Кельберт Марк Яковлевич
Факультет экономических наук
Профессиональные интересы
Должности
- Профессор-исследователь — Факультет экономических наук, Департамент статистики и анализа данных
- Ведущий научный сотрудник — Факультет экономических наук, Международная лаборатория стохастического анализа и его приложений
Био
- · Начал работать в НИУ ВШЭ в 2014 году.
- · Научно-педагогический стаж: 73 года.
Образование
- 1982 · Кандидат физико-математических наук
- 1968 · Специалитет: Московский государственный университет им. М.В. Ломоносова, факультет: мех-мат, специальность «Математика», квалификация «Математик»
Опыт работы
- · 1993-1998: Lecturer at European Business School, Swansea University, UK
- · 1998-2004: Reader at European Business School, Swansea University, UK
- · 2004-2014: Reader at Department of Mathematics, Swansea University, UK
- · 2014: Начал работать в НИУ ВШЭ в году
- · Научно-педагогический стаж: 49 лет.
Награды и поощрения
- · Почетная грамота НИУ ВШЭ (декабрь 2025)
- · Медаль "Признание - 10 лет успешной работы" НИУ ВШЭ (ноябрь 2025)
- · Благодарность департамента статистики и анализа данных НИУ ВШЭ (январь 2025)
- · Благодарность факультета экономических наук НИУ ВШЭ (январь 2022)
- · Благодарность проректора НИУ ВШЭ (август 2021)
- · Благодарственное письмо ректора НИУ ВШЭ (ноябрь 2020)
- · Надбавка за публикацию в международном рецензируемом научном издании (2022–2023, 2021–2022, 2020–2022, 2017–2019)
- · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2024–2029, 2023–2028)
- · Надбавка за статью в зарубежном рецензируемом журнале (2015–2017)
- · Победитель Конкурса лучших русскоязычных научных и научно-популярных работ работников НИУ ВШЭ – 2022
Гранты и проекты
- — · Я был научным руководителем нескольких грантов в Великобритании: EPSRC, British Academy,
- — · London Mathematical Society и т. д. Кроме того. я получал гранты в Бразилии (FAPESP).
Конференции (2)
Показать все
- · 39-я междисциплинарная школа-конференция "Информационные технологии и системы 2015", ИППИ РАН, Сочи, Сентябрь 2015.
- · "Asymptotic analysis of the Renyi, Tsallis and Fisher entropies in a Bayesian problem"
Идентификаторы исследователя
- ORCID:
0000-0002-3952-2012 - ResearcherID:
F-7255-2016 - SPIN РИНЦ:
7972-7182 - Google Scholar: https://scholar.google.com/citations?user=Okrgp24AAAAJ&hl=en
- Scopus AuthorID:
55884702600
Публикации (53)
A new view on migration processes between SIR centra: an account of the different dynamics of host and guest
2015 · ARTICLE · en
-We study an epidemic propagation between M popuilation centra. The novelty of the model lies in the explicit analysis of the dynamics of host (remaining nin the same cemtre) and guest (migrated from another centre) population separately.
Shannon's differential entropy asymptotic analysis in a Bayesian problem
2015 · ARTICLE · en
We study the asymptotic behaviour of differential entropy in a Bayesian problem of estimationg a probability of success in a series of conditionally independent trials.
Asymptotic behaviour of the weighted Renyi and Fisher entropies in a Bayesian problem
2015 · ARTICLE · en
Consider a Bayesian problem of success probability estimation in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of the weighted differential entropy for posterior probability density function conditional on x successes after n conditionally independent trials when n tends to infinity. Suppose that one is interested to know whether the coin is approximately fair with a high precision and for large n is interested in the true frequency. In other words, the statistical decision is particularly sensitive in small neighbourhood of the particular value γ = 1/2. For this aim the concept of weighted differential entropy used when the frequency γ is necessary to emphasize. It was found that the weight in suggested form does not change the asymptotic form of Shannon, Renyi, Tsallis and Fisher entropies, but changes the constants. The leading term in weighted Fisher Information is changed by some constant which depends on distance between the true frequency and the value we want to emphasize.
Asymptotic analysis of the Renyi, Tsallis and Fisher entropies in a Bayesian problem
2015 · CHAPTER · en
Consider a Bayesian problem of estimating of probability of success in a series of trials with binary outcomes. We study the asymp- totic behaviour of weighted differential entropy for posterior probability density function (PDF) conditional on x successes after n trials, when n → ∞. Suppose that one is interested to know whether the coin is fair or not and for large n is interested in true frequency. In other words, one wants to emphasize the parameter value p = 1/2. To do so the concept of weighted differential entropy introduced in [1968] is used when the frequency γ is necessary to emphasize. It was found that the weight in suggested form does not change the asymptotic form of Shannon, Renyi, Tsallis and Fisher entropies, but change the constants. The leading term in weighted Fisher Information is changed by some constant which depend on distance between the true frequency and the value we want to emphasize.
Earthquake forecasting: Statistics and Information
2015 · ARTICLE · en
The paper presents a dicision rule forming a mathematical basis of earthquake forecasting problem. We develop an axiomatic approach to earthquake forecasting in terms of a multicomponent random fields on a lattice.
Теория информации и кодирование
2014 · BOOK · ru
Этот том включает стандартный пакет информационно-теоретического материала, обычно читаемого на факультетахинформатики и электроники, а также прикладной математики, ведущих университетов, наряду с некоторыми новыми результатами. При этом излагаются как вероятнростные, так и алгебраические аспекты теории информации и кодирования, включая как основы теории, так и некоторые ее современные аспекты. Предмет этой книги критически важен для современных приложений ( телекоммуникации, обработка сигналов, информатика, криптография).
Probability and Statistics by Example, Vol. 1
2014 · BOOK · en
Probability and statistics are as much about intuition and problem solving as they are about theorem proving. Consequently, students can find it difficult to make a successful transition from lectures, to examinations, to practice because the problems involved can vary so much in nature. Since the subject is critical in so many applications, from insurance, to telecommunications, to bioinformatics, the authors have collected more than 200 worked examples to help the students develop a deep understanding of the subject rather than a superficial knowledge of sophisticated theories. With amusing stories and historical asides sprinkled thoughout, this enjoyable book will leave students better equipped to solve problems in practice and under exam conditions.
A quantum Mermin-Wagner theorem for a generalized Hubbard model
2013 · ARTICLE · en
We study symmetry properties of bosonic quantum systems over 2D graphs, with continuous spins, in the spirit of the Mermin-Wagner theorem. The Hamiltonian includes a kinetic part responsible for the motion of a particle while “trapped” by a given atom, as well as a potential part. The system under consideration can be considered as a generalized (bosonic) Hubbard model. The result of the paper is that any (appropriately defined) Gibbs states generated by the above Hamiltonian preserves continuous symmetry,provided that the thermodynamic variables (the fugacity 𝑧 and the inverse temperature 𝛽) satisfy a certain restriction. The definition of a Gibbs state (and its analysis) is based on the Feynman-Kac representation for the density matrices.
A quantum Mermin-Wagner theorem for quantum rotators on two-dimentional graph
2013 · ARTICLE · en
We study symmetry properties of quantum systems over 2D graphs or manifolds, with continuous spins, in the spirit of the Mermin-Wagner' theorem. In the model of quantum rotators the phase space of a single spin is a d-dimensional torus, and spins (or particles) are attached to sites of a graph satisfying a special bi-dimensional property. We construct the so-called infinite-volume Gibbs state, with or without boundary conditions. Next, we study the problem of preserving or spontaneous breaking of continuous symmetry.
Курсы (1)
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Методологический научно-исследовательский семинар
2023/2024 · Магистратура · рус