Standard syllabus
Advanced spatial statistics · Graduate · Math
Learning objectives from the Advanced spatial statistics syllabus, grouped by unit. Click an objective for study materials.
Topics typically covered
Click a topic for the full text and related unit practice.
Graduate Advanced spatial statistics — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Spatial stochastic processes
- Gaussian random fields — Gaussian random fields
- Variogram modeling and kriging — Variogram modeling and kriging
- Spatial prediction — Spatial prediction
- Uncertainty quantification — Uncertainty quantification
- Anisotropy — Anisotropy
- Nonstationary processes (intro) — Nonstationary processes (intro)
- Lattice data and CAR models — Lattice data and CAR models
Point patterns and areal data
- Poisson and Cox point processes — Poisson and Cox point processes
- K-functions — K-functions
- Spatial clustering tests — Spatial clustering tests
- Spatial autoregressive models for areal data — Spatial autoregressive models for areal data
- Disease mapping — Disease mapping
- BYM models (introduction) — BYM models (introduction)
- Change of support problem — Change of support problem
Computation
- Likelihood — Likelihood
- Bayesian spatial computation — Bayesian spatial computation
- INLA for spatial models (overview) — INLA for spatial models (overview)
- Large spatial datasets: approximations — Large spatial datasets: approximations
- Software: INLA, spBayes, Stan spatial examples — Software: INLA, spBayes, Stan spatial examples
Learning objectives
Click an objective for study materials.
Spatial stochastic processes
- Gaussian random fields — Gaussian random fields
- Variogram modeling and kriging — Variogram modeling and kriging
- Spatial prediction — Spatial prediction
- Uncertainty quantification — Uncertainty quantification
- Anisotropy — Anisotropy
- Nonstationary processes (intro) — Nonstationary processes (intro)
- Lattice data and CAR models — Lattice data and CAR models
Point patterns and areal data
- Poisson and Cox point processes — Poisson and Cox point processes
- K-functions — K-functions
- Spatial clustering tests — Spatial clustering tests
- Spatial autoregressive models for areal data — Spatial autoregressive models for areal data
- Disease mapping — Disease mapping
- BYM models (introduction) — BYM models (introduction)
- Change of support problem — Change of support problem
Computation
- Likelihood — Likelihood
- Bayesian spatial computation — Bayesian spatial computation
- INLA for spatial models (overview) — INLA for spatial models (overview)
- Large spatial datasets: approximations — Large spatial datasets: approximations
- Software: INLA, spBayes, Stan spatial examples — Software: INLA, spBayes, Stan spatial examples
Definitions and structure
- Gaussian random fields — Gaussian random fields
- Variogram modeling and kriging — Variogram modeling and kriging
- Spatial prediction — Spatial prediction
- Uncertainty quantification — Uncertainty quantification
- Anisotropy — Anisotropy
Proofs and reasoning
- Nonstationary processes (intro) — Nonstationary processes (intro)
- Lattice data and CAR models — Lattice data and CAR models
- Poisson and Cox point processes — Poisson and Cox point processes
- K-functions — K-functions
- Spatial clustering tests — Spatial clustering tests
Abstraction and generalization
- Spatial autoregressive models for areal data — Spatial autoregressive models for areal data
- Disease mapping — Disease mapping
- BYM models (introduction) — BYM models (introduction)
- Change of support problem — Change of support problem
- Likelihood — Likelihood
Modeling and computation
- Apply gaussian random fields in engineering contexts — Apply gaussian random fields in engineering contexts
- Apply variogram modeling and kriging in engineering contexts — Apply variogram modeling and kriging in engineering contexts
- Apply spatial prediction in engineering contexts — Apply spatial prediction in engineering contexts
- Apply uncertainty quantification in engineering contexts — Apply uncertainty quantification in engineering contexts
- Apply anisotropy in engineering contexts — Apply anisotropy in engineering contexts
Data and technology
- Use software to explore advanced spatial statistics problems numerically — Use software to explore advanced spatial statistics problems numerically
- Interpret computational results against analytic predictions — Interpret computational results against analytic predictions
- Build spreadsheets or scripts for routine calculations — Build spreadsheets or scripts for routine calculations
- Visualize functions, fields, or datasets tied to course topics — Visualize functions, fields, or datasets tied to course topics
- Connect course methods to lab, industry, or research workflows — Connect course methods to lab, industry, or research workflows
Problem-solving practice
- Nonstationary processes (intro) — Nonstationary processes (intro)
- Lattice data and CAR models — Lattice data and CAR models
- Poisson and Cox point processes — Poisson and Cox point processes
- K-functions — K-functions
- Spatial clustering tests — Spatial clustering tests
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Spatial stochastic processes
Gaussian random fields
Coming soon - Point patterns and areal data
Poisson and Cox point processes
Coming soon - Computation
Likelihood
Coming soon
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$1,162 · Advanced spatial statistics · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle.