Math 12230: Spatio-Temporal Statistics for Big Data
Course Description
This is a graduate-level topic course in spatio-temporal statistics, emphasizing big data techniques for the analysis of large spatial and spatio-temporal
data sets. Topics covered in the course will include geostatistical models and spatial prediction, lattice models and spatial econometrics, spatial point
patterns, spatio-temporal processes, computational and statistical tradeoffs, divide-and-conquer strategies, online algorithms, applications of big data
techniques to spatio-temporal analysis, software for spatio-temporal statistics and big data.
Syllabus
Lectures and Exams
| Week | Date | Topic | References |
| 1 | September 16 | Overview, stationary processes | Cressie Chapter 1, Sections 2.1 and 2.3 |
| 2 | September 23 | Variogram and covariance models | Cressie Sections 2.4–2.6 |
| 3 | September 30 | Spatial prediction and kriging | Cressie Sections 3.1–3.2 and 3.4 |
| 4 | No class | | |
| 5 | October 14 | Specifications of lattice models | Cressie Sections 6.1 and 6.3–6.4 |
| 6 | October 21 | Inference for lattice models | Cressie Sections 6.5–6.7 and 7.2–7.3 |
| 7 | October 28 | Point process theory | Cressie Sections 8.1 and 8.3 |
| 8 | November 4 | Tests and models for spatial point patterns | Cressie Sections 8.2 and 8.4–8.5 |
| 9 | November 11 | Midterm Exam 1 | Due November 18 in class |
| 10 | November 18 | Spatio-temporal covariance functions and kriging | Cressie & Wikle Sections 6.1–6.2 |
| 11 | November 25 | Differential equation models | Cressie & Wikle Section 6.3, |
| 12 | December 2 | Hierarchical dynamical spatio-temporal models | Cressie & Wikle Sections 7.1–7.2 and 8.1 |
| 13 | December 9 | Inference for hierarchical dynamical spatio-temporal models | Cressie & Wikle Sections 8.2–8.4 |
| 14 | December 15 | Geostatistics for large datasets I | , |
| 15 | December 23 | Geostatistics for large datasets II | |
| 16 | December 30 | Stategies for big data: divide-and-conquer and algorithmic weakening | |
| 17 | January 2 | Midterm Exam 2 | Due January 9 in the instructor's mailbox |
| 18 | January 13 | Final presentation 2:00–4:30 pm at Lijiao 313 | Written report due January 14 by 5 pm
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Further Reading
| No. | Topic | References |
| 1 | Valid variograms and covariance functions on the sphere | , |
| 2 | Nonparametric estimation of variograms and covariance functions | , |
| 3 | Asymptotics for covariance parameter estimation | , , |
| 4 | Screening effect | , |
| 5 | Stochastic approximation for MLEs in lattice models | , |
| 6 | Asymptotics for MLEs in lattice models | , |
| 7 | Spatial survival analysis | , |
| 8 | Inference for Cox and cluster processes | , , |
| 9 | Dynamical models in ecology | , , |
| 10 | More on differential equation models | , , , |
| 11 | Kriged Kalman filter | , |
| 12 | Asymptotics for covariance tapering | , |
| 13 | Reduced-rank and full-scale approximations for spatio-temporal data | ,
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