Lecture

Spatial Dependence: Concepts and Analysis

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In course

ENV-444: Exploratory data analysis in environmental health

This course teaches how to apply exploratory spatial data analysis to health information. Teaching focuses on the role of GIS and spatial statistics in spatial epidemiology. It proposes a context to investigate the relationship between health, quality of l ...

Description

This lecture explores the concept of spatial dependence, emphasizing the influence of nearby locations on each other. It delves into spatial autocorrelation, quantifying spatial regularity, and differentiating between observed and random spatial distributions. The instructor discusses Tobler's first law of geography and the paradox of near things being more related than distant ones. The lecture also covers classic statistical methods, bias in linear regression due to spatial dependence, and the importance of considering spatial influence in statistical analysis.

Instructors (2)

Stéphane Joost

Expertise Geographic Information Science and spatial statisticsMolecular ecology, Landscape genomics, Seascape genomicsSpatial epidemiology, Health geographics Publications Publications- List of publications Teaching & PhD PhD Students Marco André Vieira Ruas, Manon Laetitia Pribille, Martine Valérie Besse Past EPFL PhD Students Estelle Rochat, Solange Catherine Gaillard, Oliver Michele Selmoni, Anaïs Ladoy, Annie Sandrine Guillaume Past EPFL PhD Students as codirector Sylvie Stucki, Kevin Leempoel, Martí

Idris Guessous

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Related concepts (32)

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.

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Probability distribution

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.

Ratio distribution

A ratio distribution (also known as a quotient distribution) is a probability distribution constructed as the distribution of the ratio of random variables having two other known distributions. Given two (usually independent) random variables X and Y, the distribution of the random variable Z that is formed as the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio of two normally distributed variables with zero mean.

Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.

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