Spatial statistics and modeling:
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| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English French |
| Published: |
New York, NY [u.a.]
Springer
2010
|
| Series: | Springer series in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XV, 297 S. Ill., graph. Darst., Kt. |
| ISBN: | 9780387922560 9781461424994 9780387922577 |
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MARC
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| 100 | 1 | |a Gaetan, Carlo |e Verfasser |0 (DE-588)136190561 |4 aut | |
| 245 | 1 | 0 | |a Spatial statistics and modeling |c Carlo Gaetan ; Xavier Guyon. Transl. by Kevin Bleakley |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2010 | |
| 300 | |a XV, 297 S. |b Ill., graph. Darst., Kt. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Spatial analysis (Statistics) | |
| 650 | 4 | |a Spatial analysis (Statistics) |x Mathematical models | |
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| 700 | 1 | |a Bleakley, Kevin |4 trl | |
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Record in the Search Index
| _version_ | 1817681158648889344 |
|---|---|
| adam_text |
Contents
Second-order spatial models and geostatistics
.
I
1.1
Some background in stochastic processes
. 2
1
.2
Stationary processes
. 3
1.2.1
Definitions and examples
. 3
1
.2.2
Spectral representation of covarianccs
. 5
1.3
Intrinsic processes and variograms
. 8
1
.3.
1 Definitions, examples and properties
. 8
1.3.2
Variograms for stationary processes
. 10
1.3.3
Examples of covariances and variograms
.
II
1.3.4
Anisotropy
. 14
1.4
Geometric properties: continuity, differentiability
. 15
1.4.
1 Continuity and differentiability: the stationary case
. 17
1.5
Spatial modeling using convolutions
. 19
1.5.1
Continuous model
. 19
1.5.2
Discrete convolution
. 21
1.6
Spatio-temporal models
. 22
1.7
Spatial
autoregressive
models
. 25
1
.7.
1 Stationary MA and
ARMA
models
. 26
1
.7.2
Stationary simultaneous autoregression
. 28
1.7.3
Stationary conditional autoregression
. 30
1
.7.4
Non-stationary
autoregressive
models on finite networks
S
. 34
1
.7.5
Autoregressive
models with covariates
. 37
1.8
Spatial regression models
. 38
1.9
Prediction when the
covariante
is known
. 42
1.9.1
Simple kriging
. 43
1.9.2
Universal kriging
. 44
1.9.3
Simulated experiments
. 45
Exercises
. 47
Gibbs-Markov random fields on networks
. 53
2.1
Compatibility of conditional distributions
. 54
Contents
2.2
Gibbs random fields on
5. 55
2.2.1
Interaction potential and Gibbs specification
. 55
2.2.2
Examples of Gibbs specifications
. 57
2.3
Markov random fields and Gibbs random fields
. 64
2.3.1
Definitions: cliques. Markov random field
. 64
2.3.2
The Hammersley-Clifford theorem
. 65
2.4 Besag
auto-models
. 67
2.4.1
Compatible conditional distributions and auto-models
. 67
2.4.2
Examples of'auto-models
. 68
2.5
Markov random field dynamics
. 73
2.5.1
Markov chain Markov random field dynamics
. 74
2.5.2
Examples of dynamics
. 74
Exercises
. 76
Spatial point processes
. 81
3.
1 Definitions and notation
. 82
3.
1
.
1 Exponential spaces
. 83
3.1.2
Moments of a point process
. 85
3.1.3
Examples of point processes
. 87
3.2
Poisson
point process
. 89
3.3
Cox point process
. 91
3.3.1
log-Gaussian Cox process
. 91
3.3.2
Doubly stochastic
Poisson
point process
. 92
3.4
Point process density
. 92
3.4.1
Definition
. 93
3.4.2
Gibbs point process
. 94
3.5
Nearest neighbor distances for point processes
. 98
3.5.1
Palm measure
. 98
3.5.2
Two nearest neighbor distances for X
. 99
3.5.3
Second-order reduced moments
.
КЮ
3.6
Markov point process
.102
3.6.
1 The Ripley-Kelly Markov property
. 102
3.6.2
Markov nearest neighbor property
. 104
3.6.3
Gibbs point process on R''
.
1
07
Exercises
. 108
Simulation of spatial models
.
Ill
4.
1 Convergence of Markov chains
.112
4.1.1
Strong law of large numbers and central limit theorem
for a homogeneous Markov chain
.117
4.2
Two Markov chain simulation algorithms
.118
4.2.1
Gibbs sampling on product spaces
.118
4.2.2
The Metropolis-Hastings algorithm
.120
4.3
Simulating a Markov random field on a network
.
1
24
4.3.1
The two standard algorithms
.124
Contents xj
43.2
Examples
.
1
25
4.3.3
Constrained simulation
.128
4.3.4
Simulating Markov chain dynamics
.129
4.4
Simulation of a point process
.129
4.4.
1 Simulation conditional on a fixed number of points
.130
4.4.2
Unconditional simulation
.130
4.4.3
Simulation of a Cox point process
.131
4.5
Performance and convergence of MCMC methods
.
1
32
4.5.1
Performance of MCMC methods
.132
4.5.2
Two methods for quantifying rates of convergence
.133
4.6
Exact simulation using coupling from the past
.
I
36
4.6.1
The Propp-Wilson algorithm
.136
4.6.2
Two improvements to the algorithm
.138
4.7
Simulating Gaussian random fields on
5
C ť'
.140
4.7.
1 Simulating stationary Gaussian random fields
.140
4.7.2
Conditional Gaussian simulation
.144
Exercises
.144
5
Statistics for spatial models
.149
5.1
Estimation in geostatistics
.
1
50
5.1.1
Analyzing the variogram cloud
.150
5.1.2
Empirically estimating the variogram
.151
5.1.3
Parametric estimation for variogram models
.
1
54
5.1.4
Estimating variograms when there is a trend
.156
5.
1
.5
Validating variogram models
.158
5.2
Autocorrelation on spatial networks
.165
5.2.1
Moran's index
.166
5.2.2
Asymptotic test of spatial independence
.167
5.2.3
Geary "s index
.169
5.2.4
Permutation test for spatial independence
.170
5.3
Statistics for second-order random fields
.173
5.3.
1 Estimating stationary models on Z''
.
1
73
5.3.2
Estimating
autoregressive
models
.177
5.3.3
Maximum likelihood estimation
.178
5.3.4
Spatial regression estimation
.179
5.4
Markov random field estimation
.188
5.4.
1 Maximum likelihood
.
1
89
5.4.2
Besag's conditional pseudo-likelihood
.191
5.4.3
The coding method
.198
5.4 4
Comparing asymptotic variance of estimators
.201
5.4.5
Identification of the neighborhood structure of a Markov
random field
.203
x¡¡
Contents
5.5
Statistics for spatial point processes
.207
5.5.1
Testing spatial homogeneity using quadrat counts
.207
5.5.2
Estimating point process intensity
.208
5.5.3
Estimation of second-order characteristics
.210
5.5.4
Estimation of a parametric model for a point process
.218
5.5.5
Conditional pseudo-likelihood of a point process
.219
5.5.6
Monte Carlo approximation of Gibbs likelihood
.223
5.5.7
Point process residuals
.226
5.6
Hierarchical spatial models and Bayesian statistics
.230
5.6.1
Spatial regression and Bayesian kriging
.231
5.6.2
Hierarchical spatial generalized linear models
.232
Exercises
.240
A Simulation of random variables
.249
A.
1
The inversion method
.249
A.
2
Simulation of a Markov chain with a finite number of states
.251
A.3 The acceptance-rejection method
.251
A.4 Simulating normal distributions
.252
В
Limit theorems for random fields
.255
B.I Ergodicity and laws of large numbers
.255
B.
1.1
Ergodicity and the ergodic theorem
.255
B.I.
2
Examples of ergodic processes
.256
B.I
.3
Ergodicity and the weak law of large numbers in L?
.257
B.I
.4
Strong law of large numbers under L2 conditions
.258
B.2 Strong mixing coefficients
.258
B.3 Central limit theorem for mixing random fields
.260
B.4 Central limit theorem for a functional of a Markov random field
. 261
С
Minimum contrast estimation
.263
C.
1
Definitions and examples
.264
C.2 Asymptotic properties
.269
C.2.
1
Convergence of the estimator
.269
C.2.2 Asymptotic normality
.271
C.3 Model selection by penalized contrast
.274
C.4 Proof of two results in Chapter
5.275
C.4.1 Variance of the maximum likelihood estimator for
Gaussian regression
.275
C.4.2 Consistency of maximum likelihood for stationary Markov
random fields
.276
D
Software
.279
References
.283
Index
.293 |
| any_adam_object | 1 |
| author | Gaetan, Carlo Guyon, Xavier |
| author2 | Bleakley, Kevin |
| author2_role | trl |
| author2_variant | k b kb |
| author_GND | (DE-588)136190561 |
| author_facet | Gaetan, Carlo Guyon, Xavier Bleakley, Kevin |
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| building | Verbundindex |
| bvnumber | BV035906002 |
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| classification_rvk | QH 250 RB 10103 RB 10104 SK 820 SK 850 |
| ctrlnum | (OCoLC)444390151 (DE-599)DNB996515860 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften Geographie |
| format | Book |
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| id | DE-604.BV035906002 |
| illustrated | Illustrated |
| indexdate | 2024-12-06T09:03:55Z |
| institution | BVB |
| isbn | 9780387922560 9781461424994 9780387922577 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018763365 |
| oclc_num | 444390151 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-20 DE-703 DE-11 DE-824 DE-739 DE-384 DE-83 DE-521 |
| owner_facet | DE-19 DE-BY-UBM DE-20 DE-703 DE-11 DE-824 DE-739 DE-384 DE-83 DE-521 |
| physical | XV, 297 S. Ill., graph. Darst., Kt. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spelling | Gaetan, Carlo Verfasser (DE-588)136190561 aut Spatial statistics and modeling Carlo Gaetan ; Xavier Guyon. Transl. by Kevin Bleakley New York, NY [u.a.] Springer 2010 XV, 297 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Hier auch später erschienene, unveränderte Nachdrucke Mathematisches Modell Spatial analysis (Statistics) Spatial analysis (Statistics) Mathematical models Statistisches Modell (DE-588)4121722-6 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 s Statistisches Modell (DE-588)4121722-6 s DE-604 Guyon, Xavier Verfasser aut Bleakley, Kevin trl Erscheint auch als Online-Ausgabe 10.1007/978-0-387-92257-7 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018763365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gaetan, Carlo Guyon, Xavier Spatial statistics and modeling Mathematisches Modell Spatial analysis (Statistics) Spatial analysis (Statistics) Mathematical models Statistisches Modell (DE-588)4121722-6 gnd Räumliche Statistik (DE-588)4386767-4 gnd |
| subject_GND | (DE-588)4121722-6 (DE-588)4386767-4 |
| title | Spatial statistics and modeling |
| title_auth | Spatial statistics and modeling |
| title_exact_search | Spatial statistics and modeling |
| title_full | Spatial statistics and modeling Carlo Gaetan ; Xavier Guyon. Transl. by Kevin Bleakley |
| title_fullStr | Spatial statistics and modeling Carlo Gaetan ; Xavier Guyon. Transl. by Kevin Bleakley |
| title_full_unstemmed | Spatial statistics and modeling Carlo Gaetan ; Xavier Guyon. Transl. by Kevin Bleakley |
| title_short | Spatial statistics and modeling |
| title_sort | spatial statistics and modeling |
| topic | Mathematisches Modell Spatial analysis (Statistics) Spatial analysis (Statistics) Mathematical models Statistisches Modell (DE-588)4121722-6 gnd Räumliche Statistik (DE-588)4386767-4 gnd |
| topic_facet | Mathematisches Modell Spatial analysis (Statistics) Spatial analysis (Statistics) Mathematical models Statistisches Modell Räumliche Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018763365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gaetancarlo spatialstatisticsandmodeling AT guyonxavier spatialstatisticsandmodeling AT bleakleykevin spatialstatisticsandmodeling |