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 hands-on 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: Local-global principles for norms and products of norms over semi-global fields

Abstract: A well-known result of Hasse states that the local-global 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 non-archimedean places of F.  In this talk, we would discuss local-global 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).