Spatial Statistics and Spatial Stochastic Processes

30 Jul 2008 10:14

That is, statistics for random variables spread out in space, and possibly evolving in time --- the spatiotemporal case is the one which really interests me. Includes statistical image processing, which is important but doesn't really grab me as an application.

J.-R. Chazottes, P. Collet, C. Kuelske and F. Redig, "Deviation inequalities via coupling for stochastic processes and random fields", math.PR/0503483
David Griffeath, "Introduction to Markov Random Fields", ch. 12 in Kemeny, Knapp and Snell, Denumerable Markov Chains [One of the proofs of the equivalence between the Markov property and having a Gibbs distribution, conventionally but misleadingly called the Hammersley-Clifford Theorem. Pollard, below, provides an on-line summary.]
Peter Guttorp, Stochastic Modeling of Scientific Data
Xavier Guyon, Random Fields on a Network
Gary King, A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data [Review]
Ulrich Parlitz and Christian Merkwirth, "Prediction of Spatiotemporal Time Series Based on Reconstructed Local States," Physical Review Letters 84 (2000): 1890--1893
David Pollard, "Markov random fields and Gibbs distributions" [Online PDF. A proof of the theorem linking Markov random fields to Gibbs distributions, following the approach of David Griffeath.]
Brian D. Ripley, Statistical Inference for Spatial Processes
Rinaldo B. Schinazi, Classical and Spatial Stochastic Processes
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

Jian Liu, Zhen-Su She, Hongyu Guo, Liang Li and Qi Ouyang, "Hierarchical structure description of spatiotemporal chaos", Physical Review E 70 (2004): 036215 = nlin.PS/0408024
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
Gyorgy Szabo, Hajnalka Gergely, and Beata Oborny, "Generalized contact process on random environments," cond-mat/0202461
Scott M. Zoldi and Henry S. Greenside, "Karhunen-Loève Decomposition of Extensive Chaos," chao-dyn/9610007 ["to appear in PRL" --- presumably has by now]
Scott M. Zoldi, Jun Liu, Kapil M. S. Bajaj, Henry S. Greenside and Guenter Ahlers, "Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State," chao-dyn/9808006

CRS, "Optimal Nonlinear Prediction of Random Fields on Networks," Discrete Mathematics and Theoretical Computer Science vol. "AB(DMCS)" (2003), pp. 11--30 = math.PR/0305160

Markus Abel, "Nonparametric modeling and spatiotemporal dynamical systems," nlin.PS/0202058
Jan Ambjorn et al., Quantum Geometry: A Statistical Field Theory Approach [Blurb. I am interested in the stuff about random surfaces.]
Alexei Andreanov, Giulio Biroli, Jean-Philippe Bouchaud, and Alexandre Lefèvre, "Field theories and exact stochastic equations for interacting particle systems", Physical Review E 74 (2006): 030101 = cond-mat/0602307
Alberto Alvarez, Cristobal Lopez, Margalida Riera, Emilio Hernandez-Garcia and Joaquin Tintore, "Forecasting the SST space-time variability of the Alboran Sea with genetic algorithms," chao-dyn/9911012 = Geophysical Research Letters 27 (2000): 739--742
Renato M. Assuncao and Pablo A. Ferrari, "Detection of spatial pattern through independence of thinned processes," math.PR/0103104
Sergei A. Avdonin and Sergei A. Ivanov, Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems
K. Bahlali, M. Eddahbi and M. Mellouk, "Stability and genericity for SPDEs driven by spatially correlated noise", math.PR/0610174
Raluca M. Balan, "A strong invariance principle for associated random fields", Annals of Probability 33 (2005): 823--840 = math.OR/0503661
M. S. Bartlett, "Physical Nearest-Neighbour Models and Non-Linear Time Series", Journal of Applied Probability 8 (1971): 222--232 [JSTOR]
Michel Bauer, Denis Bernard, "2D growth processes: SLE and Loewner chains", math-ph/0602049
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
Alexander Bulinski and Alexey Shashkin, "Strong invariance principle for dependent random fields", math.PR/0608237
Ruslan K. Chornei, Hans Daduna, and Pavel S. Knopov
- "Controlled Markov Fields with Finite State Space on Graphs", Stochastic Models 21 (2005): 847--874 [PS.gz preprint]
- Control of Spatially Structured Random Processes and Random Fields with Applications [Blurb]
David B. Chua, Eric D. Kolaczyk, and Mark Crovella, "Network Kriging", math.ST/0510013
Piero Cipriani and Antonio Politi, "An open-system approach for the characterization of spatio-temporal chaos," nlin.CD/0301003
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
Giuseppe Da Prato, Arnaud Debussche and Luciano Tubaro, "Coupling for some partial differential equations driven by white noise", math.AP/0410441
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
S. De Iaco, M. Palma and D. Posa, "Modeling and prediction of multivariate space-time random fields", Computational Statistics and Data Analysis 48 (2004): 525--547
Jean-Dominique Deuschel and Andreas Greven (eds.), Interacting Stochastic Systems [This looks deeply cool]
Rick Durrett, Stochastic Spatial Models: A Hyper-Tutorial
Vlad Elgart and Alex Kamenev, "Rare Events Statistics in Reaction--Diffusion Systems", cond-mat/0404241 [i.e., large deviations]
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 [Open access. 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 some kind of averaging.]
P. A. Ferrari and L. R. G. Fontes, "Fluctuations of a Surface Submitted to a Random Average Process," Electronic Journal of Probability 3 (1998): 6 [HTML]
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
Gerson Francisco and Paulsamy Muruganandam, "Local dimension and finite time prediction in spatiotemporal chaotic systems," nlin.CD/0212015
L. Garcia-Ojalvo and J. Sancho, Noise in Spatially Extended Systems
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
Roman O. Grigoriev, Sanjay G. Lall and Geir E. Dullerud, "Localized Optimal Control of Spatiotemporal Chaos," chao-dyn/9710013
Henry S. Greenside, "Spatiotemporal Chaos in Large Systems: The Scaling of Complexity with Size," chao-dyn/9612004
Priscilla E. Greenwood and Wolfgang Wefelmeyer, "Characterizing Efficient Empirical Estimators for Local Interaction Gibbs Fields", Statistical Inference for Stochastic Processes 2 (1999): 119--134
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
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
Niels Jacob and Alexander Potrykus, "Some thoughts on multiparameter stochastic processes", math.PR/0607744
Mark Kaiser, "Statistical Dependence in Markov Random Field Models" [abstract, preprint]
M. Kerscher, "Constructing, characterizing, and simulating Gaussian and higher-order point distributions," astro-ph/0102153
Ross Kindermann and J. Laurie Snell, Markov Random Fields and Their Applications [Free online!]
P. Kotelenez, Stochastic Space-Time Models and Limit Theorems
Nhu D. Le and James V. Zidek, Statistical Analysis of Environmental Space-Time Processes [Blurb]
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
Jean-Francois Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations
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
Cristobal Lopez and Emilio Hernandez-Garcia, "Low-dimensional dynamical system model for observed coherent structures in ocean satellite data," nlin.CD/0009039
Cristobal Lopez, Alberto Alvarez and Emilio Hernandez-Garcia, "Forecasting confined spatiotemporal chaos with genetic algorithms," nlin.CD/0003060 = Physical Review Letters 85 (2000): 2300--2303
Zudi Lu and Xing Chen, "Spatial kernel regression estimation: weak consistency", Statistics and Probability Letters 68 (2004): 125--136
Andrew J. Majda and Marcus J. Grote, "Explicit off-line criteria for stable accurate time filtering of strongly unstable spatially extended systems", Proceedings of the National Academy of Sciences (USA) 104 (2007): 1124--1129
S. Mandelj, I. Grabec, E. Govekar, "Statistical approach to modeling of spatiotemporal dynamics," International Journal of Bifurcations and Chaos 11 (2001): 2731--2738
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
Jonathan C. Mattingly, "On Recent Progress for the Stochastic Navier Stokes Equations", math.PR/0409194 ["We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations."]
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
T. J. Muller and J. Timmer, "Fitting parameters in partial differential equations from partially observed noisy data," Physica D 171 (2002): 1--7
Werner G. Muller, Collecting Spatial Data: Optimum Design of Experiments for Random Fields
Girish Nathan and Gemunu Gunaratne, "Set of measures to analyze the dynamics of nonequilibrium structures", Physical Review E 71 (2005): 035101(R)
A. I. Olemskoi, D. O. Kahrchenko and I. A. Knyaz', "Phase transitions induced by noise cross-correlations", cond-mat/0403583
Edward Ott, Brian R. Hunt, Istvan Szunyogh, Matteo Corazza, Eugenia Kalnay, D. J. Patil, and James A. Yorke, "Exploiting Local Low Dimensionality of the Atmospheric Dynamics for Efficient Ensemble Kalman Filtering," physics/0203058
E. Ott, B. R. Hunt, I. Szunyogh, A. V. Zimin, E. J. Kostelich, M. Corazza, E. Kalnay, D.J. Patil and J.A. Yorke, "Estimating the state of large spatio-temporally chaotic systems", Physics Letters A 330 (2004): 365--370
Rupert Paget, "Strong Markov Random Field Model", IEEE Transactions on Pattern Analysis and Machine Intelligence 26 (2004): 408--413
Nita Parekh, V. Ravi Kumar and B. D. Kulkarni, "Synchronization and Control of Spatiotemporal Chaos using Time-Series Data from Local Regions," chao-dyn/9711002
Liang Qiao, Radek Erban, C. T. Kelley and Ioannis G. Kevrekidis, "Spatially Distributed Stochastic Systems: equation-free and equation-assisted preconditioned computation", q-bio.QM/0606006
Havard Rue and Leonhard Held, Gaussian Markov Random Fields: Theory and Applications
Peter St. Jean, Pockets of Crime: Broken Windows, Collective Efficacy, and the Criminal Point of View [blurb]
A. Sitz, J. Kurths, and H. U. Voss, "Identification of nonlinear spatiotemporal systems via partitioned filtering", Physical Review E 68 (2003): 016202
M. L. Stein, "Space-Time Covariance Functions", Technical Report No. 4, University of Chicago Center for Integrating Statistical and Environmental Sciences (May 2003) [PDF]
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
Martin Treiber and Dirk Helbing, "An adaptive smoothing method for traffic state identification from incomplete information," cond-mat/0210050
M. N. M. van Lieshout, "Markovianity in space and time", math.PR/0608242
H. Voss, M. J. Bünner and M. Abel, "The Identification of Continuous, Spatiotemporal Systems," Physical Review E 57 (1998): 2820
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
X. Xia and H. Leung, "Nonlinear Spatial-Temporal Prediction Based on Optimal Fusion", IEEE Transactions on Neural Networks 17 (2006): 975--988
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