## Spatial Statistics

*02 Sep 2014 09:39*

That is, statistics for random variables spread out in space. Includes statistical image processing, which is important but doesn't really grab me as an application.

The case where the random variables also evolve in time, the spatio-temporal case, is interesting enough to get its own notebook.

See also: Network Data Analysis Pattern Formation; Random Fields; Statistics

- Recommended, general:
- Carlo Gaetan and Xavier Guyon, Spatial Statistics and Modeling [Mini-review]
- Peter Guttorp, Stochastic Modeling of Scientific Data
- Brian D. Ripley, Statistical Inference for Spatial Processes

- Recommended, of more specialized interest:
- A. C. Davison, S. A. Padoan and M. Ribatet, "Statistical Modeling
of Spatial
Extremes", Statistical
Science
**27**(2012): 161--186 [with discussion and response] - Florence Forbes, Myriam Charras-Garrido, Lamiae Azizi, Senan Doyle, and David Abrial, "Spatial risk mapping for rare disease with hidden Markov fields and variational EM", Annals of Applied Statistics
**7**(2013): 1992--1216 - M. Ghosh and J. N. K. Rao, "Small Area Estimation: An Appraisal", Statistical Science
**9**(1994): 55--76 [Plus discussions and reply] - Karen Kafadar, "Smoothing Geographical Data, Particularly
Rates of Disease", Statistics in Medicine
**15**(1996): 2539--2560 [PDF reprint via Prof. Kafadar] - Gary King, A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data [Review]
- S. N. Lahiri, Resampling Methods for Dependent Data [Mini-review]
- Elizaveta Levina and Peter J. Bickel, "Texture synthesis and
nonparametric resampling of random
fields", Annals
of Statistics
**34**(2006): 1751--1773 - John Novembre and Matthew Stephens, "Interpreting principal
component analyses of spatial population genetic
variation", Nature
Genetics
**40**(2008): 646--649 [Many PCA patterns commonly taken to be signs of ancestral population movements can also be produced as artifacts from null models. This is distressing, since many of the results based on PCA maps are things which make sense and I'd like to be true, but Novembre and Stephens's arguments check out.] - R. Piasecki, M. T. Martin, and A. Plastino, "Inhomogeneity and complexity measures for spatial patterns," cond-mat/0107471
- Peter I. Saparin, Wolfgang Gowin, Jürgen Kurths, and Dieter
Felsenber, "Quantification of cancellous bone structure using symbolic dynamics
and measures of complexity", Physical Review
E
**58**(1998): 6449--6459 - Grace Wahba, Spline Models for Observational Data
- Michael E. Wall, Andreas Rechtsteiner and Luis M. Rocha, "Singular Value Decomposition and Principal Component Analysis," physics/0208101
- Rongjing Xiang and Jennifer Neville, "Relational Learning with One Network: An Asymptotic Analysis", AI Stats 2011 [PDF reprint]

- To read:
- Stéphanie Allassonniere, Estelle Kuhn, "Convergent Stochastic Expectation Maximization algorithm with efficient sampling in high dimension. Application to deformable template model estimation", arxiv:1207.5938
- Renato M. Assuncao and Pablo A. Ferrari, "Detection of spatial pattern through independence of thinned processes," math.PR/0103104
- Yves F. Atchade, "Estimation of Network structures from partially observed Markov random fields", arxiv:1108.2835
- Claus Beisbart, Thomas Buchert and Herbert Wagner, "Morphometry of Spatial Patterns," astro-ph/0007459
- Claus Beisbart, Martin Kerscher and Klaus Mecke, "Mark correlations: relating physical properties to spatial distributions," physics/0201069
- Claus Beisbart, Robert Dahlke, Klaus Mecke, and Herbert Wagner, "Vector- and tensor-valued descriptors for spatial patterns," physics/0203072
- A. Brezger, L. Fahrmeir, A. Hennerfeind, "Adaptive Gaussian Markov random fields with applications in human brain mapping", Journal of the Royal Statistical Society C
**56**(2007): 327--345 - E. Ceyhan, C. E. Priebe, D. J. Marchette, "A New Family of Random Graphs for Testing Spatial Segregation", Canadian Journal of Statistics
**35**(2007): 27--50, arxiv:0802.0615 - David B. Chua, Eric D. Kolaczyk, and Mark Crovella, "Network Kriging", math.ST/0510013
- Cressie, Statistics for Spatial Data
- S. Dachian, "Nonparametric estimation for Gibbs random fields
specified through one-point systems", Statistical Inference for
Stochastic Processes
**1**(1998): 245--264 - Jorn Davidsen, Peter Grassberger and Maya Paczuski, "Networks of Recurrent Events, a Theory of Records, and an Application to Finding Causal Signatures in Seismicity", physics/0701190
- Tilman M. Davies, Martin L. Hazelton, Jonathan. C Marshall, "sparr: Analyzing Spatial Relative Risk Using Fixed and Adaptive Kernel Density Estimation in R", Journal of Statistical Software
**39:1**(2011) - Mohamed El Machkouri, "Asymptotic normality of the Parzen-Rosenblatt density estimator for strongly mixing random fields", arxiv:1008.1342
- Samuel Elogne and Dionisis Hristopulos, "On the Inference of Spartan Spatial Random Field Models for Geostatistical Applications", math.ST/0603430
- Bryan K. Epperson, Geographical Genetics
- Jacob Feldman and Manish Singh, "Bayesian estimation of the shape
skeleton", Proceedings of the National
Academy of Sciences (USA)
**103**(2006): 18014--18019 [From the abstract, it sounds like this could really have been "penalized maximum likelihood estimation of the shape skeleton", since they're just doing MAP rather than any kind of averaging, or otherwise working with the posterior distribution.] - C. Fonseca, H. Ferreira, L. Pereira A.P., Martins, "Stability and contagion measures for spatial extreme value analyses", arxiv:1206.1228
- Florence Forbes and Nathalie Peyrard, "Hidden Markov Random Field
Model Selection Criteria Based on Mean Field-Like Approximations", IEEE Transactions on
Pattern Analysis and Machine Intelligence
**25**(2003): 1089--1101 [PostScript preprint] - Marie-Josie Fortin and Mark R. Dale, Spatial Analysis: A Guide for Ecologists
- Michael Friendly, "A.-M. Guerry's Moral Statistics of France: Challenges for Multivariable Spatial Analysis", Statistical Science
**22**(2007): 368--399, arxiv:0801.4263 - Anandamohan Ghosh, V. Ravi Kumar and B. D. Kulkarni, "Parameter
estimation in spatially extended systems: The Karhunen-Loeve and Galerkin
multiple shooting approach," nlin.CD/0112029 =
Physical Review E
**64**(2001): 056222 - Tilmann Gneiting, Hana Ševčíková, and Donald B. Percival, "Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data", Statistical Science
**27**(2012): 247--277 - Priscilla E. Greenwood and Wolfgang Wefelmeyer, "Characterizing
Efficient Empirical Estimators for Local Interaction Gibbs Fields",
Statistical Inference for Stochastic Processes
**2**(1999): 119--134 - Aude Grelaud, Christian Robert, Jean-Michel Marin, Francois Rodolphe, Jean-Francois Taly, "ABC likelihood-freee methods for model choice in Gibbs random fields", arxiv:0807.2767
- Xavier Guyon, Random Fields on a Network
- D. T. Hristopulos and S. N. Elogne, "Fast Spatial Prediction from Inhomogeneously Sampled Data Based on Generalized Random Fields with Gibbs Energy Functionals", physics/0609071
- John Hughes, Murali Haran, "Dimension reduction and alleviation of confounding for spatial generalized linear mixed models", Journal of the Royal Statistical Society B
**75**(2013): 139--159 - Jun-ichi Inoue and Kazuyuki Tanaka, "Dynamics of the Maximum Marginal Likelihood Hyper-parameter Estimation in Image Restoration: Gradient Descent vs. EM Algorithm," cond-mat/0107023
- Mark S. Kaiser, Soumendra N. Lahiri, and Daniel J. Nordman, "Goodness of fit tests for a class of Markov random field models", Annals of Statistics
**40**(2012): 104--130, arxiv:1205.6086 - Wolfgang Karcher, Elena Shmileva, Evgeny Spodarev, "Extrapolation of stable random fields", arxiv:1107.1654
- Nhu D. Le and James V. Zidek, Statistical Analysis of Environmental Space-Time Processes
- U. K. Lee, H. Choi, B. U. Park and K. S. Yu, "Local likelihood
density estimation on random fields", Statistics and
Probability Letters
**68**(2004): 347--357 - Loic Le Gratiet and Claire Cannamela, "Kriging-based sequential design strategies using fast cross-validation techniques with extensions to multi-fidelity computer codes", arxiv:1210.6187
- Pei-Sheng Lin and Murray K. Clayton, "Analysis of binary spatial
data by quasi-likelihood estimating equations", math.ST/0505602 = Annals of
Statistics
**33**(2005): 542--555 - Zudi Lu and Xing Chen, "Spatial kernel regression estimation: weak
consistency", Statistics and
Probability Letters
**68**(2004): 125--136 - Jorge Mateu and Francisco Montes, "Pseudo-likelihood Inference for
Gibbs Processes with Exponential Families through Generalized Linear
Models", Statistical Inference for Stochastic
Processes
**4**(2001): 125--154 - Klaus R. Mecke and D. Stoyan (eds.)
- Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation
- Morphology of Condensed Matter: Physics and Geometry of Spatially Complex Systems

- Werner G. Muller, Collecting Spatial Data: Optimum Design of Experiments for Random Fields
- Enza Orlandi, Eva Loecherbach, "On the neighborhood radius estimation in Variable-neighborhood Markov Random Fields", arxiv:1002.4850
- Marcelo Pereyra, Nicolas Dobigeon, Hadj Batatia, Jean-Yves Tourneret, "Computing the Cramer-Rao bound of Markov random field parameters: Application to the Ising and the Potts models", arxiv:1206.3985
- Xin Qi and Hongyu Zhao, "Asymptotic efficiency and finite-sample properties of the generalized profiling estimation of parameters in ordinary differential equations", Annals of Statistics
**38**(2010): 435--481 - Laura M. Sangalli, James O. Ramsay, Timothy O. Ramsay, "Spatial spline regression models", Journal of the Royal Statistical Society B
**75**(2013): 681--703 - Peter St. Jean, Pockets of Crime: Broken Windows, Collective Efficacy, and the Criminal Point of View [blurb]
- Jeffrey E. Steif, "Consistent estimation of joint distributions for sufficiently mixing random fields", Annals of
Statistics
**25**(1997): 293--304 [Extension of the Marton-Shields result to random fields in higher dimensions] - Michael L. Stein, "When does the screening effect hold?",
Annals of Statistics
**39**(2011): 2795--2819 - Ne-Zheng Sun, "Structure reduction and robust experimental design
for distributed parameter identification", Inverse
Problems
**21**(2005): 739--758 - Youngchul Sung, Lang Tong and H. Vincent Poor, "A Large Deviations Apoproach to Sensor Scheduling for Detection of Correlated Random Fields", cs.IT/0501056
- Lionel Truquet, "On a nonparametric resampling scheme for Markov random fields", Electronic Journal of Statistics
**5**(2011): 1503--1536 - Nicolas Verzelen, "Adaptive estimation of stationary
Gaussian fields", Annals of Statistics
**38**(2010): 1363--1402 - Melanie W. Wall, "A close look at the spatial structure implied by
the CAR and SAR models", Journal of
Statistical Planning and Inference
**121**(2004): 311-324 - Gerhard Winkler, Image Analysis, Random Fields, and Markov Chain Monte Carlo: A Mathematical Introduction
- Xiaoxi Zhang, Timothy D. Johnson, Roderick J. A. Little, Yue Cao,
"Quantitative magnetic resonance image analysis via the EM algorithm with
stochastic variation", Annals of Applied
Statistics
**2**(2008): 736--755, arxiv:0807.4672 [More of interest to me for the getting at uncertainty in estimation of hidden Markov random fields]