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)
Gaussian limit theorem for posterior distribution in the problem of conflicting expert opinions
2023 · ARTICLE · en
. Suppose we have n experts who have their prior opinions about the unknown probability q in the experiment with a binary outcome. It is known that expert opinions are in conflict with each other. To model “conflicting” expert opinions a prior distribution based on Selberg’s integral is constructed. We prove a theorem regarding the limiting properties of the posterior distribution. Also, differential entropy and the Kullback-Leibler (KL) divergence of such posterior are studied.
Response-adaptive randomization for multiarm clinical trials using context-dependent information measures
2023 · ARTICLE · en
Theoretical-information approach applied to the clinical trial designs appeared to bring several advantages when tackling a problem of finding a balance between power and expected number of successes (ENS). In particular, it was shown that the built-in parameter of the weight function allows finding the desired trade-off between the statistical power and number of treated patients in the context of small population Phase II clinical trials. However, in real clinical trials, randomized designs are more preferable. The goal of this research is to introduce randomization to a deterministic entropy-based sequential trial procedure generalized to multiarm setting. Several methods of randomization applied to an entropy-based design are investigated in terms of statistical power and ENS. Namely, the four design types are considered: (a) deterministic procedures, (b) naive randomization using the inverse of entropy criteria as weights, (c) block randomization, and (d) randomized penalty parameter. The randomized entropy-based designs are compared to randomized Gittins index (GI) and fixed randomization (FR). After the comprehensive simulation study, the following conclusion on block randomization is made: for both entropy-based and GI-based block randomization designs the degree of randomization induced by forward-looking procedures is insufficient to achieve a decent statistical power. Therefore, we propose an adjustment for the forward-looking procedure that improves power with almost no cost in terms of ENS. In addition, the properties of randomization procedures based on randomly drawn penalty parameter are also thoroughly investigated.
Wasserstein and weighted metrics for multidimensional Gaussian distributions
2023 · ARTICLE · en
We present a number of low and upper bounds for L\эevy – ´Prokhorov, Wasserstein, Frechet, and Hellinger distances between ´ probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the minimum of different errors in sensitive hypothesis testing are proved
ON A MIXED SINGULAR/SWITCHING CONTROL PROBLEM WITH MULTIPLE REGIMES
2022 · ARTICLE · en
This paper studies a mixed singular/switching stochastic control problem for a multidimensional di usion with multiple regimes on a bounded domain. Using probabilistic, partial di erential equation (PDE) and penalization techniques, we show that the value function associated with this problem agrees with the solution to a Hamilton-Jacobi-Bellman (HJB) equation. In that way, we see that the regularity of the value function is smooth enough.
Weighted Gaussian entropy and determinant inequalities
2022 · ARTICLE · en
We produce a series of results extending information-theoretical inequalities (dis- cussed by Dembo and CoverThomas in 1988-1991) to a weighted version of entropy. Most of the resulting inequalities involve the Gaussian weighted entropy; they imply a number of new relations for determinants of positive-definite matrices. Unlike the Shannon entropy where the contribution of an outcome depends only upon its prob- ability, the weighted (or context-dependent) entropy takes into account a `value' of an outcome determined by a given weight function '. An example of a new result is a weighted version of the strong Hadamard inequality (SHI) between the determinants of a positive-definitenite d by d matrix and its square blocks (sub-matrices) of different size. When the weight equals 1, the weighted inequality becomes a `standard' SHI; in general, the weighted version requires some assumptions upon '. The SHI and its weighted version generalize a widely known `usual' Hadamard inequality.
What scientific folklore knows about the distances between the most popular distributions?
2022 · ARTICLE · en
We present a number of upper and low bounds for the total variation distances between the most popular probability distributions. In particular, some estimates of the total variation distances between one-dimensional Gaussian distributions, between two Poisson distributions, between two binomial distributions, between a binomial and a Poisson distribution, and also between two negative binomial distributions are given. The Kolmogorov – Smirnov distance is also presented.
Response Adaptive Designs for Phase II Trials with Binary Endpoint Based on Context-Dependent Information Measures
2021 · ARTICLE · en
In many rare disease Phase II clinical trials, two objectives are of interest to an investigator: maximising the statistical power and maximising the number of patients responding to the treatment. These two objectives are competing, therefore, clinical trial designs offering a balance between them are needed. Recently, it was argued that response-adaptive designs such as families of multi-arm bandit (MAB) methods could provide the means for achieving this balance. Furthermore, response-adaptive designs based on a concept of context-dependent (weighted) information criteria were recently proposed with a focus on Shannon’s differential entropy. The information-theoretic designs based on the weighted Renyi, Tsallis and Fisher informations are also proposed. Due to built-in parameters of these novel designs, the balance between the statistical power and the number of patients that respond to the treatment can be tuned explicitly. The asymptotic properties of these measures are studied in order to construct intuitive criteria for arm selection. A comprehensive simulation study shows that using the exact criteria over asymptotic ones or using information measures with more parameters, namely Renyi and Tsallis entropies, brings no sufficient gain in terms of the power or proportion of patients allocated to superior treatments. The proposed designs based on information-theoretical criteria are compared to several alternative approaches. For example, via tuning of the built-in parameter, one can find designs with powercomparable to the fixed equal randomisation’s but a greater number of patients responded in the trials.
Вероятность и статистика в примерах и задачах: в 3 т.
2021 · BOOK · ru
Для освоения теории вероятностей и математической статистики тре- нировка в решении задач и выработка интуиции важны не меньше, чем изучение доказательств теорем; большое разнообразие задач по этому пред- мету затрудняет студентам переход от лекций к экзаменационным задачам, а от них—к практике. Специфический предмет этого тома, цепи Маркова и их применения, переживает последнее время большой подъем. Многие замечательные тео- ретические результаты были получены в этой области, которая долгое вре- мя рассматривалась многими специалистами как «мертвая» зона. Активную роль в развитии этой области играют именно прикладные исследования. Предмет этой книги критически важен как для современных приложений (финансовая математика, менеджмент, телекоммуникации, обработка сиг- налов, биоинформатика), так и для приложений классических (актуарная математика, социология, инженерия). Авторы собрали большое количество упражнений, снабженных полны- ми решениями. Эти решения адаптированы к нуждам и умениям учащихся. Необходимые теоретические сведения приводятся по ходу изложения; кроме того, текст снабжен историческими отступлениями. Настоящее издание осуществляется в двух выпусках. Часть I в основном ориентирована на студентов и преподавателей. Часть II в основном ориен- тирована на аспирантов и научных работников.
Fair Insurance Premium Rate in Connected SEIR Model under Epidemic Outbreak
2021 · ARTICLE · en
In this paper, we aim to determine an optimal insurance premium rate for health-care in deterministic and stochastic SEIR models. The studied models consider two standard SEIR centres characterised by migration fluxes and vaccination of population. The premium is calculated using the basic equivalence principle. Even in this simple set-up, there are non-intuitive results that illustrate how the premium depends on migration rates, the severity of a disease and the initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program affects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.
Response adaptive designs for Phase II trials with binary endpoint based on context-dependent information measures
2021 · ARTICLE · en
In many rare disease Phase II clinical trials, two objectives are of interest to an investigator: maximising the statistical power and maximising the number of patients responding to the treatment. These two objectives are competing, therefore, clinical trial designs offering a balance between them are needed. Recently, it was argued that response-adaptive designs such as families of multi-arm bandit (MAB) methods could provide the means for achieving this balance. Furthermore, response-adaptive designs based on a concept of context-dependent (weighted) information criteria were recently proposed with a focus on Shannon’s differential entropy. The information-theoretic designs based on the weighted Renyi, Tsallis and Fisher informations are also proposed. Due to built-in parameters of these novel designs, the balance between the statistical power and the number of patients that respond to the treatment can be tuned explicitly. The asymptotic properties of these measures are studied in order to construct intuitive criteria for arm selection. A comprehensive simulation study shows that using the exact criteria over asymptotic ones or using information measures with more parameters, namely Renyi and Tsallis entropies, brings no sufficient gain in terms of the power or proportion of patients allocated to superior treatments. The proposed designs based on information-theoretical criteria are compared to several alternative approaches. For example, via tuning of the built-in parameter, one can find designs with power comparable to the fixed equal randomisation’s but a greater number of patients responded in the trials.
Курсы (1)
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Методологический научно-исследовательский семинар
2023/2024 · Магистратура · рус