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GIS and Spatial Modeling

# GIS and Spatial Modeling - Introduction to Spatial Modeling...

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Introduction to Spatial Modeling Statistical options tend to be limited in most GIS applications. This is likely to be redressed in the future. We will look at spatial statistics in general terms, and conclude with a review of the software available.

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Basic Concepts Spatial statistics differ from ‘ordinary’ statistics by the inclusion of locational properties. This makes spatial statistics more complex. The book by Bailey and Gatrell (1995) provides an accessible introduction. They identify four categories: Point pattern data; Spatially continuous data; Areal data; and Interaction data. Obvious correspondence with conceptual models.
Scale Levels Attribute data can be classified by measurement scale: Nominal: e.g. 1=females, 2=males. Ordinal: e.g. 1=good, 2=medium, 3=poor. Interval (+ ratio): e.g. degrees Centigrade, percentages. Bailey and Gatrell classify techniques by purpose: Visualisation Exploration Modelling – this is involved in all statistical inference and hypothesis testing)

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Random Variables Statistical models deals with phenomena that are stochastic (i.e. are subject to uncertainty). A random variable Y has values that are subject to uncertainty (but may not necessarily be random). The distribution of possible values is referred to as the probability distribution . Represented by a function f Y (y) Random variables may be discrete or continuous .
Probabilities Probability that y is between a and b is given by: if Y is discrete i f Y is continuous (probability density) Cumulative probability ( or distribution function ) F Y is given by: if Y is discrete if Y is continuous ( 29 = b a y Y y f ( 29 b a Y dy y f ( 29 ( 29 -∞ = = y u Y Y u f y F ( 29 ( 29 du u f y F y Y Y - =

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Expected Values The expected value of Y is its mean E(Y): or The expected value of a function of Y, say g(Y) is : or Variance is: VAR(Y) = Σ ([Y - E(Y)] 2 ) The square root of this is the standard deviation ( σ Y ) ( 29 ( 29 -∞ = = y Y y f y Y E . ( 29 ( 29 - = dy y f y Y E Y . ( 29 ( 29 ( 29 ( 29 y f y g Y g E Y . = ( 29 ( 29 ( 29 ( 29 dy y f y g Y g E Y - = .
Joint Probability Can generalise to situations where there is more than one random variable. Joint probability distribution

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GIS and Spatial Modeling - Introduction to Spatial Modeling...

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