The next meeting of the National Seminar on Probability and Statistics will be held on February 14, 2024, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Computable inference for generalised Wright-Fisher processes will be delivered by Nathan Judd (University of Warwick, UK). Abstract.In this talk, we will introduce a class of [0,1]-valued Markov processes with jumps that, as signals in hidden Markov models, admits a computable (exact) filter. By computable filter we mean that each filtering distribution, i.e., the law of the signal at a time t given the data up to time t, is explicitly and exactly available as a finite mixture of Dirichlet distributions. We exploit the tractability of the Wright-Fisher diffusion, in particular, its [...]

The next meeting of the National Seminar on Probability and Statistics will be held on January 24, 2024, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Wave field source localization using antenna arrays as a statistical problem of multidimensional linear system parameter estimation will be delivered by Alexander Varypaev (National Institute of Geophysics, Geodesy and Geography, BAS). Abstract. The problem of statistical estimation of the coordinates of wave field sources from observations masked by additive random noise is considered. A likelihood-based estimate of source parameters is proposed for an unknown deterministic source function and additive noise correlated in time and space. The property of this estimate to suppress spatially correlated noise is mathematically justified. A statistical justification [...]

The next meeting of the National Seminar on Probability and Statistics will be held on December 6, 2023, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Brownian Motion Conditioned to Spend Limited Time Outside a Bounded Interval - An Extreme Example of Entropic Repulsion will be delivered by Dominic Т. Schickentanz (TU Darmstadt). Abstract. We condition a Brownian motion on \mathbb{R}_{\ge 0} on spending a total of at most s>0 time units outside a bounded interval. We describe the resulting process in terms of an SDE and discuss the surprising result in the context of entropic repulsion. Moreover, we explicitly determine the exact asymptotic behavior of the probability that a Brownian motion on [0,T] [...]

The next meeting of the National Seminar on Probability and Statistics will be held on November 15, 2023, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Anti-concentration of Rademacher sums and Tomaszewski's counterpart problem will be delivered by Julien Portier, University of Cambridge. Abstract

The next meeting of the National Seminar on Probability and Statistics will be held on November 8, 2023, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: Hamiltonicity of randomly perturbed graphs will be delivered by Alberto Espuny Díaz (Postdoctoral researcher at Universität Heidelberg, Germany). Abstract. In parallel to the development of smoothed analysis of algorithms, the study of randomly perturbed graphs has thrived in the combinatorics community. The setup is the following: one considers a dense graph $H$ which fails to satisfy some increasing property and then sprinkles edges randomly until the property appears. A main goal in the area is to understand how many random edges are needed, and which graphs $H$ are "worst" for this [...]

The next meeting of the National Seminar on Probability and Statistics will be held on June 28, 2023, at 2:00 p.m. in Room 503 of the Institute of Mathematics and Informatics. A talk on: The inverse first-passage time problem for general stochastic processes including Lévy processes and diffusions (joint work with Mladen Savov) will be delivered by Alexander Klump (postdoctoral fellow (DAAD) at the IMI-BAS).  Abstract. The inverse first-passage time problem for a stochastic process X(t), t ≥ 0, consists of the following question. Given a distribution on the positive real numbers, does there exist a function b such that the first-passage time τ = inf{t > 0 : X_t ≥ b(t)} has this given distribution? In this talk we will give conditions on [...]

The next meeting of the National Seminar on Probability and Statistics will be held on May 31, 2023, at 2:00 p.m. (UTC +2) in Room 503 of the Institute of Mathematics and Informatics. A talk on: Upper and lower bounds on extreme Value-at-Risk: Optimization in infinite measure spaces will be delivered by Stilian Stoev (Department of Statistics, University of Michigan,Ann Arbor). The talk is based on joint work with Robert Yuen and Dan Cooley.    

The next meeting of the National Seminar on Probability and Statistics will be held on April 26, 2023, at 2:00 p.m. (UTC +2) in Room 503 of the Institute of Mathematics and Informatics. A talk on: On two problems and results which Kolmogorov considered to be among the most surprising ones will be delivered by Yordan M. Stoyanov (IMI - BAS, Shandong University, China).    

The next meeting of the National Seminar on Probability and Statistics will be held on March 1, 2023, at 2:00 p.m. (UTC +2) in Room 403 of the Institute of Mathematics and Informatics. A talk on: The inverse first-passage time problem for Brownian motion will be delivered by Alexander Klump (postdoctoral fellow (DAAD) at the IMI-BAS). Abstract: Given a fixed probability distribution on the positive real numbers, the inverse first-passage time problem is to find a time-varying boundary such that the first-passage time by a Brownian motion over that boundary has the fixed distribution. The aim of this talk is to give an overview of the existing literature, which is concerned with existence, uniqueness and properties of solutions, as well as to present an [...]

The next meeting of the National Seminar on Probability and Statistics will be held on February 15, 2023, at 2:00 p.m. (UTC +2) in Room 403 of the Institute of Mathematics and Informatics. A talk on: The Disorder Problem. A POMDP approach will be delivered by Doncho Donchev (FMI - SU). Abstract: We revisit the discrete time disorder problem. The classical approach to it is based on optimal stopping rules and martingale techniques. We include it into the framework of Partially Observable Markov Decision Processes which improves the quality of detection, and allows, in some cases, to find solutions to Bellman's equation.