A PRACTICAL APPROACH TO SPATIO-TEMPORAL ANALYSIS

This paper introduces a spatio-temporal statistical analysis approach ap- propriate for monitoring or managing a physical system in which measurements are taken over dense time resolution but at sparse locations. The proposed approach is designed for implementation in an automated and ecient operation with manual intervention required only for scenario analysis. The method is based on a mod- eling framework for complex predictor-response and spatio-temporal relationships, and issues model-based prediction intervals. To accommodate varying practical situations, the method also includes an automated decision criterion for choosing between parametric and nonparametric spatial covariance models. The approach is illustrated using a data center thermal management problem.

[1]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[2]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[3]  Breda Munoz,et al.  Design‐based empirical orthogonal function model for environmental monitoring data analysis , 2008 .

[4]  M. Stein.  Space–Time Covariance Functions , 2005 .

[5]  Alexandra M. Schmidt,et al.  Spatially Varying Autoregressive Processes , 2011, Technometrics.

[6]  T. Gneiting.  Nonseparable, Stationary Covariance Functions for Space–Time Data , 2002 .

[7]  F. J. Alonso,et al.  The Kriged Kalman filter , 1998 .

[8]  Mark F. J. Steel,et al.  A general class of nonseparable space–time covariance models , 2011 .

[9]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[10]  J. Andrew Royle,et al.  Multiresolution models for nonstationary spatial covariance functions , 2002 .

[11]  P. Guttorp,et al.  Nonparametric Estimation of Nonstationary Spatial Covariance Structure , 1992 .

[12]  P. Guttorp,et al.  Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry , 2007 .

[13]  David Higdon,et al.  Non-Stationary Spatial Modeling , 2022, 2212.08043.

[14]  P. Diggle,et al.  A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure , 2010 .

[15]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[16]  Madhusudan K. Iyengar,et al.  Uncovering energy-efficiency opportunities in data centers , 2009, IBM J. Res. Dev..

[17]  Roger Woodard,et al.  Interpolation of Spatial Data: Some Theory for Kriging , 1999, Technometrics.

[18]  Mikyoung Jun,et al.  Nonstationary covariance models for global data , 2008, 0901.3980.

[19]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[20]  Tilmann Gneiting,et al.  Space–Time Covariance Models , 2013 .

[21]  C. Obled,et al.  Some developments in the use of empirical orthogonal functions for mapping meteorological fields , 1986 .