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Lecture

Spatial Autocorrelation: Determining Geographic Object Neighborhoods

Description

This lecture covers the determination of neighborhood criteria for geographic objects, the importance of defining neighborhood in spatial weighting schemes, and the evaluation of spatial autocorrelation using the Moran's I index and Monte Carlo method.

In MOOC

Geographical Information Systems 2

Official source

Quiz

Related concepts (6)

Spatial analysis

Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures.

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.

Markov chain Monte Carlo

In statistics, Markov chain Monte Carlo (MCMC) methods comprise a class of algorithms for sampling from a probability distribution. By constructing a Markov chain that has the desired distribution as its equilibrium distribution, one can obtain a sample of the desired distribution by recording states from the chain. The more steps that are included, the more closely the distribution of the sample matches the actual desired distribution. Various algorithms exist for constructing chains, including the Metropolis–Hastings algorithm.

Autocorrelation

Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies.

Geographic information system

A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database, however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider such a system also to include human users and support staff, procedures and workflows, the body of knowledge of relevant concepts and methods, and institutional organizations.

Related lectures (6)

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Spatial Autocorrelation: An Introduction to GIS MOOC: Geographical Information Systems 2

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Discrete variables: Geometric properties MOOC: Geographical Information Systems 2

Covers geometric properties of discrete variables in GIS, including location, size, and shape.

Spatial Global Autocorrelation MOOC: Geographical Information Systems 2

Covers spatial autocorrelation, Moran's I interpretation, weighting schemes, and connectivity analysis in GIS.

Autocorrelation and Spatial Dependence MOOC: Geographical Information Systems 2