##### AM-85 - Propagation of error in geospatial modeling

- Compare and contrast error propagation techniques (e.g., Taylor, Monte Carlo)
- Explain how some operations can exacerbate error while others dampen it (e.g., mean filter)

This knowledge area embodies a variety of data driven analytics, geocomputational methods, simulation and model driven approaches designed to study complex spatial-temporal problems, develop insights into characteristics of geospatial data sets, create and test geospatial process models, and construct knowledge of the behavior of geographically-explicit and dynamic processes and their patterns.

Topics in this Knowledge Area are listed thematically below. Existing topics are in regular font and linked directly to their original entries (published in 2006; these contain __only__ Learning Objectives). Entries that have been **updated and expanded are in bold. **Forthcoming, *future topics are italicized*.

Conceptual Frameworks for Spatial Analysis & Modeling |
Data Exploration & Spatial Statistics |
Network & Location Analysis |

Basic Primitives |
Spatial Sampling for Spatial Analysis |
Intro to Network & Location Analysis |

Spatial Relationships |
Exploratory Spatial Data Analysis (ESDA) |
Network Route & Tour Problems |

Neighborhoods | Kernels & Density Estimation | Location & Service Area Problems |

First & Second Laws of Geography |
Spatial Interation | Accessibility Modeling |

Spatial Statistics |
Cartographic Modeling | Location-allocation Modeling |

Methodological Context |
Multi-criteria Evaluation | The Classic Transportation Problem |

Spatial Analysis as a Process |
Spatial Process Models | Space-Time Analysis & Modeling |

Geospatial Analysis & Model Building |
Grid-based Statistics and Metrics | Time Geography |

Changing Context of GIScience |
Landscape Metrics | Capturing Spatio-Temporal Dynamics in Computational Modeling |

Data Manipulation |
DEM and Terrain Metrics | GIS-Based Computational Modeling |

Point, Line, and Area Generalization | Point Pattern Analysis | Computational Movement Analysis |

Coordinate transformations | Hot-spot and Cluster Analysis | Accounting for Errors in Space-Time Modeling |

Data conversion | Global Measures of Spatial Association | Geocomputational Methods & Models |

Impacts of transformations | Local Measures of Spatial Association | Cellular Automata |

Raster resampling | Simple Regression & Trend Surface Analysis | Agent-based Modeling |

Vector-to-raster and raster-to-vector conversions | Geographically Weighted Regression | Simulation Modeling |

Generalization & Aggregation | Spatial Autoregressive & Bayesian Methods | Simulation & Modeling Systems for Agent-based Modeling |

Transaction Management |
Spatial Filtering Models | Artificial Neural Networks |

Building Blocks |
Genetic Algorithms & Evolutionary Computing | |

Spatial & Spatiotemporal Data Models | Surface & Field Analysis |
Big Data & Geospatial Analysis |

Length & Area Operatoins | Modeling Surfaces | Problems & Issues with Large Spatial Databases |

Polyline & Polygon Operations | Surface Geometry |
Pattern Recognition & Matching |

Overlay & Combination Operations | Intervisibility | Artificial Intelligence Approaches |

Areal Interpolation | Watersheds & Drainage |
Data Mining Approaches |

Classification & Clustering | Gridding, Interpolation, and Contouring | Rule Learning for Spatial Data Mining |

Boundaries & Zone Membership | Deterministic Interpolation Models | Machine Learning Approaches |

Tesselations & Triangulations | Inverse Distance Weighting |
CyberGIS |

Spatial Queries | Radial Basis & Spline Functions |
Analysis of Errors & Uncertainty |

Distance Operations | Triangulation |
Problems of Currency, Source, and Scale |

Buffers | Polynomial Functions |
Problems of Scale & Zoning |

Directional Operations | Core Concepts in Geostatistics |
Theory of Error Propagation |

Grid Operations & Map Algebra | Kriging Interpolation | Propagation of Error in Geospatial Modeling |

Fuzzy Aggregation Operators | ||

Mathematical Models of Uncertainty |

- Compare and contrast error propagation techniques (e.g., Taylor, Monte Carlo)
- Explain how some operations can exacerbate error while others dampen it (e.g., mean filter)

- Evaluate methods used by contemporary GIS software to resample raster data on-the-fly during display
- Select appropriate interpolation techniques to resample particular types of values in raster data (e.g., nominal using nearest neighbor)
- Resample multiple raster data sets to a single resolution to enable overlay
- Resample raster data sets (e.g., terrain, satellite imagery) to a resolution appropriate for a map of a particular scale
- Discuss the consequences of increasing and decreasing resolution

- List the possible sources of error in a selected and fitted model of an experimental semi-variogram
- Describe the conditions under which each of the commonly used semi-variograms models would be most appropriate
- Explain the necessity of defining a semi-variogram model for geographic data
- Apply the method of weighted least squares and maximum likelihood to fit semi-variogram models to datasets
- Describe some commonly used semi-variogram models

- Explain Anselin’s typology of spatial autoregressive models
- Demonstrate how the parameters of spatial auto-regressive models can be estimated using univariate and bivariate optimization algorithms for maximizing the likelihood function
- Justify the choice of a particular spatial autoregressive model for a given application
- Implement a maximum likelihood estimation procedure for determining key spatial econometric parameters
- Apply spatial statistic software (e.g., GEODA) to create and estimate an autoregressive model
- Conduct a spatial econometric analysis to test for spatial dependence in the residuals from least-squares models and spatial autoregressive models

- Perform an analysis using the geographically weighted regression technique
- Discuss the appropriateness of GWR under various conditions
- Describe the characteristics of the spatial expansion method
- Explain the principles of geographically weighted regression
- Compare and contrast GWR with universal kriging using moving neighborhoods
- Explain how allowing the parameters of the model to vary with the spatial location of the sample data can be used to accommodate spatial heterogeneity
- Analyze the number of degrees of freedom in GWR analyses and discuss any possible difficulties with the method based on your results

- Identify modeling situations where spatial filtering might not be appropriate
- Demonstrate how spatial autocorrelation can be “removed” by resampling
- Explain how dissolving clusters of blocks with similar values may resolve the spatial correlation problem
- Explain how the Getis and Tiefelsdorf-Griffith spatial filtering techniques incorporate spatial component variables into OLS regression analysis in order to remedy misspecification and the problem of spatially auto-correlated residuals
- Explain how spatial correlation can result as a side effect of the spatial aggregation in a given dataset
- Describe the relationship between factorial kriging and spatial filtering

## AM-87 - Problems of currency, source, and scale