RIT on Spatial Statistics

Mon. 3:30-4:30pm,  Rm  MTH 0104                                                Fall 2017
 

Eric Slud        Paul Smith        Statistics Program , Math Department

         Interested participants should send email to        evs@math.umd.edu      or      pjs@math.umd.edu

Reading list

Schedule of Talks

Research Focus: This semester's Statistics RIT will be on the topic of Statistical Inference for Spatial Statistical Models. This concerns analysis of datasets distributed in space (the surface of the earth, in R2, as in geostatistics or spatial econometrics, or in R2 in environmetrics -- concerning monitoring of the atmosphere by earth-bound or aerial or remote-sensing data -- or many other kinds of data collected in the form of subsequences of realized values of random fields. Related topics include:

  • descriptive statistics for spatial variation expressed in terms of maps (heat maps, contour maps, etc.) and the variogram;
  • extensions of spectral (Fourier transformed) properties of time series to the random-field or spatial case;
  • models for occurrences of spatially distributed point events (such as disease occurrence via point processes;
  • models for continuous spatial variation in terms of spatial autoregressive, conditional autoregressive and other parametric descriptions;
  • spatial extensions of concepts of stationarity, ergodicity, mixing and likelihood to enable asymptotic descriptions of spatial data in terms of either increasing-window or infill asymptotics;
  • Bayesian hierarchical descriptions of spatially distributed data;

    • plus many other topics. We will study chapters from a Handbook or textbook and journal papers from a few of these areas, focusing on areas of interest to the RIT attendees.

    Graduate Prerequisites: To benefit from this research activity, a graduate student should have completed Stat 700-701 and Stat 600.

    Graduate Program: Graduate students will be involved in reading and presenting book-chapters and papers from the statistical literature concerning provable all aspects of Spatial Statistics.

    Work Schedule: We will meet weekly in the fall of 2017, Mondays at 3:30-4:30 pm. The basic textbook background material for this RIT will be taken from will be drawn from

    Ribeiro, P. and Diggle, P., Model Based Geostatistics (2007) (on line at    https://link.springer.com/book/10.1007%2F978-0-387-48536-2 ) and

    Gaetan, C. and Guyon, X. (2010), Spatial Statistics and Modeling (on line at    https://link.springer.com/book/10.1007%2F978-0-387-92257-7 )

    Material for talks can also be drawn from

    Handbook of Spatial Statistics (2010), eds. A. Gelfand, P. Diggle, M. Fuentes, and P. Guttorp, CRC / Chapman & Hall.

    and as an older supplementary reference,

    N. Cressie (2015), Statistics for Spatial Data, revised edition, Wiley.

    Reading List

    The Handbook cited above has useful chapters on "Classical Geiostatistical Methods" (by D. Zimmermann and M. Stein), on "Likelihood-based Methods" (by D. Zimmermann), on "Spectral Domain" (by M. Fuentes), on "Asymptotics for Spatial Processes" (by M. Stein), on "Hierarchical Modeling with Spatial Data" (by C. Wikle), on "Non-Gaussian and Nonparametric Models for Continuous Spatial Data" (by M. Steel and M. Fuentes), on "Discrete Spatial Variation" (by H. Rue and L. Held), on "Conditional and Intrinsic Autoregressions" (by L. Held and H. Rue), on "Disease Mapping" (by L. Waller and B. Carlin) and on "Spatial Econometrics" (by R. Pace and J. LeSage).

    Papers        (with more still to be added)

    Besag, J. and Kooperberg, C. (1995), On conditional and inrinsic autoregressions, Biometrika 82, 733-746.

    Bradley, R.C. and Tone, C. (2015), A central limit theorem for non-stationary strong mixing random fields. Journal of Theoretical Probability.

    Cressie, N. and Lahiri, S. (1996), Asymptotics for REML estimation of spatial covariance parameters, Jour.~Statist.~Planning \& Inference 50, 327-341.

    Kaiser, M.S., Lahiri, S.N. and Nordman, D. (2012). A goodness of fit test for conditionally specified spatial models and its asymptotic properties. Annals of Statistics 40 104-130.

    Katzfuss, M., Stroud, J. and Wikle, C. (2016) Understanding the ensemble Kalman filter, American Statistician 70, 350-357.

    Kent, J. and Mardia, K. (1996), Spectral and circulant approximations to the likelihood for stationary Gaussian random fields, Jour.~Statist.~Planning & Inference 50, 379-394.

    Lahiri, S.N. (1996). Asymptotic expansions for sums of random vectors under polynomial mixing rates. Sankhya, Series A 58, 206 - 224.

    Lahiri, S.N. (1996). On inconsistency of estimators under infill asymptotics for spatial data. Sankhya, Series A 58, 403-417.

    Lahiri, S.N. (2003). Central Limit Theorems for weighted sums under some stochastic and fixed spatial sampling designs. Sankhya, Ser. A 65, 356-388.

    Mardia, K. and Marshall, R. (1984), Maximum likelihood estimation of models for residual covariance in spatial statistics, Biometrika 71, 135-146.

    Zhang, H. and Zimmermann, D. (2005), Towards reconciling two asymptotic frameworks in spatial statistics, Biometrika 92, 921-936.

    Schedule of Talks ---

  • September 18, 2017:    Organizational meeting and Introduction of the Spatial Statistics topic by Paul Smith.

  • September 25, 2017:    Eric Slud, Introduction to random fields and some background for large-sample theory and asymptotics.

  • October 2, 2017:    Benjamin Kedem, Spatial Interpolation by a Bayesian Method.

  • October 9, 2017:    Paul Smith, Descriptive Analysis of Geostatistical Data.

  • October 16, 2017:    Mark Wymer, Gaussian models for geostatistical data (Chapter 3 from Diggle and Ribeiro).

  • October 23, 2017:    Ying Han, Follow-on with Gaussia Models and Later Material from Diggle and Ribeiro.

  • October 30, 2017:    Cheng Wang, Spatial Data Visualization in R.

  • November 6, 2017:    Hatice Sahinoglu, Prediction in Spatial Data (Ch.6 of Diggle & Ribeiro).

  • November 13, 2017:    Yiming Lyu, Generalized Linear Geostatistical Models (Ch.4 of Diggle and Ribeiro)

  • November 20, 2017:    Guowei Sun, Overview of Byesian Optimization., `stochastic kriging' in `metamodels' with
    reference to 3 papers: a tutorial on Bayesian optimization, one on computer experiments, and one on efficient global optimization.

  • November 27, 2017:    Lu Yu Sun, Ensemble Kalman Filter for Spatio-Temporal Data, with reference to a tutorial paper and to an
    additional paper on Non-Gaussian Data Assimilation.


    • © Last updated Nov. 29, 2017.