithm for Finite Mixture Analysis
........... 91
4.4.1
Kullhack
Leihler
Markov chain Monte Carlo with
random permutation sampler
............ 98
5.
Applications of HDMCMC. KLMGMC. and
H
PS
101
5.1
Galaxy Data
.......................... 101
5.2
Simulated Nonlinear Normal Mixture Model
........ 109
5.3
Linear Normal Mixture Model: Hoys and Girls
...... 112
Γι.
4
Nonlinear Pharumcokinet
ics
Model and Selection of Prior
Distributions
......................... 12!
5.5
Nonlinear Mixture Models in
(iene
Kxprossion Studies
. . 13 )
5.5.1
Simulated
dataset
.................. 138
(>.
Nonparaiiietric Methods
143
fi.
I Definition of the Basic
Moí
Iel................
144
fi.
2
NOnparametric Maximum Likelihood
............ 145
fi.
2.1
Render s decomposition
............... 1
4fi
fi.
2.2
Convex optimization over
а Пх«ч1 дгі<1
Ci
...... 147
ii.
2.3
Interior
|x>int
methods
............... 148
(i.
2.
I
Nonparamet
rie
adaptive #rid algorithm
......
14í)
fi.
2.· )
Pharmacokinetic
population analysis
problem
. . 151
f».
3
Nonparaiiietric Bavesian Approach
............. 154
fi.
3.1
Linear model
..................... 158
fi.
3.2
Diriclilct distribution
................ 159
fi.
3.3
Dirichlet process for discrete distributions
..... 159
I» I (iibl>s Sampler for the Dirichlft Process»
..........
Kil
fi.
4.1
Implementat
юн
of the
C Íibl>s
sampler
.......
lf»2
t>
ì
NfHiparametric Bavesian Kxainples
.............
l(il
x
Nonlinear Mixture Models: A Bayesian Approach
6.5.1
Binomial/beta model
................
164
6.5.2
Normal prior and linear model
........... 166
(5.5.3
One-dimensional linear case
............. 168
6.5.4
Two-dimensional linear case
............ 169
6.5.5
Plotting the posterior using Gibbs sampling
... 170
6.5.6
Galaxy
dataset
.................... 170
6.6
Technical Notes
........................ 171
6.6.1
Treatment of multiplicity
.............. 172
6.7
Stick-Breaking Priors
..................... 175
6.7.1
TVuncations of the stick-breaking process
..... 176
6.7.2
Blocked Gibbs algorithm
.............. 176
6.8
Examples of Stick-Breaking
................. 178
6.8.1
Binomial/beta: Rolling thumbtacks example
. . . 179
6.8.2
Determination of the number of mixture
components in the binomial/beta model
...... 181
6.8.3
Poisson/gamma Eye-TYacking example
...... 186
6.8.4
Determination of the number of mixture
components in Poisson/gamma case
........ 187
6.8.5
Stephens relabeling for Poisson/gamma case
. . . 191
6.8.6
Pharmaeokinetics example
............. 192
6.9
Maximum Likelihood and Stick-Breaking (A Connection
Between NPML and NPB Approaches)
........... 196
6.9.1
Galaxy
dataset
.................... 197
7.
Вауезііаіі
Clustering Methods
199
7.1
Brief Review of Clustering Methods in Microarray
Analysis
....................... 199
7.2
Application of KLMCMC to Gene Expression Time-Series
Analysis
..................... 201
7.3
Kuilhark Leibler Clustering
................. 205
7.3.1
Phannacokinet ic example
.............. 209
7.4
Simulated Time-Series Data with an Unknown Number of
Components (Zhou Model)
................. 213
7.4.1
Model description
.................. 214
7.4.2
Reductive stepwise method
............. 215
7.4.3
Zhou model using KLC algorithm
......... 217
7.4.4
Zhou model using KLMCMC
............ 218
7.5
Transcription Start Sites Prediction
........... 222
( otiti
rits
X¡
7.()
Conclusions..........................
228
Appendix A Standard Probability Distributions
2.41
Appendix
В
Full Conditional Distributions
2 Л Л
B.I Binomial/Beta
........................
2.Ì5
Appendix
С
Computation of
t
lie Weighted
Kullback
Leibler
Distami
2^57
C.I Weighted
Kullback
Leibler
Distance for a Mixture of
l invariate
Normals
...................... 237
( 2 Weight
счі
Kullback
Leibler
Distance for a Mixture of
Mult
і
variate
Normals
.....................
2.ÍÍ)
С..Ч
Weighted
Kuliback Leibler
Distance for a Mixture of Beta
Distributions
......................... 212
Appendix
D
BUGS Codes
215
D.I BUGS Code for the Kyes Model
............... 215
D.2
BUC
ÏS
Code for the Boys ami Girls Kxample
....... 2
IS
D..Ï
BUGS Code for thumbtack Data
.............. 2 10
D.I BUGS Code for Kye-Tracking Data
............. 251
1)5
BUGS Code for PK Kxample.
Non
parametric Bayesian
Approach with Stick-Breaking Priors
............
25. i
255
Ни
|
| any_adam_object | 1 |
| author | Tatarinova, Tatiana Schumitzky, Alan |
| author_GND | (DE-588)1068295872 (DE-588)1084346818 |
| author_facet | Tatarinova, Tatiana Schumitzky, Alan |
| author_role | aut aut |
| author_sort | Tatarinova, Tatiana |
| author_variant | t t tt a s as |
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| bvnumber | BV041826178 |
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| ctrlnum | (OCoLC)904904033 (DE-599)BSZ372771750 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/33 |
| dewey-search | 519.2/33 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV041826178 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:06:17Z |
| institution | BVB |
| isbn | 9781848167568 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027271151 |
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| physical | xxv, 269 Seiten Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Imperial College press |
| record_format | marc |
| spelling | Tatarinova, Tatiana Verfasser (DE-588)1068295872 aut Nonlinear mixture models a Bayesian approach Tatiana Tatarinova, University of California, USA; Alan Schumitzky, University of California, USA London Imperial College press [2015] © 2015 xxv, 269 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Markov-Kette (DE-588)4037612-6 gnd rswk-swf Bayes-Regel (DE-588)4144221-0 gnd rswk-swf Bayes-Regel (DE-588)4144221-0 s Markov-Kette (DE-588)4037612-6 s DE-604 Schumitzky, Alan Verfasser (DE-588)1084346818 aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027271151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tatarinova, Tatiana Schumitzky, Alan Nonlinear mixture models a Bayesian approach Markov-Kette (DE-588)4037612-6 gnd Bayes-Regel (DE-588)4144221-0 gnd |
| subject_GND | (DE-588)4037612-6 (DE-588)4144221-0 |
| title | Nonlinear mixture models a Bayesian approach |
| title_auth | Nonlinear mixture models a Bayesian approach |
| title_exact_search | Nonlinear mixture models a Bayesian approach |
| title_full | Nonlinear mixture models a Bayesian approach Tatiana Tatarinova, University of California, USA; Alan Schumitzky, University of California, USA |
| title_fullStr | Nonlinear mixture models a Bayesian approach Tatiana Tatarinova, University of California, USA; Alan Schumitzky, University of California, USA |
| title_full_unstemmed | Nonlinear mixture models a Bayesian approach Tatiana Tatarinova, University of California, USA; Alan Schumitzky, University of California, USA |
| title_short | Nonlinear mixture models |
| title_sort | nonlinear mixture models a bayesian approach |
| title_sub | a Bayesian approach |
| topic | Markov-Kette (DE-588)4037612-6 gnd Bayes-Regel (DE-588)4144221-0 gnd |
| topic_facet | Markov-Kette Bayes-Regel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027271151&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tatarinovatatiana nonlinearmixturemodelsabayesianapproach AT schumitzkyalan nonlinearmixturemodelsabayesianapproach |