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, Ramsay et al. (2007) |
| 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 | Sun, Li & Genton (2012), Bevilacqua et al. (2012) |
| 15 | December 23 | Geostatistics for large datasets II | Sun, Li & Genton (2012) |
| 16 | December 30 | Stategies for big data: divide-and-conquer and algorithmic weakening | Jordan (2013) |
| 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 | Huang, Zhang & Robeson (2011), Gneiting (2013) |
| 2 | Nonparametric estimation of variograms and covariance functions | Huang, Hsing & Cressie (2011), Choi, Li & Wang (2013) |
| 3 | Asymptotics for covariance parameter estimation | Zhang (2004), Zhang & Zimmerman (2005), Kaufman & Shaby (2013) |
| 4 | Screening effect | Stein (2002), Stein (2011) |
| 5 | Stochastic approximation for MLEs in lattice models | Gu & Zhu (2001), Pettitt, Friel & Reeves (2003) |
| 6 | Asymptotics for MLEs in lattice models | Mardia & Marshall (1984), Lee (2004) |
| 7 | Spatial survival analysis | Li & Lin (2006), Li et al. (2015) |
| 8 | Inference for Cox and cluster processes | Diggle et al. (2013), Deng, Waagepetersen & Guan (2014), Guan, Jalilian & Waagepetersen (2015) |
| 9 | Dynamical models in ecology | Wood (2010), Coyte, Schluter & Foster (2015), Mao, Sabanis & Renshaw (2003) |
| 10 | More on differential equation models | Qi & Zhao (2010), Xue, Miao & Wu (2010), Xun et al. (2013), Hall and Ma (2014) |
| 11 | Kriged Kalman filter | Mardia et al. (1998), Wikle & Cressie (1999) |
| 12 | Asymptotics for covariance tapering | Du, Zhang & Mandrekar (2009), Wang & Loh (2011) |
| 13 | Reduced-rank and full-scale approximations for spatio-temporal data | Cressie, Shi & Kang (2010), Zhang, Sang & Huang (2015)
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