## Caput Statistics

 Faculteit Science and Engineering Jaar 2022/23 Vakcode WMMA011-05 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 pair-correlation 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 hands-on 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 re-exam.)
Vaksoort master
Coördinator C.P. Hirsch
Docent(en) C.P. Hirsch
Verplichte literatuur
Titel Auteur ISBN Prijs
Geometric and Topological Inference Jean-Daniel Boissonnat, Frédéric Chazal , Mariette Yvinec 9781108297806
Statistical Inference and Simulation for Spatial Point Processes
Jesper Møller, Rasmus, P. Waagepetersen 9781584882657
Entreevoorwaarden Prior knowledge presumed: Probability theory; Linear Algebra
Opmerkingen
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