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Estimation of Moran’s I in the Context of Uncertain Mobile Sensor Measurements

Authors Dominik Bucher , Henry Martin, David Jonietz, Martin Raubal , René Westerholt

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Author Details

Dominik Bucher
  • Institute of Cartography and Geoinformation, ETH Zurich, Switzerland
Henry Martin
  • Institute of Cartography and Geoinformation, ETH Zurich, Switzerland
David Jonietz
  • HERE Technologies Switzerland, Zurich, Switzerland
Martin Raubal
  • Institute of Cartography and Geoinformation, ETH Zurich, Switzerland
René Westerholt
  • School of Spatial Planning, TU Dortmund University, Germany

Funding

This research was supported by the Swiss Data Science Center (SDSC) and by the Swiss Innovation Agency Innosuisse within the Swiss Competence Center for Energy Research (SCCER) Mobility.

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Dominik Bucher, Henry Martin, David Jonietz, Martin Raubal, and René Westerholt. Estimation of Moran’s I in the Context of Uncertain Mobile Sensor Measurements. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part I. Leibniz International Proceedings in Informatics (LIPIcs), Volume 177, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.GIScience.2021.I.2

Abstract

Measures of spatial autocorrelation like Moran’s I do not take into account information about the reliability of observations. In a context of mobile sensors, however, this is an important aspect to consider. Mobile sensors record data asynchronously and capture different contexts, which leads to considerable heterogeneity. In this paper we propose two different ways to integrate the reliability of observations with Moran’s I. These proposals are tested in the light of two case studies, one based on real temperatures and movement data and the other using synthetic data. The results show that the way reliability information is incorporated into the Moran’s I estimates has a strong impact on how the measure responds to volatile available information. It is shown that absolute reliability information is much less powerful in addressing the problem of differing contexts than relative concepts that give more weight to more reliable observations, regardless of the general degree of uncertainty. The results presented are seen as an important stimulus for the discourse on spatial autocorrelation measures in the light of uncertainties.

Subject Classification

ACM Subject Classification
  • Information systems → Geographic information systems
  • Information systems → Sensor networks
  • Mathematics of computing → Statistical paradigms
  • Applied computing → Earth and atmospheric sciences
Keywords
  • mobile sensors
  • Moran’s I
  • uncertainty
  • probabilistic forecasting

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References

  1. J Aldstadt, M Widener, and N Crago. Detecting irregular clusters in big spatial data. In N. Xiao, M.-P. Kwan, M. F. Goodchild, and S. Shekhar, editors, Proceedings of the 7th International Conference on Geographic Information Science (GIScience 2012), Columbus, OH, 2012. Google Scholar
  2. Lilia Angelova, Puck Flikweert, Panagiotis Karydakis, Daniël Kersbergen, Roos Teeuwen, Kotryna Valečkaitė, Edward Verbree, Martijn Meijers, and Stefan van der Spek. Using a dynamic sensor network to obtain spatiotemporal data in an urban environment. In Peter Kiefer, Haosheng Huang, Nico Van de Weghe, and Martin Raubal, editors, Adjunct Proceedings of the 14th International Conference on Location Based Services, pages 13-18, Zürich, Switzerland, 2018. ETH Zurich. Google Scholar
  3. Luc Anselin. Local indicators of spatial association - LISA. Geographical Analysis, 27(2):93-115, 1995. Google Scholar
  4. Luc Anselin and Anil K Bera. Spatial dependence in linear regression models with an introduction to spatial econometrics. In Aman Ullah and David E. A. Giles, editors, Handbook of Applied Economic Statistics, pages 237-290. Marcel Dekker AG, New York, NY, 1998. Google Scholar
  5. Renato M Assuncao and Edna A Reis. A new proposal to adjust Moran’s I for population density. Statistics in Medicine, 18(16):2147-2162, 1999. Google Scholar
  6. Matthias Bluemke, Bernd Resch, Clemens Lechner, René Westerholt, and Jan-Philipp Kolb. Integrating geographic information into survey research: Current applications, challenges and future avenues. Survey Research Methods, 11(3):307-327, 2017. Google Scholar
  7. Jean-Pierre Bocquet-Appel and Robert R Sokal. Spatial autocorrelation analysis of trend residuals in biological data. Systematic Zoology, 38(4):333-341, 1989. Google Scholar
  8. Jean-Paul Chiles and Pierre Delfiner. Geostatistics: Modeling spatial uncertainty. John Wiley & Sons, New York, NY, 2009. Google Scholar
  9. Yongwan Chun and Daniel A Griffith. Spatial statistics and geostatistics: Theory and applications for geographic information science and technology. Sage, London, UK, 2013. Google Scholar
  10. AD Cliff and JK Ord. The problem of spatial autocorrelation. London Papers in Regional Science, pages 25-55, 1969. Google Scholar
  11. AD Cliff and John K Ord. Space-time modelling with an application to regional forecasting. Transactions of the Institute of British Geographers, pages 119-128, 1975. Google Scholar
  12. Jens S Dangschat. Raumkonzept zwischen struktureller Produktion und individueller Konstruktion. Ethnologie und Raum, 9(1):24-44, 2007. Google Scholar
  13. P De Jong, C Sprenger, and F Van Veen. On extreme values of Moran’s I and Geary’s c. Geographical Analysis, 16(1):17-24, 1984. Google Scholar
  14. Michel Denuit, Christian Genest, and Étienne Marceau. Stochastic bounds on sums of dependent risks. Insurance: Mathematics and Economics, 25(1):85-104, 1999. Google Scholar
  15. Mario Di Francesco, Sajal K Das, and Giuseppe Anastasi. Data collection in wireless sensor networks with mobile elements: A survey. ACM Transactions on Sensor Networks, 8(1):7, 2011. Google Scholar
  16. Jean Dubé and Diègo Legros. A spatio-temporal measure of spatial dependence: An example using real estate data. Papers in Regional Science, 92(1):19-30, 2013. Google Scholar
  17. Bradley Efron and Carl Morris. Stein’s estimation rule and its competitors—-an empirical Bayes approach. Journal of the American Statistical Association, 68(341):117-130, 1973. Google Scholar
  18. Robert C Geary. The contiguity ratio and statistical mapping. The Incorporated Statistician, 5(3):115-146, 1954. Google Scholar
  19. Arthur Getis. Reflections on spatial autocorrelation. Regional Science and Urban Economics, 37(4):491-496, 2007. Google Scholar
  20. Arthur Getis. Spatial weights matrices. Geographical Analysis, 41(4):404-410, 2009. Google Scholar
  21. Arthur Getis. Spatial autocorrelation. In Manfred M. Fischer and Arthur Getis, editors, Handbook of Applied Spatial Analysis, pages 255-278. Springer, Heidelberg, Germany, 2010. Google Scholar
  22. Arthur Getis. Analytically derived neighborhoods in a rapidly growing west african city: The case of Accra, Ghana. Habitat International, 45:126-134, 2015. Google Scholar
  23. Arthur Getis and J. K. Ord. The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3):189-206, 1992. Google Scholar
  24. Tilmann Gneiting. Probabilistic forecasting. Journal of the Royal Statistical Society. Series A (Statistics in Society), pages 319-321, 2008. Google Scholar
  25. Daniel A Griffith. A linear regression solution to the spatial autocorrelation problem. Journal of Geographical Systems, 2(2):141-156, 2000. Google Scholar
  26. Bruce Hajek. Random processes for engineers. Cambridge University Press, Cambridge, UK, 2015. Google Scholar
  27. David Hasenfratz, Olga Saukh, Silvan Sturzenegger, and Lothar Thiele. Participatory air pollution monitoring using smartphones. In Proceedings of the 2nd International Workshop on Mobile Sensing: From Smartphones and Wearables to Big Data, Cambridge, MA, 2012. Academic Press. Google Scholar
  28. David Hasenfratz, Olga Saukh, Christoph Walser, Christoph Hueglin, Martin Fierz, Tabita Arn, Jan Beutel, and Lothar Thiele. Deriving high-resolution urban air pollution maps using mobile sensor nodes. Pervasive and Mobile Computing, 16:268-285, 2015. Google Scholar
  29. Mary Hegarty, Daniel R Montello, Anthony E Richardson, Toru Ishikawa, and Kristin Lovelace. Spatial abilities at different scales: Individual differences in aptitude-test performance and spatial-layout learning. Intelligence, 34(2):151-176, 2006. Google Scholar
  30. Bo Huang, Bo Wu, and Michael Barry. Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices. International Journal of Geographical Information Science, 24(3):383-401, 2010. Google Scholar
  31. Bret Hull, Vladimir Bychkovsky, Yang Zhang, Kevin Chen, Michel Goraczko, Allen Miu, Eugene Shih, Hari Balakrishnan, and Samuel Madden. Cartel: a distributed mobile sensor computing system. In Andrew Campbell, Philippe Bonnet, and John S. Heidemann, editors, Proceedings of the 4th International Conference on Embedded Networked Sensor Systems, pages 125-138. ACM, 2006. Google Scholar
  32. Paul H Jung, Jean-Claude Thill, and Michele Issel. Spatial autocorrelation statistics of areal prevalence rates under high uncertainty in denominator data. Geographical Analysis, 51(3):354-380, 2019. Google Scholar
  33. Teruyuki Kato, Yukihiro Terada, Masao Kinoshita, Hideshi Kakimoto, Hiroshi Isshiki, Masakatsu Matsuishi, Akira Yokoyama, and Takayuki Tanno. Real-time observation of tsunami by RTK-GPS. Earth, Planets and Space, 52(10):841-845, 2000. Google Scholar
  34. Roman Krzysztofowicz. The case for probabilistic forecasting in hydrology. Journal of Hydrology, 249(1-4):2-9, 2001. Google Scholar
  35. Jay Lee and Shengwen Li. Extending Moran’s index for measuring spatiotemporal clustering of geographic events. Geographical Analysis, 49(1):36-57, 2017. Google Scholar
  36. Yun Shin Lee and Stefan Scholtes. Empirical prediction intervals revisited. International Journal of Forecasting, 30(2):217-234, 2014. Google Scholar
  37. Fernando A López-Hernández and Coro Chasco-Yrigoyen. Time-trend in spatial dependence: Specification strategy in the first-order spatial autoregressive model. Estudios de Economia Aplicada, 25(2), 2007. Google Scholar
  38. Kevin M Lynch, Ira B Schwartz, Peng Yang, and Randy A Freeman. Decentralized environmental modeling by mobile sensor networks. IEEE Transactions on Robotics, 24(3):710-724, 2008. Google Scholar
  39. GD Makarov. Estimates for the distribution function of a sum of two random variables when the marginal distributions are fixed. Theory of Probability & its Applications, 26(4):803-806, 1982. Google Scholar
  40. Roger J Marshall. Mapping disease and mortality rates using empirical Bayes estimators. Journal of the Royal Statistical Society: Series C (Applied Statistics), 40(2):283-294, 1991. Google Scholar
  41. Russell L Martin and JE Oeppen. The identification of regional forecasting models using space: Time correlation functions. Transactions of the Institute of British Geographers, pages 95-118, 1975. Google Scholar
  42. Harvey J Miller. Tobler’s first law and spatial analysis. Annals of the Association of American Geographers, 94(2):284-289, 2004. Google Scholar
  43. Patrick AP Moran. Notes on continuous stochastic phenomena. Biometrika, 37(1/2):17-23, 1950. Google Scholar
  44. Enrico Natalizio and Valeria Loscrí. Controlled mobility in mobile sensor networks: Advantages, issues and challenges. Telecommunication Systems, 52(4):2411-2418, 2013. Google Scholar
  45. Roger B. Nelsen. An introduction to copulas. Springer, New York, NY, 1999. Google Scholar
  46. Neal Oden. Adjusting Moran’s I for population density. Statistics in Medicine, 14(1):17-26, 1995. Google Scholar
  47. J Keith Ord and Arthur Getis. Local spatial autocorrelation statistics: Distributional issues and an application. Geographical Analysis, 27(4):286-306, 1995. Google Scholar
  48. J Keith Ord and Arthur Getis. Local spatial heteroscedasticity (LOSH). The Annals of Regional Science, 48(2):529-539, 2012. Google Scholar
  49. Edzer J Pebesma and Cees G Wesseling. Gstat: A program for geostatistical modelling, prediction and simulation. Computers & Geosciences, 24(1):17-31, 1998. Google Scholar
  50. Peter A Rogerson. The detection of clusters using a spatial version of the chi-square goodness-of-fit statistic. Geographical Analysis, 31(2):130-147, 1999. Google Scholar
  51. Ludger Rüschendorf. Random variables with maximum sums. Advances in Applied Probability, pages 623-632, 1982. Google Scholar
  52. Yasar Guneri Sahin. Animals as mobile biological sensors for forest fire detection. Sensors, 7(12):3084-3099, 2007. Google Scholar
  53. Chenhua Shen, Chaoling Li, and Yali Si. Spatio-temporal autocorrelation measures for nonstationary series: A new temporally detrended spatio-temporal Moran’s index. Physics Letters A, 380(1-2):106-116, 2016. Google Scholar
  54. Steven M Smith and Edward Vela. Environmental context-dependent memory: A review and meta-analysis. Psychonomic Bulletin & Review, 8(2):203-220, 2001. Google Scholar
  55. Enrico Steiger, René Westerholt, and Alexander Zipf. Research on social media feeds-A GIScience perspective. In Christina Capineri, Muki Haklay, Haosheng Huang, Vyron Antoniou, Juhani Kettunen, Frank Ostermann, and Ross Purves, editors, European Handbook of Crowdsourced Geographic Information, pages 237-254. Ubiquity Press, London, UK, 2016. Google Scholar
  56. Xing Su, Hanghang Tong, and Ping Ji. Activity recognition with smartphone sensors. Tsinghua Science and Technology, 19(3):235-249, 2014. Google Scholar
  57. Mila Sugovic and Jessica K Witt. An older view on distance perception: Older adults perceive walkable extents as farther. Experimental Brain Research, 226(3):383-391, 2013. Google Scholar
  58. Michael Tiefelsdorf and Barry Boots. The exact distribution of Moran’s I. Environment and Planning A, 27(6):985-999, 1995. Google Scholar
  59. Michael Tiefelsdorf, Daniel A Griffith, and Barry Boots. A variance-stabilizing coding scheme for spatial link matrices. Environment and Planning A, 31(1):165-180, 1999. Google Scholar
  60. Waldo R Tobler. A computer movie simulating urban growth in the Detroit region. Economic Geography, 46(sup1):234-240, 1970. Google Scholar
  61. Sabrina Wahl, Christoph Bollmeyer, Susanne Crewell, Clarissa Figura, Petra Friederichs, Andreas Hense, Jan D Keller, and Christian Ohlwein. A novel convective-scale regional reanalysis COSMO-REA2: Improving the representation of precipitation. Meteorologische Zeitschrift, 26(4):345-361, 2017. Google Scholar
  62. Thomas Waldhör. The spatial autocorrelation coefficient Moran’s I under heteroscedasticity. Statistics in Medicine, 15(7-9):887-892, 1996. Google Scholar
  63. SD Walter. The analysis of regional patterns in health data: I. Distributional considerations. American Journal of Epidemiology, 136(6):730-741, 1992. Google Scholar
  64. SD Walter. The analysis of regional patterns in health data: II. The power to detect environmental effects. American Journal of Epidemiology, 136(6):742-759, 1992. Google Scholar
  65. Elisabeth M Weiss, Georg Kemmler, Eberhard A Deisenhammer, W Wolfgang Fleischhacker, and Margarete Delazer. Sex differences in cognitive functions. Personality and Individual Differences, 35(4):863-875, 2003. Google Scholar
  66. Karl F Wender, Daniel Haun, Björn Rasch, and Matthias Blümke. Context effects in memory for routes. In Christian Freksa, Wilfried Brauer, Christopher Habel, and Karl F. Wender, editors, International Conference on Spatial Cognition (Spatial Cognition III), pages 209-231, Heidelberg, Germany, 2002. Springer. Google Scholar
  67. René Westerholt. The impact of the spatial superimposition of point based statistical configurations on assessing spatial autocorrelation. In A. Mansourian, P. Pilesjö, L. Harrie, and R. von Lammeren, editors, Geospatial Technologies for All: Short Papers, Posters and Poster Abstracts of the 21th AGILE Conference on Geographic Information Science, Lund, Sweden, 2018. Google Scholar
  68. René Westerholt, Bernd Resch, Franz-Benjamin Mocnik, and Dirk Hoffmeister. A statistical test on the local effects of spatially structured variance. International Journal of Geographical Information Science, 32(3):571-600, 2018. Google Scholar
  69. René Westerholt, Bernd Resch, and Alexander Zipf. A local scale-sensitive indicator of spatial autocorrelation for assessing high-and low-value clusters in multiscale datasets. International Journal of Geographical Information Science, 29(5):868-887, 2015. Google Scholar
  70. René Westerholt, Enrico Steiger, Bernd Resch, and Alexander Zipf. Abundant topological outliers in social media data and their effect on spatial analysis. PLOS ONE, 11(9):e0162360, 2016. Google Scholar
  71. WH Williams and ML Goodman. A simple method for the construction of empirical confidence limits for economic forecasts. Journal of the American Statistical Association, 66(336):752-754, 1971. Google Scholar
  72. Min Xu, Chang-Lin Mei, and Na Yan. A note on the null distribution of the local spatial heteroscedasticity (LOSH) statistic. The Annals of Regional Science, 52(3):697-710, 2014. Google Scholar
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