# Probability and statistics seminar

- Date:
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
- Lecturer: Estate Khmladze
- Contact person: Tony Johansson
- Seminarium

Estate Khmladze (https://en.wikipedia.org/wiki/Estate_Khmaladze) from Victoria University of Wellington will talk about two topics.

The first topic is about differentiation of set-valued functions with application to infinitesimal image analysis and to change-set problem of spatial statistics. We will consider relatively new notion of 'fold-up derivatives' (which may not sound promising as "unfold" would be better associated with derivatives), and we will see how and why it is connected to change-set problems of spatial statistics, and how it is different from generalised functions. The source is Khm & Weil (2017, AISM) and Khm (2007, JMAA).

The second topic is about what can happen if we complement function-parametric empirical processes by appropriate unitary operators. The group of operators creates strangely wide equivalent classes of problems and leads to new understanding of which problems are actually equivalent. As a result, we will see that distribution-free testing theory emerges in parts of statistics, where it did not exist before. For example, in testing problems for point processes (with random intensities), in testing for parametric families of discrete distributions (taking us outside the chi-square world), and testing for transition matrices of Markov chains. The source is Khm (2013, AoS) and Khm (2016, Bernoulli). Two more is work in progress.