Seminar
Speaker: Dr. Sanjay Chaudhuri, Department of Statistics, University of Nebraska-Lincoln, USA
Host: Koushik Saha
Title: On an Empirical Likelihood-Based Solution to the Approximate Bayesian Computation Problem
Time, day and date: 10:00:00 AM - 11:00:00 AM, Tuesday, February 24
Venue: Online (TBA)
Abstract: For many complex models studied in natural, engineering, and environmental sciences, it is nearly impossible to specify a likelihood for the observed data.  Approximate Bayesian Computation (ABC) methods try to estimate such model parameters only by comparing the given observation and some replicates generated from the model for various input parameter values. No explicit relationship between the parameters and the data is postulated.  In this article, we propose an empirical likelihood (EL) based solution to the ABC problem. By construction, our method is based on an interpretable likelihood (i.e., the EL) which is computed using estimating equations completely specified by the observed and the replicated data and a few well-chosen summary statistics.  The proposed method can be justified through information projections on a specified class of densities.  We further show that the posterior is consistent and discuss several of its favourable large sample and large replication properties.  Illustrative examples from various real-life applications will also be presented.        

This work is joint with Subhroshekhar Ghosh and Pham Thi Kim Cuc, all from the National University of Singapore.

Keywords: ABC; Empirical likelihood; Data-dependent estimating equations; Modified empirical likelihood.

Deep Learning Methods in Mathematical Physics
Speaker: Prof. Ovidiu Calin, Department of Mathematics & Statistics, Eastern Michigan University
Host: S Baskar
Title: Hamilton-Jacobi Theory
Time, day and date: 11:30:00 AM – 12:30:00 PM, Tuesday, February 24
Venue: Ramanujan Hall
Abstract: This lecture presents the Hamilton–Jacobi theory from a neural-network perspective. We study how neural networks can be used to solve the Hamilton–Jacobi equation and recover system dynamics, with applications to the eikonal equation and distance computation. The lecture highlights neural-network-based approaches to solving first-order nonlinear PDEs and demonstrates how Riemannian distances and optimal trajectories can be computed in a data-driven framework.

Pre-synopsis
Speaker: Saikat Maji, IIT Bombay
Host: Mayukh Mukherjee
Title: Perturbative Nodal Geometry: Stability of Nodal Sets and Applications to Dumbbells
Time, day and date: 2:00:00 PM – 3:00:00 PM, Tuesday, February 24
Venue: Room 114
Abstract: -

Statistics and Probability seminar
Speaker: Arnab Chowdhury, TIFR Centre For Applicable Mathematics
Host: Parthanil Roy
Title: Invariant Measures of Branching Brownian Motion
Time, day and date: 3:00:00 PM - 4:00:00 PM, Tuesday, February 24
Venue: Room 113
Abstract: We will discuss the fixed points of one-dimensional, binary branching Brownian motion (BBM). The recent work of Chen, Garban, and Shekhar (PTRF, 2023) classified the fixed points of BBM with the critical drift under the assumption that the fixed points have a top particle almost surely. A related result for supercritical drifts was obtained by Kabluchko (J. Appl. Prob., 2012), but under the more restrictive assumption of a locally finite intensity measure. We study the BBM with both critical and supercritical drifts and obtain a complete characterization of the fixed points without any additional assumptions, thereby removing the top particle hypothesis in the critical drift case. (This talk is based on a joint work with Xinxin Chen, Atul Shekhar, and Shuo Zhu.)

APS
Speaker: Prerna Gupta, IIT Bombay
Host: Prachi Mahajan
Title: Geometry and Analysis in Several Complex Variables
Time, day and date: 3:00:00 PM – 4:00:00 PM, Tuesday, Friday 24
Venue: Ramanujan Hall
Abstract: -