There are three distinctive subjects in spatial statistics: geostatistics, lattice data analysis, and spatial point pattern analysis. Because of the resemblance between the spatial distribution of observations in coordinates and the notion of spatially random points, spatial statistics in astronomy has leaned more toward the spatial point pattern analysis than the other subjects. In other fields from immunology to forestry to geology whose data are associated spatial coordinates of underlying geometric structures or whose data were sampled from lattices, observations depend on these spatial structures and scientists enjoy various applications from geostatistics and lattice data analysis. Particularly, kriging is the fundamental notion in geostatistics whose application is found many fields.

Hitherto, I expected that the term kriging can be found rather frequently in analyzing cosmic micro-wave background (CMB) data or large extended sources, wide enough to assign some statistical models for understanding the expected geometric structure and its uncertainty (or interpolating observations via BLUP, best linear unbiased prediction). Against my anticipation, only one referred paper from ADS emerged:

Topography of the Galactic disk – Z-structure and large-scale star formation
by Alfaro, E. J., Cabrera-Cano, J., and Delgado (1991)
in ApJ, 378, pp. 106-118

I attribute this shortage of applying kriging in astronomy to missing data and differential exposure time across the sky. Both require underlying modeling to fill the gap or to convolve with observed data to compensate this unequal sky coverage. Traditionally the kriging analysis is only applied to localized geological areas where missing and unequal coverage is no concern. As many survey and probing missions describe the wide sky coverage, we always see some gaps and selection biases in telescope pointing directions. So, once this characteristics of missing is understood and incorporated into models of spatial statistics, I believe statistical methods for spatial data could reveal more information of our Galaxy and universe.

A good news for astronomers is that nowadays more statisticians and geo-scientists working on spatial data, particularly from satellites. These data are not much different compared to traditional astronomical data except the direction to which a satellite aims (inward or outward). Therefore, data of these scientists has typical properties of astronomical data: missing, unequal sky coverage or exposure and sparse but gigantic images. Due to the increment of computational power and the developments in hierarchical modeling, techniques in geostatistics are being developed to handle these massive, but sparse images for statistical inference. Not only denoising images but they also aim to produce a measure of uncertainty associated with complex spatial data.

For those who are interested in what spatial statistics does, there are a few books I’d like to recommend.

• Cressie, N (1993) Statistics for spatial data
  (the bible of statistical statistics)
• Stein, M.L. (2002) Interpolation of Spatial Data: Some Theory for Kriging
  (it’s about Kriging and written by one of scholarly pinnacles in spatial statistics)
• Banerjee, Carlin, and Gelfand (2004) Hierarchical Modeling and Analysis for Spatial Data
  (Bayesian hierarchical modeling is explained. Very pragmatic but could give an impression that it’s somewhat limited for applications in astronomy)
• Illian et al (2008) Statistical Analysis and Modelling of Spatial Point Patterns
  (Well, I still think spatial point pattern analysis is more dominant in astronomy than geostatistics. So… I feel obliged to throw a book for that. If so, I must mention Peter Diggle’s books too.)
• Diggle (2004) Statistical Analysis of Spatial Point Patterns
  Diggle and Ribeiro (2007) Model-based Geostatistics
  

• [astro-ph:0804.1809] H. Khiabanian, I.P. Dell’Antonio
  A Multi-Resolution Weak Lensing Mass Reconstruction Method (Maximum likelihood approach; my naive eyes sensed a certain degree of relationship to the GREAT08 CHALLENGE)

• [astro-ph:0804.1909] A. Leccardi and S. Molendi
  Radial temperature profiles for a large sample of galaxy clusters observed with XMM-Newton

• [astro-ph:0804.1964] C. Young & P. Gallagher
  Multiscale Edge Detection in the Corona

• [astro-ph:0804.2387] C. Destri, H. J. de Vega, N. G. Sanchez
  The CMB Quadrupole depression produced by early fast-roll inflation: MCMC analysis of WMAP and SDSS data

• [astro-ph:0804.2437] P. Bielewicz, A. Riazuelo
  The study of topology of the universe using multipole vectors

• [astro-ph:0804.2494] S. Bhattacharya, A. Kosowsky
  Systematic Errors in Sunyaev-Zeldovich Surveys of Galaxy Cluster Velocities

• [astro-ph:0804.2631] M. J. Mortonson, W. Hu
  Reionization constraints from five-year WMAP data

• [astro-ph:0804.2645] R. Stompor et al.
  Maximum Likelihood algorithm for parametric component separation in CMB experiments (separate section for calibration errors)

• [astro-ph:0804.2671] Peeples, Pogge, and Stanek
  Outliers from the Mass–Metallicity Relation I: A Sample of Metal-Rich Dwarf Galaxies from SDSS

• [astro-ph:0804.2716] H. Moradi, P.S. Cally
  Time-Distance Modelling In A Simulated Sunspot Atmosphere (discusses systematic uncertainty)

• [astro-ph:0804.2761] S. Iguchi, T. Okuda
  The FFX Correlator

• [astro-ph:0804.2742] M Bazarghan
  Automated Classification of ELODIE Stellar Spectral Library Using Probabilistic Artificial Neural Networks

• [astro-ph:0804.2827]S.H. Suyu et al.
  Dissecting the Gravitational Lens B1608+656: Lens Potential Reconstruction (Bayesian)

With the 5th year WMAP data release, there were many WMAP related papers and among them, most statistical papers are listed. WMAP specific/related:

• [astro-ph:0803.0586] J. Dunkley et. al.
    Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data (likelihoods)

• [astro-ph:0803.0715] B. Gold et. al.
    Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Foreground Emission (MCMC)

• [astro-ph:0803.0889] Ichikawa, Sekiguchi, & Takahashi
    Probing the Effective Number of Neutrino Species with Cosmic Microwave Background

And others:

• [astro-ph:0802.4464] M. Sahlén et.al.
    The XMM Cluster Survey: Forecasting cosmological and cluster scaling-relation parameter constraints

• [astro-ph:0803.0918] J.M. Colberg et.al.
    The Aspen–Amsterdam Void Finder Comparison Project (TFE, tessellation field estimator)

• [astro-ph:0803.0885] J.Ballot et.al.
    On deriving p-mode parameters for inclined solar-like stars (MLE, maximum likelihood estimator)

By the way, I noticed [astro-ph:0802.4464] used Monte Carlo Markov Chain, whereas [astro-ph:0803.0715] used Markov chain Monte Carlo. Do they mean different? Or the former is a typo?

To find the paper or other interesting ones, click

• [astro-ph:0801.0638]
  AIC, BIC, Bayesian evidence and a notion on simplicity of cosmological model M Szydlowski & A. Kurek

• [astro-ph:0801.0642]
  Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications S. Ho et.al.

• [astro-ph:0801.0780]
  The Distance of GRB is Independent from the Redshift F. Song

• [astro-ph:0801.1081]
  A robust statistical estimation of the basic parameters of single stellar populations. I. Method X. Hernandez and D. Valls–Gabaud

• [astro-ph:0801.1106]
  A Catalog of Local E+A(post-starburst) Galaxies selected from the Sloan Digital Sky Survey Data Release 5 T. Goto (Carefully built catalogs are wonderful sources for classification/supervised learning, or semi-supervised learning)

• [astro-ph:0801.1358]
  A test of the Poincare dodecahedral space topology hypothesis with the WMAP CMB data B.S. Lew & B.F. Roukema

In cosmology, a few candidate models to be chosen, are generally nested. A larger model usually is with extra terms than smaller ones. How to define the penalty for the extra terms will lead to a different choice of model selection criteria. However, astronomy papers in general never discuss the consistency or statistical optimality of these selection criteria; most likely Monte Carlo simulations and extensive comparison across those criteria. Nonetheless, my personal thought is that the field of model selection should be encouraged to astronomers to prevent fallacies of blindly fitting models which might be irrelevant to the information that the data set contains. Physics tells a correct model but data do the same.

• [astro-ph:0712.1038]
  Extended Anomalous Foreground Emission in the WMAP 3-Year Data G. Dobler and D. P. Finkbeiner

• [astro-ph:0712.1217]
  Generalized statistical models of voids and hierarchical structure in cosmology A. Z. Mekjian

• [astro-ph:0712.1155]
  The colour-lightcurve shape relation of Type Ia supernovae and the reddening law S. Nobili and A. Goobar

• [astro-ph:0712.1297]
  The Structure of the Local Supercluster of Galaxies Revealed by the Three-Dimensional Voronoi’s Tessellation Method O. V. Melnyk, A. A. Elyiv, and I. B. Vavilova

• [astro-ph:0712.1594]
  Photometric Redshifts with Surface Brightness Priors H. F. Stabenau, A. Connolly and B. Jain

• [stat.ME:0712.1663]
  Efficient Blind Search: Optimal Power of Detection under Computational Cost Constraints N. Meinshausen, P. Bickel and J. Rice

• [astro-ph:0712.1917]
  Are solar cycles predictable? M. Schuessler

Voronoi Tessellation for nonparametric density estimation (mass distribution in the universe) interest me very much. If you are working on the topic, would you kindly share useful informations or write your thoughts on the subject here?

• [astro-ph:0711.1353]
  How to use the SEDs produced by synthesis models (inside and outside the VO)? by M. Cervino and V. luridiana
• [astro-ph:0711.1355]
  Synthesis models in a probabilistic framework: metrics of fitting by M. Cervino and V. luridiana
• [astro-ph:0711.1633]
  Post Main Sequence Orbital Circularization of Binary Stars in the Large and Small Magellanic Clouds by L. Faccioli
• [astro-ph:0711.1860]
  Cosmic Covariance and the Low Quadrupole Anisotropy of the Wilkinson Microwave Anisotropy Probe (WMAP) Data by L. Chiang, P. D. Naselsky and P. Coles
• [astro-ph:0711.2068]
  Type Ia Supernovae are Good Standard Candles in the Near Infrared: Evidence from PAIRITEL by W. M. Wood-Vasey
• [astro-ph:0711.2147]
  A Deconvolution technique for VHE Gamma-ray Astronomy, and its application to the morphological study of shell-type supernova remnants by G. Maurin, A. Djannati-Atai, and P. Espigat
• [astro-ph:0711.2163]
  Predicting spectral features in galaxy spectra from broad-band photometry by F. B. Abdalla, et.al.
• [astro-ph:0711.2222]
  X-ray afterglow light curves : toward standard candle ? by B. Gendre et.al.
• [astro-ph:0711.2234]
  Consequences of statistical sense determination for WIMP directional detection by A, M. Green and B. Morgan
• [astro-ph:0711.2477]
  Photometric Redshift Estimation on SDSS Data Using Random Forests S. Carliles et. al.
• [astro-ph:0711.2480]
  Alignments of Voids in the Cosmic Web E. Platen, R. van de Weygaert and B. J.T. Jones