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Unformatted text preview: University of WisconsinMilwaukee Geographic Information Science Geography 625 Intermediate Geographic Information Science Instructor : Changshan Wu Department of Geography The University of WisconsinMilwaukee Fall 2006 Week4: Point Pattern Analysis University of WisconsinMilwaukee Geographic Information Science Outline 1. Revisit IRP/CSR 2. First and second order effects 3. Introduction to point pattern analysis 4. Describing a point pattern 5. Densitybased point pattern measures 6. Distancebased point pattern measures 7. Assessing point patterns statistically University of WisconsinMilwaukee Geographic Information Science 1. Revisit IRP/CSR Independent random process (IRP) Complete spatial randomness (CSR) 1. Equal probability : any point has equal probability of being in any position or, equivalently, each small subarea of the map has an equal chance of receiving a point. 2. Independence : the positioning of any point is independent of the positioning of any other point. 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 k n k x x x k n x n k P  = 1 1 ) , , ( ! ) ( k e k P k λ λ = x n = λ and University of WisconsinMilwaukee Geographic Information Science 2. First and second order effects The independent random process is mathematically elegant and forms a useful starting point for spatial analysis, but its use is often exceedingly naive and unrealistic. If realworld spatial patterns were indeed generated by unconstrained randomness, geography would have little meaning or interest, and most GIS operations would be pointless. IRP/CSR is not realistic University of WisconsinMilwaukee Geographic Information Science 2. First and second order effects 1. Firstorder effect The assumption of Equal probability cannot be satisfied The locations of disease cases tends to cluster in more densely populated areas Plants are always clustered in the areas with favored soils. From (http://www.crimereduction.gov.uk/toolkits/fa020203.htm) University of WisconsinMilwaukee Geographic Information Science 2. First and second order effects 2. Secondorder effect The assumption of Independence cannot be satisfied New developed residential areas tend to near to existing residential areas Stores of McDonald tend to be far away from each other. University of WisconsinMilwaukee Geographic Information Science 2. First and second order effects In a point process the basic properties of the process are set by a single parameter, the probability that any small area will receive a point – the intensity of the process. Firstorder stationary : no variation in its intensity over space....
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 Summer '08
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 Statistics, Geography, Distance, Geographic information system, Geographic Information Science, UNIVERSITY OF WISCONSINMILWAUKEE

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