Beyond mule kicks: The poisson distribution in geographical analysis

Geographical Analysis

Volumn 38, Issue 2, 2006, Pages 123-139

  Griffith, Daniel A ^a   Haining, Robert ^b  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CAUSE OF DEATH;

EID: 33644947906     PISSN: 00167363     EISSN: 15384632     Source Type: Journal    
DOI: 10.1111/j.0016-7363.2006.00679.x     Document Type: Article

References (51)

1. Anselin, L. (1995). "Local Indicators of Spatial Association - LISA." Geographical Analysis 27, 93-115.
2. Barnet, V., and T. Lewis. (1978). Outliers in Statistical Data. New York: Wiley.
3. Berry, B., and D. Marble. (1968). Spatial Analysis: A Reader in Statistical Geography. Englewood Cliffs, NJ: Prentice Hall.
4. Besag, J. (1974). "Spatial Interaction and the Statistical Analysis of Lattice Systems." Journal of Royal Statistical Society 36B, 192-225.
5. Besag, J., and J. Newell. (1991). "The Detection of Clusters in Rare Diseases." Journal of the Royal Statistical Society 154A, 143-55.
6. Bolduc, D., M. Dagenais, and M. Gaudry. (1989). "Spatially Autocorrelated Errors in Origin-Destination Models: A New Specification Applied to Aggregate Mode Choice." Transportation Research 23B, 361-72.
7. Bolduc, D., R. Laferrière, and G. Santarossa. (1992). "Spatial Autoregressive Error Components in Travel Flow Models."Regional Science and Urban Economics 22, 371-85.
8. Bolduc, D., R. Laferrière, and G. Santarossa. (1995). "Spatial Autoregressive Error Components in Travel Flow Models: An Application to Aggregate Mode Choice." In New Directions in Spatial Econometrics, 96-108, edited by L. Anselin and R. Florax. Berlin, Germany: Springer-Verlag.
9. Bowley, A. (1901). Elements of Statistics. London: King & Son.
10. Choynowski, M. (1959). "Maps Based on Probabilities." Journal of the American Statistical Association 54, 385-88.
11. Cressie, N. (1991). Statistics for Spatial Data. New York: Wiley.
12. Curry, L. (1972). "Spatial Analysis of Gravity Flows." Regional Studies 6, 131-47.
13. Dacey, M. (1964). "Modified Poisson Probability Law for Point Pattern More Regular Than Random." Annals, Association of American Geographers 54, 559-65.
14. Dacey, M. F. (1966a). "A Compound Probability Law for a Pattern More Dispersed than Random and With Areal Inhomogeneity." Economic Geography 42, 172-79.
15. Dacey, M. (1966b). "A County Seat Model for the Areal Pattern of an Urban System." Geographical Review 56, 527-42.
16. Falk, M., J. Hüsler, and R.-D. Reiss. (1994). Laws of Small Numbers: Extremes and Rare Events. Basel, Switzerland: Birkhäuser Verlag.
17. Flowerdew, R., and M. Aitkin. (1982). "A Method of Fitting the Gravity Model Based on the Poisson Distribution." Journal of Regional Science 22, 191 - 202.
18. Flowerdew, R., and A. Geddes. (1999). "Poisson Regression Analysis of Limiting Long-Term Illness Data for Parts of North East England." Geographical & Environmental Modelling 3 (1), 63-82.
19. Flowerdew, R., and A. Lovett. (1988). "Fitting Constrained Poisson Regression Models to Interurban Migration Flows." Geographical Analysis 20, 297-307.
20. Gatrell, A., T. Bailey, P. Diggle, and B. Rowlingson. (1996). "Spatial Point Pattern Analysis and its Application in Geographical Epidemiology." Transactions, Institute of British Geographers 21, 256-74.
21. Getis, A., and B. Boots. (1978). Models of Spatial Processes. Cambridge, UK: Cambridge University Press.
22. Getis, A., and J. K. Ord. (1992). "The Analysis of Spatial Association by Use of Distance Statistics." Geographical Analysis 24, 189 - 206 (with correction, 1993, 25, p. 276).
23. Griffith, D. (1983). "The Boundary Value Problem in Spatial Statistical Analysis." Journal of Regional Science 23, 377-87.
24. Griffith, D. (1985). "An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Contemporary Methods." Geographical Analysis 17, 81-88.
25. Griffith, D. (2002). "A Spatial Filtering Specification for the Auto-Poisson Model." Statistics and Probability Letters 58, 245-51.
26. Griffith, D. (2003). Spatial Autocorrelation and Spatial Filtering: Gaining Understanding through Theory and Scientific Visualization. Berlin, Germany: Springer-Verlag.
27. Griffith, D., and C. Amrhein. (1983). "An Evaluation of Correction Techniques for Boundary Effects in Spatial Statistical Analysis: Traditional Methods." Geographical Analysis 15, 352-60.
28. Griffith, D., and K. Jones. (1980). "Explorations into the Relationship Between Spatial Structure and Spatial Interaction" Environment and Planning A 12, 187-201.
29. Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. New York: Wiley.
30. Haining, R. (1982). "Describing and Modeling Rural Settlement Maps." Annals, Association of American Geographers 27, 211-23.
31. Haining, R. (1990). Spatial Data Analysis in the Social and Environmental Sciences. Cambridge, UK: Cambridge University Press.
32. Haining, R. (2003). Spatial Data Analysis: Theory and Practice. Cambridge, UK: Cambridge University Press.
33. Hoaglin, V. (1980). "A Poissonness Plot. "The American Statistician 34, 146-49.
34. Holt, D., D. Steel, and M. Tranmer. (1996a). "Area Homogeneity and the Modifiable Areal Unit Problem." Geographical Systems 3, 181-200.
35. Holt, D., D. Steel, M. Tranmer, and N. Wrigley. (1996b). "Aggregation and Ecological Effects in Geographically Based Data." Geographical Analysis 28, 244-61.
36. Kaiser, M., and N. Cressie. (1997). "Modeling Poisson Variables with Positive Spatial Dependence."Statistics and Probability Letters 35, 423-32.
37. King, L. (1962). "A Quantitative Expression of the Pattern of Urban Settlements in Selected Areas of the United States." Tijdschrift Voor Economische en Sociale Geographie 53, 1-7.
38. Kulldorff, M. (1997). "A Spatial Scan Statistic." Communications in Stat istics: Theory and Methods 26, 1481-96.
39. Kulldorff, M. (1998). "Statistical Methods for Spatial Epidemiology: Tests for Randomness."In GIS and Health, 49-62, edited by A. Gatrell and M. Löytönen. London: Taylor & Francis.
40. Lovett, A., and R. Flowerdew. (1989). "Analysis of Count Data Using Poisson Regression." Professional Geographer 41, 190-98.
41. Matui, I. (1932). "Statistical Study of the Distribution of Scattered Villages in Two Regions of the Tonami Plain, Toyama Prefecture."Japan Journal of Geology and Geography 9, 251-66.
42. McCullagh, P., and J. Nelder. (1989). Generalized Linear Models. London: Chapman & Hall.
43. Meyer, P. (1970). Introductory Probability and Statistical Applications, 2nd ed. Reading, MA: Addison Wesley.
44. Openshaw, S., M. Charlton, C. Wymer, and A. Craft. (1987). "A Mark 1 Geographical Analysis Machine for the Automated Analysis of Point Datasets."International Journal of Geographical Information Systems 1, 335-58.
45. Ripley, B. (1981). Spatial Statistics. New York: Wiley.
46. Spiegelhalter, D., N. Best, B. Carlin, and A. Van der Linde. (2002). "Bayesian Measures of Model Complexity and Fit (with Discussion)."Journal of the Royal Statistical Society 64B, 583-640.
47. Tiefelsdorf, M. (2003). "Misspecifications in Interaction Model Distance Decay Relations: A Spatial Structure Effect." Journal of Geographical Systems 5, 25-50.
48. Tranmer, M., and D. Steel. (1998). "Using Census Data to Investigate the Causes of the Ecological Fallacy."Environment and Planning A 30, 817-31.
49. Unwin, D., and N. Wrigley. (1987). "Control Point Distribution in Trend Surface Modelling Revisited: An Application of the Concept of Leverage." Transactions, Institute of British Geographers 12, 147-60.
50. Wakefield, J., N. Best, and L. Waller. (2000). "Bayesian Approaches to Disease Mapping." In Spatial Epidemiology: Methods and Applications, 104-27, edited by P. Elliott, J. Wakefield, N. Best, and D. Briggs. Oxford, UK: Oxford University Press.
51. Wolpert, R., and K. Ickstadt. (1998). "Poisson/Gamma Random Field Models for Spatial Statistics." Biometrika 85, 251-67.