Stochastic Processes¶
Geometric aspects of smooth random fields¶
Topics¶
- Gaussian processes:
- general properties;
- representations;
- continuity and smoothness
- exceedence probabilities
- Geometric tools:
- Euler characteristic
- (some) Morse theory
- Tube formulae
- (some) integral geometry
- Kac-Rice formula
- Geometry and Gaussian fields:
- Expected Euler characteristic for stationary fields
- Expected Euler characteristic for non-stationary (but marginally stationary) fields
- Gaussian Kinematic Formula and examples
- Exceedence probabilities for smooth fields
- Structure of excursion sets
- Palm distributions
- Local strucutre of Gaussian maxima
- High local maxima
- Applications
- Signal detection in neuroimaging
- Astrophysics
- Selective inference
- Others ?
Instructor & TAs¶
Teaching Assistants¶
TBA
Email list¶
The course has an email list that reaches TAs as well as the professor: stats317-win1718-staff@lists.stanford.edu.
Schedule & Location¶
T-Th 1:30-2:50, 420-050
Textbook¶
We will be using this draft of a textbook authored by Robert Adler, myself and the late Keith Worsley.
Evaluation¶
- 2-3 homeworks: 50%
- project + presentation 50%.