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# Spatial Statistics and Spatial Econometrics

### Overview

ABOUT THE COURSE: The purpose of this course is to introduce the analytical framework for analyzing spatial data and its target audience are students from social sciences (specifically, economics, political science and cognitive psychology), engineers, earth and geosciences, and applied physics. In the past decade or so, much interest has grown in the area due to readily-available spatially-delineated data, particularly when in 2008 the U.S. Geological Survey stopped charging for its high-resolution LANDSAT archive. However, modeling spatial data and spatial relationships necessitate the use of analytic tools beyond the standard statistical methods such as the ordinary least squares. Characterisation of spatial autocorrelation in spatial datasets for the purpose of statistical inference and statistical prediction is a focus of this course. In addition, we will ask: how and why does spatial autocorrelation arise; how is it measured and understood; how does it relate to issues of spatial heterogeneity and spatial dependence; and how these factors inform the specification and estimation of regression models. Specific modeling techniques include spatial autocorrelation measures (Moran's I, Geary's C, Variogram and Kriging estiators) and spatial regression models.INTENDED AUDIENCE: Students of physical, computation and social sciences who are interested in characterizing and modeling the spatial dimension in modern datasets and conduct statistical inference for real-world applications, including (but not restricted to) natural resource management, LULC change models, inventory management, PREREQUISITES: Students should have the knowledge of basic probability and statistics, linear algebra and differential calculusINDUSTRY SUPPORT: Major consulting firms like Deloitte, PwC, McKinsey and Co. etc., specifically for the purpose of risk analysis and management. In addition, the IT sector, Geospatial industry, and several other industrial sectors value the knowledge of spatial data analysis.

### Syllabus

Week 1:Introduction to spatial data and spatial models: Geostatistical data; Lattice sata; and Point data.
Week 2:Stationarity and Ergodicity of spatial random process.
Week 3:Characterising Spatial Autocorrelation: Variaogram, Semi-variaogram; Covariogram and Correlogram. Fitting a Variogram: Miminum Norm Quadratic Estimation; Generalized Least Squares Estimation; Maximum-likelihood and Restricted Maximum-Likelihood Estimation.
Week 4:Characterising Spatial Autocorrelation: Variaogram, Semi-variaogram; Covariogram and Correlogram. Fitting a Variogram: Miminum Norm Quadratic Estimation; Generalized Least Squares Estimation; Maximum-likelihood and Restricted Maximum-Likelihood Estimation - Cont.
Week 5:Spatial Prediction: Stochastic approach and decision-theoretic considerations. Spatial Interpolation: Ordinary Kirging; Kriging with Spatial Covariance.
Week 6:Spatial Econometrics and Regional Science: Moving from characterization of spatial pattens to deducing explanatory factors and inference. Spatial Dependence and Spatial Heterogeneity.
Week 7:The formal expression of spatial dependence structures: Spatial contiguity matrix, generalized spatial weight matrix; and spatial lag operators.
Week 8:Spatial externalities: Spatial multipliers and spatial regression; Global and Local Moran's-I Statistics.
Week 9:Estimation and hypothesis testing: Maximum likelihood estimation with spatial dependece in the dependent variable and the model errors. Likelihood ratio test and Lagrange multiplier tests for spatial process models.
Week 10:Applications on ArcGIS (incl. ArcPy - Python for ArcGIS)
Week 11:Applications on ArcGIS (incl. ArcPy - Python for ArcGIS) - Cont.
Week 12:Applications on R.

### Taught by

Prof. Gaurav Arora

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