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Irregularly Spaced Spatial Marked Point Process Data Analysis

This dataset contains water heights in Saratoga Valley, Wyoming, with irregular spacing. The model used is y(s) = v(s)β + x(s) + e(s), where v is the known regressor function and x is the stationary Gaussian signal. Stationary Gaussian white noise e is estimated using maximum likelihood estimation after approximating the autcov C(t|ϕ) step. The estimated v(s)β + x(s) is obtained through ECM. The method and program are verified using simulation. Other related works by Shumway involve the EM algorithm and dynamic mixed models for irregularly observed time series.

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Irregularly Spaced Spatial Marked Point Process Data Analysis

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  1. An example of data with irregular spacing. spatial m.p.p. Water heights, Saratoga Valley, Wyoming Yucel and Shumway (1996) Stochastic Hydrology & Hydrolics

  2. A model. Underlying surface, y(s), s location in R2 Spatial marked point process data, {sj,Mj}, Mj = y(sj) y(s) = v(s)' + x(s) + e(s), v: known regressor function x: signal, stationary Gaussian, autcov C(t|), spectrum f(|) e: stationary Gaussian white noise mle obtained via ECM after approximating C step

  3. Estimated v(s)' + x(s)

  4. Method and program checked by simulation Other Shumway work related to irregular spacing. "Some applications of the EM algorithm to analyzing incomplete time series data." Pp 290-324 in Time Series Analysis of Irregularly Observed Data, ed. E. Parzen (1984) "Dynamic mixed models for irregularly observed time series." Resenhas 4, 433-456 (2000). R. H. Shumway and D. S.Stoffer, Time Series Analysis and Its Applications, with R Examples. Springer missing values in equispaced time series state space models

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