


Lecture series on Bayesian analytics
22 Feb 11:35 am to 1:00 pm
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Venues: Ramanujan Hall
Host: Radhendushka Srivastava
Speaker: Prof. Sujit Ghosh, NCSU.
Title: A short course on "Bayesian Analytics in Practice".
Abstract: The Bayesian paradigm provides a natural and practical way for building complex analytical models by expressing the joint model through a sequence of simpler conditional models, making it useful for various hierarchical data structures. This series of lectures will first introduce the general notions of Bayesian methods via hierarchical models, and then expand the topic with the more realistic and complex models that have recently emerged as a result of current Machine Learning (ML) literature. These models will be illustrated through practical applications to various real case studies avoiding much of the theoretical underpinnings. However, pointers to relevant theory will be provided as supplements with additional resources. Participants with basic knowledge of probability theory and statistical inferential framework will find the lectures useful in expanding their toolkit with the advanced use of Bayesian analytical methods. Popular topics such as prior sensitivity analysis, model comparisons, and uncertainty quantification for machine learning methods will be covered. In particular, the lectures will provide the necessary theory and practice for handling missing and censored data, a topic largely ignored in traditional ML methods. The concepts and methods discussed will be demonstrated primarily using R software illustrations, but the methodologies presented can also be carried out by other software (e.g., Python). Group activities during lab will be encouraged, allowing participants to have a handson experience.
Algebra and Number Theory Seminar
Thursday, 22 February 2024, 4:00 pm
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Venue: Ramanujan hall
Host: Sandip Singh
Speaker: Sumit Chandra Mishra
Affiliation: IISER Mohali
Title: Localglobal principles for norms and products of norms over semiglobal fields
Abstract: A wellknown result of Hasse states that the localglobal principle holds for norms over number fields for cyclic extensions. In other words, if L/F is a cyclic extension of number fields then an element \lambda \in F^{\times} is in the image of norm map N_{L/F}: L^{\times} \rightarrow F^{\times} if and only if \lambda is in the image of the norm map locally everywhere, i.e., for completions associated to all archimedean and nonarchimedean places of F. In this talk, we would discuss localglobal principles for norms and product of norms over fields which are function fields of curves over complete discretely valued fields, for example, \mathbb{C}((t))(x).