#### Noon Lecture, Department of Applied Mathematics, MFF

*E. Werner:* Floating bodies and approximation of convex bodies by polytopes

#### Noon Lecture, Department of Applied Mathematics, MFF

Praha, Czech Republic

##### August 28, 2018, 12:15, room S8

#### presentation (pdf)

### Abstract

How well can a convex body be approximated by a polytope? This is a fundamental question in convex geometry, also in view of applications in many other areas of mathematics and related fields. It often involves side conditions like a prescribed number of vertices and a requirement that the body contains the polytope or vice versa. Accuracy of approximation is often measured in the symmetric difference metric but other metrics can and have been considered. We will present several results, mostly related to approximation by "random polytopes". We will introduce floating bodies and an affine invariant from affine differential geometry associated to them, the affine surface area. This affine invariant appears naturally as an important ingredient in approximation questions.## Workshop on Functional Data Analysis

##### July 12, 2018

### Thursday, July 12, 2018 - K6 - KPMS, MFF, Sokolovská 83, Praha

- 13:00-14:00 Frédéric Ferraty (University of Toulouse):

*Estimation of temperature-dependent growth profiles of fly larvae with application to criminology* - 14:00-14:30 Jiří Dvořák:

*Envelope tests in functional data analysis* - 14:30-15:00 Veronika Římalová (Palacký university Olomouc):

*An inferential framework for the analysis of spatio-temporal geochemical data* - 15:00-15:30 Zuzana Rošťáková (Slovak Academy of Sciences):

*Probabilistic modelling and functional data analysis of sleep structure* - 15:30-16:00 Stanislav Nagy:

*Nonparametric analysis of the shape of random curves*

### Frédéric Ferraty: Estimation of temperature-dependent growth profiles of fly larvae with application to criminology

#### presentation (pdf)

Joint work with D. Pigoli, J.A.D. Aston, A. Mazumder, C. Richards and M.J.R. Hall.

### Jiří Dvořák: Envelope tests in functional data analysis

#### presentation (pdf)

### Veronika Římalová: An inferential framework for the analysis of spatio-temporal geochemical data

#### presentation (pdf)

Joint work with A. Menafoglio, A. Pini and E. Fišerová.

### Zuzana Rošťáková: Probabilistic modelling and functional data analysis of sleep structure

#### presentation (pdf)

Joint work with R. Rosipal.

### Stanislav Nagy: Nonparametric analysis of the shape of random curves

#### presentation (pdf)

## Introductory Workshop PRIMUS

##### January 30 and 31, 2018

### Tuesday, January 30, 2018 - "Praktikum" KPMS, MFF

- 09:00-10:00 Daniel Hlubinka:

*Estimation of levels sets* - 10:00-11:00 Jiří Dvořák:

*On point processes, Monte Carlo testing and stochastic reconstruction* - 11:00-12:00 Pavel Valtr:

*From geometry to data depth* - 12:00-13:00 Jan Rataj:

*Curvature measures and integral-geometric formulae*

### Wednesday, January 31, 2018 - "Praktikum" KPMS, MFF

- 16:00-17:00 Martin Balko:

*Ramsey-type problems on ordered hypergraphs and connections to discrete geometry*

### Jiří Dvořák: On point processes, Monte Carlo testing and stochastic reconstruction

#### presentation (pdf)

### Jan Rataj: Curvature measures and integral-geometric formulae

#### presentation (pdf)

### Martin Balko: Ramsey-type problems on ordered hypergraphs and connections to discrete geometry

#### presentation (pdf)

*S. Nagy:* Statistical Data Depth and its Applications

#### Seminar, Department of Cybernetics, ČVUT

Praha, Czech Republic

##### February 22, 2018

#### presentation (pdf)

### Abstract

In nonparametric statistics the concept of quantiles is of paramount importance. In multivariate spaces, however, quantiles cannot be defined directly, due to the lack of natural ordering of points. In the talk we focus on one possible solution to this problem, using a tool called data depth. Depth is a function that quantifies the "centrality" of points, with respect to a given probability distribution. Points with high depth values form the "inner" quantile regions of the distribution; points of low depth lie on the outskirts of the data cloud. We discuss approaches to the definition of data depth, and illustrate these in a series of simple examples. The applications of this methodology include data visualisation,(robust) estimation, classification, clustering, or outlier detection for multivariate, high-dimensional, and even functional (infinite-dimensional) datasets.*S. Nagy:* Theory of Functional Data Depth

#### Aalto Stochastics and Statistics Seminar

Helsinki, Finland

##### February 7, 2018

### Abstract

Depth has become a quite popular concept in functional data analysis. In the talk we discuss its general framework. We show that most known functional depths can be classified into few groups, within which they share similar theoretical properties. We focus on uniform consistency results for the sample versions of these functionals, and demonstrate that some well-known approaches to depth assessment are hardly theoretically adequate.*S. Nagy:* On Symmetry of Multivariate Random Variables (in Slovak)

#### 20th Winter School ROBUST

Rybník, Czech Republic

##### January 26, 2018

#### presentation (pdf)

### Abstract

Na rozdiel od distribúcií na reálnej osi, vo viacrozmerných priestoroch neexistuje jednoznačne prijímaná definícia symetrie rozdelenia. Niekoľko rôznych prístupov kategorizujú Zuo a Serfling (2000), z čoho neskôr vychádza Serfling (2006) pri uvádzaní týchto definícií do štatistickej literatúry. V príspevku preskúmame niektoré tvrdenia Zua a Serflinga (2000) a ukážeme, že najzaujímavejšie dôkazy v ich článku nie sú úplné. Pri ďalšom skúmaní týchto problémov narazíme na neznámy dôkaz Funkovej charakterizácie symetrie konvexných telies - problému, formulovaného v roku 1913, ktorý bol vyriešený až v roku 1970. Pokiaľ vieme, jedná sa o prvý elementárny dôkaz tohto významného tvrdenia v literatúre.*S. Nagy:* Data Depth and Its Place in Modern Mathematics (in Slovak)

#### Department of Probability and Math. Statistics, Charles University

##### October 2, October 30, and December 11, 2017

- Časť I: Štatistická hĺbková funkcia
- Časť II: Miery symetrie
- Časť III: Plávajúce telesá