Stanislav Molchanov, UNC Charlotte

*Title: *On the infinite divisibility of random geometric progressions

November 23, 2022 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *On the infinite divisibility of random geometric progressions

November 15, 2022 by Michael Grabchak

Categories: Probability Seminar

Zhiyi Zhang, UNC Charlotte

Title: Entropy Talk 02: Entropic Statistics.

Abstract: In this talk, I will introduce a framework of Entropic Statistics, including entropic sample space,

entropic censorship, entropic distributions, entropic parameters, entropic moments, entropic basis,

and an entropic characteristic function, etc. Finally I will present two recently established results:

two useful Gaussian processes that could serve as a basis for statistical inference.

October 31, 2022 by Michael Grabchak

Categories: Probability Seminar

Zhiyi Zhang, UNC Charlotte

*Title:* Entropy Talk 00: What is Entropy?

*Abstract*: In this seminar, I would like to start with a discussion on a very fundamental question about entropy: what is entropy? After that, I would like to present some of my thoughts on several other questions:

1) Why is Statistics (as we know it) not a bigger part of modern data sciences, such as Machine Learning and Artificial Intelligence?

2) Why have my submitted papers been rejected from left to right by Statistics journals in recent years?

3) What differences are there between the way of thinking in classical Statistics and that of entropy based Statistics?

Several examples will be used to illustrate my arguments. Finally, I will present an entropic version of the Glivenko-Cantelli Theorem,

as a fundamental theorem of entropy based Statistics.

October 19, 2022 by Michael Grabchak

Categories: Probability Seminar

Vladimir Panov, HSE University

*Title:* Mellin Transform Techniques for Statistical Inference

*Abstract*: My talk is devoted to the application of Mellin transform techniques to various statistical problems arising in the context of mixture models. For variance-mean mixtures, I will present a new semiparametric approach based on the properties of the superposition of Mellin and Laplace transforms. Later, I will show an adaptation of this method to more complicated models of moving average Levy processes, which is closely related to a wide (and rather popular) class of models known as the ambit fields. Also we will present some new theoretical facts concerning the Mellin transform (e.g., the analogue of the Berry-Esseen inequality), which yield some fresh ideas for the statistical estimation in the classical model of multiplicative mixtures.

October 19, 2022 by Michael Grabchak

Categories: Probability Seminar

Zhiyi Zhang, UNC Charlotte

*Title: * Entropy Talk 1: Khinchin’s 4th Axiom Revisited

*Abstract*: Shannon’s information entropy is great. But do there exist any other entropies that are as good or better? The answer is YES. In this seminar, I will show you a few of such entropies and tell you how I found them.

September 25, 2022 by Michael Grabchak

Categories: Probability Seminar

Isaac Sonin, UNC Charlotte

*Title: * Locks-Bombs-Testing Model

*Abstract*: I will discuss a very general Defense/Attack resource allocation model, where the Defender has some number of “locks” to protect n vulnerable boxes (sites), and the Attacker is trying to destroy these boxes, having some number of “bombs”, which can be placed into the boxes. Similar models were studied in game theory – e.g. (Colonel) Blotto games, but our model has a feature that is absent from the previous literature. Here, the Attacker tests the vulnerability of all sites before allocating her resources. These tests are not perfect and a test can give a positive result for a box without a lock and a negative result for a box with a lock. I will describe the full solution for several special cases and will discuss a possible approach to a solution for the general case. The only prerequisite for this talk is knowledge of the Total Probability formula and Bayes’ formula.

September 13, 2022 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *Random geometric progressions and diffusions on affine groups

September 13, 2022 by Michael Grabchak

Categories: Probability Seminar

Michael Grabchak, UNC Charlotte

*Title: *Does Molchanov’s transform preserve infinite divisibility?

March 10, 2020 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *An Introduction to Markov Dynamics

February 18, 2020 by Michael Grabchak

Categories: Probability Seminar

Stanislav Molchanov, UNC Charlotte

*Title: *Random Permutations and Dickman’s Law Part 3