Probability model approach to map pattern analysis

Bachi, R. 1963: Standard distance measures and related methods for spatial analysis. Papers and Proceedings of the Regional Science Associalion 10, 83-112.

Baker, E.J. and Lee, Y. 1975: Alternative analyses of geographical contingency tables. Professional Geographer 27, 179-88.

Bannister, G. 1975: Population change in southern Ontario. Annals of the Association of American Geographers 65, 177-88.

1976: Spacc-time components of urban population change. Economic Geography 52, 228-40.

Bassett, K. 1972: Numerical methods for map analysis. In Board, C. , Chorlcy, R. J. , Haggett, P. and Stoddart, D. R. , editors, Progress in geography: international reviews of current research 4, London: Edward Arnold.

Bassett, K. and Chorley, R.J. 1971 : An experiment in terrain filtering. Area 3, 78-91.

Betak,J.F. 1975: The conceptual loeus of a two-dimensional language: some implications for human responses to two-dimensional displays. Geographical Analysis 7, 1-17.

Board, C. 1967: Maps as models. In Chorley, R. J. and Haggett, P. , editors, Models in geogrephy, London: Methuen .

Boots, B.N. 1973: Some models of the random subdivision of space. Gcografiska Annaler 55B,34-48.

1974: Delaunay triangles: an ahernative approach to point pattern analysis. Proceedings of the Association of American Geographers 6, 26-9.

1975a: Some observations on the structure of socio-economie cellular networks. Canadian Geographer 19, 107-20.

1975b: Patterns of urban settlements revisited. Professional Geographer 27. 426-31.

1976 : Some angular properties of Dclaunay triangles for point patterns generated by a compound negative binomial process. Wilfrid Laurier University, Department of Geography, unpublished paper.

forthcoming: A note on the use of contact number properties in the study of cellular networks. To appear in Geographical Analysis.

Boots, B.N. and Merk, G.G. 1973: People on beaches: some indications of the utility of a search for mierolevel location theory. Proceedings of the Middle States Ditision, Associalion of American Geographers 7, 41-5.

Caprio,R.J. 1970: Centrography and geostatisties. Professional Geographer 12. 15-19.

Cassetti, E. 1966: Analysis of spatial association by trignometrie polynomials . Canadian Geographer 10, 199-204.

Chorley, R.J. 1972: Spatial analysis in geomorphology. London: Methuen.

Cliff, A.D. and Ord, J.K. 1973: Spatial autocorrelation. London : Pion.

1975: Model building and the analysis of spatial pattern in human geography (with discussion). Journal of the Royal Statistical Society, Series B37, 297-348.

Cliff, A.D. , Martin R.L. and Ord, J.K. 1975: A test for spatial autocorrelation in choroplcth maps based upon a modified Z2 statistic. Transactions of the Institute of British Geographers 65, 109-29.

Collins, R. 1972: Mclting and statistical geomectry of simple liquids . In Domb, C. and Green M. S. , editors, Phase transitions and critical phenomena 2.

Cox, K.R. and Agnew, J.A. 1974: Optimal and non-optimal territorial partitions: a possible approach toward conflict. Papers of the Peace Scietice Society (International) 23, 123-38.

Dacey, M.F. 1962: Analysis of central place and point patterns by a nearest-neighbor method . Lund Studies in Geography, Series B 24, 55-75.

1965 : Numerical measure of random sets. Geographical Information Systems Project, Technical Report 5. Evanston, Illinois: Department of Geography, Northwestern University.

1966: A probability model for central place locations. Annals of the Association of American Geographers 56, 550-68.

1968: An empirical study of the arcal distribution of houses in Puerto Rico. Transactions of the Institute of British Grographers 45, 51-69.

1969 : Similarities in the areal distribution of houses in Japan and Puerto Rico. Area I, 35-7.

1971a: A picture language for periodic strip patterns. Geographical Analysis 3, 320-33.

1971b : Linguistic aspects of maps and geographic information . Ontario Geography 5, 71-80.

1975: Evaluation of the Poisson approximation to measures of the random pattern in the square. Ceographical Analysis 7, 351-67.

Dacey, M.F. and Tung, T. 1962: The identification of randomness in point patterns. Journal of Regional Science 4, 83-96.

De Vos, S. 1973: The use of nearest neighbor methods. Tidjschrift roor Sociale en Economische Geografie 64, 307-19.

Dueker, K.J. 1966: Spatial data systems. Urban and Transportation Irformation Systems, Technical Reports 4,5, 6. Evanston, Illinois: Department of Geography, Northwestern University.

Eichenbaum, J. and Gale, S. 1971: Form, function, and process: a methodological inquiry. Economic Geography 47, 525-44.

Gale, S. 1971 : A simple device for the recognition of geographic patterns . Geographical Analysis 3, 187-201.

Getis, A. 1964: Temporal land-use patterns analysis with the use of nearest-neighbor and quadrat methods. Annals of the Association of American Geographers 54, 391-9.

1967 : Occupancy theory and map pattern analysis. University of Bristol, Department of Geography, Seminar Paper Series A, I.

1974 : Representation of spatial point processes by Polya models . In Yeates. M., editor, Proceedings of the 1972 meeting of the IGU Commission on Qantitative Geography, Montreal: McGill-Queen's University Press.

Getis, A. and Boots, B.N. 1977: Models of spatial processes: an approach to the study of point, line, and area patterns. Cambridge: Cambridge University Press.

Getis, A. and Merk, G.G. 1973: Spacing of human groups. Proceedings of the Association of American Geographers 5. 80-3.

Gilbert, E.N. 1962: Random subdivisions of space into crystals. Annals of Mathematical Statistics 33, 958-72.

Green, F.H.W. 1955: Local accessibility. Chessington , Surrey: Director General of the Ordnance Survey.

Green, J.R. and Hegazy, Y.A.S. 1976: Powerful modified EDF goodness-of-fit tests. Journal of the American Statistical Association 71, 204-9.

Haggett, P. and Bassett, K. 197o: The use of trend-surface parameters in inter-urban comparisons . Enrironment and Planning 2, 225-37.

Hall, E.T. 1966: The hidden dimension. Garden City, NY: Doubleday.

Hammersley, J.M. and Handscomb, D.C. 1964: Monte Carlo methods. London : Methuen.

Harvey, D.W. 1968a: Some methodological problems in the use of Neyman Type A and negative binomial probability distributions in the analysis of spatial series. Transactions of the Institule of British Geographers 43, 85-95.

1968b: Pattern, process, and the scale problem in geographical research. Transactions of the Institute of British Geographers 45, 71-8.

1969 : Explanation in geography. London: Edward Arnold.

Hodder, I.R. 1972a: Locational models and the study of Romano-British settlement . In Clarke, D. L. , editor, Models in archaeology, London: Methuen.

1972b: The interpretation of spatial patterns in archacology: two examples. Area 4, 223-9.

Hodder, I.R. and Hassall, M. 1971: The non-random spacing of Romano-British walled towns . Man 6, 391-407.

Horn, L.H. and Bryson, R.A. 1960: Harmonic analysis of the annual march of precipitation. Annals of the Association of American Geographers 50, 157-71.

Hsu, S-Y. and Mason, J.D. 1972: Towards a better understanding of the boundary effect on the decision making process in the Poisson model of point distribution in space. Proceedings of the Association of American Geographers 4, 46-9.

1974 : The nearest-neighbor statistics for testing randamness of point distributions in a bounded two-dimensional space. In Ycates, M., editor, Proceedings of the 1972 meeting of the IGU Commission on Quantitative Ceography, Montreal: McGill-Queen's University Press .

Hudson, J.C. 1969: Pattern recognition in empirical map analysis. Journal of Regional Science 9, 189-99.

1971: Structure of point processes. Geographical Analysis 3, 262-7.

James, G.A. , Cliff, A.D. and Haggett, P. 1970: Some discrete distributions for graphs with applications to regional transport networks. Geografiska Annaler 52B, 14-21.

Johnson, N.L. and Kotz, S. 1969: Distributions in statistics: Discrete distributions . Boston: Houghton Mifflin.

Johnson, W.A. and Mehl, R.F. 1939: Reaction kinetics in processes of nucleation and growth . Transactions of the Institute of American Mining and Metalurgical Engineers 135, 416-58.

Kendall, M.G. and Moran, P.A.P. 1963: Geometrical probability. New York: Hafner.

Keuls, M. , Over, H.J. and De Wit, C.T. 1963: The distance method for estimating densities. Statista Neerlandic 17, 71-91.

Kiang, T. 1966: Random fragmentation in two and three dimensions. Zeitschrift für Astrophysik 64, 433-9.

King, L.J. 1962 ; A quantitative expression of the pattern of urban settlements in selected areas of the United States. Tidjschrift voor Sociale en Economische Geografie 53, I-7.

1969: The analysis of spatial form and its relation to geographic theory. Annals of the Association of American Geographers 59, 573-95.

Kummer, H. 1971: Spacing mechanisms and social behavior. In Eisenberg, J. F. and Dillon, W. E. , editors, Man and beast: comparative social beharior , Washington, DC: Smithsonian Institution Press.

Little, D.V. 1974: A third note on recent research in geometrical prolsability . Advances in Applied Probability, 6, 103-30.

MacDougall, E.B. 1969: Spatial filtering. Department of Geography, University of Toronto, Discussion Papers I.

Macomber, L. 1971: Utility of trend surfaces in interregional map comparison . Journal of Regional Science II, 87-90.

Mardia, K.V. 1972: Statistics of directional data. London : Academic Press.

Massam,B.H. and Goodchild, M.F. 1971: Temporal trends in the spatial organization of a service agency. Canadian Geographer 15, 193-206.

Matern,B. 1959: Nagra tillampningar an teorin for geometriska sannolikheter. Srenska skogsvardsforeningens tidschrift 3, 453-8.

Mead, R. 1974: A test for spatial pattern at several scales using data from a grid of contiguous quadrats. Biometrics 30, 295-307.

Medvedkov, Y.U. 1967: The concept of entropy in settlement pattern analysis . Papers and Proceedings of the Regional Science Association 18, 165-8.

1968: An application of topology in central place analysis. Papers and Proceedings of the Regional Science Association 20, 77-84.

Meijering, J.L. 1953: Interface area, edge length, and number of vertices in crystal aggregatcs with random nucleation. Philips Research Reports 8, 270-90.

Merk, G.G. 1973: Spacing and territoriality in man. Rulgers University, Department of Geography, Discussion Papers 5.

Miles, R.E. 1970: On the homogeneous planar Poisson point process. Mathematical Biosciences 6,85-127.

1972: The random division of space. Advances in Applied Probability (supplement), 243-66.

1974 : On the elimination of edge effects in planar sampling. In Harding, E. F. and Kendall, D. G. , editors, Stochastic geometry, London: Wiley.

Mitchell, B. 1971 : A comparison of chi-square and Kolmogorov-Smirnov tests. Area 3, 237-41.

Moran, P.A.P. 1966: A note on recent research in geometrical probability. Journal of Applied Probability 3, 453-63.

1969: A second note on recent research in geometrical probability . Advances in Applied Probability I, 73-89.

Neft, D.S. 1967: Statistical analysis for areal distributions. Regional Science Research Institute, Monograph Series 2.

Norcliffe, G.B. 1969 : On the use and limitations of trend-surfacc models. Canadian Geographer 13, 338-48.

Persson, O. 1964: Distance methods. Studia Forestallia Sueccia 15.

1971 : The robustness of estimating density by distance measurements . In Patil, G. P. , Pielou, E. C. , and Waters, W. E. , editors, Statistical Ecology 2: Sampling and modeling biological poprrlalions and population dynamics, Univcrsity- Park, Pennsylvania: Pennsylvania State University Press.

Pielou, E.C. 1969: An introduction to mathemalical ccology. New York: Wiley.

1974 : Population and community ecology: principles and methods . New York: Gordon and Breach Science Publishers.

Rayner, J.N. and Golledge, R.G. 1972; Spectral analysis of settlement patterns in diverse physical and economic environments. Environment and Planning 4, 347-71.

1973: The spectrum of US Route 40 reexamined. Geographiral Analysis 4, 338-50.

Robinson, G. and Salih, K.B. 1974: An illustration of four-variable trend analysis applied to regional growth. Regional Studies 8, 47-55.

Roder, W. 1975: A procedure for assessing point patterns without reference to area or density. Professional Geographer 27, 432-40.

Rogers, A. 1974: Statistical analysis of spatial dispersion. London: Pion.

Royaltey, H.H. , Astrachan, E. and Sokal, R.R. 1975: Tests for patterns of gcographic variation. Geographical Analysis 7, 369-95.

Sabbagh, M.E. and Bryson, R.A. 1962: Aspects of the precipitation climaurlogy of Canada investigated by the method ofharmonic analysis, Annals of the Association of American Geographers 52, 426-40.

Semple, R.K. and Golledge, R.G. 1970: An analysis of entropy changes in a settlement pattern over time. Economic Gragraphy 46, 157-60.

Smalley, I.J. 1966 : Contraction crack networks in basalt flows. Geologiral Magazine 103, 110-14.

Smith, D.M. 1975: Patterns in human geography: an introdurtion to numerical methods. Newton Abbot: David and Charles.

Sommer, R. 1969: Personal space: the behavioral basis of design . Englewood Cliffs, NJ: Prentice-Hall .

Stephens, M.A. 1974: EDF slatistics for goodness of fit and some comparisons. Journal of the American Statistical Association 69 (347), 730-7.

Switzer, P. 1967: Reconstructing patterns from sample data. Annals of Mathematical Statistics 38, 138-58.

1976 : Applications of random process models to the description of spatial distributions of qualitative geologic variables. In Merriam, D. F. , editor, Random processes in geology, New York: Springer-Verlag .

Tapiero, C.S. and Boots, B. 1974: Structural inference in transportation networks. Enviroment and Planning A 6, 411-18.

Thomas, K.W. and Reeve, D.E. 1976: The role of Bose-Einstein statistics in point pattern analysis . Geooraphical Analysis 9, 113-36.

Thompson, D'Arcy W. 1942: On growth and form. Cambridge : Cambridge University Press.

Tobler, W.R. 1969a: Geographical filters and their inverses. Geographical Analysis I, 234-53.

1969b: The spectrum of US 40. Papers and Proceedings of the Regional Science Association 23, 45-52.

Woldenberg, M.J. 1972: The average hexagon in spatial hierarchies. In Chorley, R. J., editor, Spatial analysis in geomorphology, London: Methuen.

Yapa, L.S. 1975: Analytical alternatives to the Monte Carlo simulation of spatial diffusion . Annals of the Association of American Geographers 65, 163-76.

1976: On the statistical significance of the observed map in spatial diffusion. Gcographical Analysis 8, 255-68.