Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WMMA01105 
Vaknaam  Caput Statistics 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Caput Statistics  
Leerdoelen  At the end of the course, the student is able to: 1. leverage the Poisson point process for formulating null hypotheses based on complete spatial randomness. The student can compute characteristics under the null hypothesis through the multivariate Mecke formula; 2. describe statistical tests for repulsion and attraction in point patterns based on the paircorrelation function. The student is able to describe basic models incorporating such features; 3. leverage the machinery of simplicial complexes to capture intricate geometric interactions in complex data sets. The student can extract key insights through homology and Betti numbers; 4. describe the concept behind the persistence homology. The student is able to compute the persistence diagram on a given data set and extract insights. 

Omschrijving  In topological data analysis (TDA), invariants from algebraic topology are used to gain new insights into data. While this approach initially emerged as a vague idea, TDA is now an established tool to explain cosmic arrangement of galaxies, to describe protein structures and to statistically analyze the fine structure of granular materials. All of these application domains share a common challenge: uncovering the structure in massive amounts of data that is embedded in a space of potentially high dimension. Surprisingly, classical invariants from algebraic topology relating to holes, connected components or loops yield tools that are an invaluable asset for modern data scientists. The course resides on two pillars. The first pillar, spatial statistics, builds the foundation for the stochastic modeling and statistical analysis of random point patterns in space. The second, algebraic topology, provides the tools to extract geometric characteristics from complex data sets. The synthesis of these two pillars is topological data analysis. The course covers both the conceptual mathematical side as well as handson programming practice in R. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM)  
Toetsvorm 
Mondeling tentamen (OR), Opdracht (AST)
(Assessment takes place through homework assignments and oral exam: Final = 0.1 x (HW1+HW2+HW3) + 0.7 x OE where HWi is homework grade for ith homework set, OE oral exam grade) only if OE >=4.5 otherwise Final = OE. The homework grades do not count for the reexam.) 

Vaksoort  master  
Coördinator  C.P. Hirsch  
Docent(en)  C.P. Hirsch  
Verplichte literatuur 


Entreevoorwaarden  Prior knowledge presumed: Probability theory; Linear Algebra  
Opmerkingen  
Opgenomen in 
