Ashit Baran Aich

Agnideep Aich, Sameera Hewage, Md Monzur Murshed et al.

In this paper, we introduce the A2 Copula Spatial Bayesian Neural Network (A2-SBNN), a predictive spatial model designed to map coordinates to continuous fields while capturing both typical spatial patterns and extreme dependencies. By embedding the dual-tail novel Archimedean copula viz. A2 directly into the network's weight initialization, A2-SBNN naturally models complex spatial relationships, including rare co-movements in the data. The model is trained through a calibration-driven process combining Wasserstein loss, moment matching, and correlation penalties to refine predictions and manage uncertainty. Simulation results show that A2-SBNN consistently delivers high accuracy across a wide range of dependency strengths, offering a new, effective solution for spatial data modeling beyond traditional Gaussian-based approaches.

Jose Cribeiro-Ramallo, Agnideep Aich, Florian Kalinke et al.

Kernel Stein discrepancies (KSDs) have emerged as a powerful tool for quantifying goodness-of-fit over the last decade, featuring numerous successful applications. To the best of our knowledge, all existing KSD estimators with known rate achieve $\sqrt n$-convergence. In this work, we present two complementary results (with different proof strategies), establishing that the minimax lower bound of KSD estimation is $n^{-1/2}$ and settling the optimality of these estimators. Our first result focuses on KSD estimation on $\mathbb R^d$ with the Langevin-Stein operator; our explicit constant for the Gaussian kernel indicates that the difficulty of KSD estimation may increase exponentially with the dimensionality $d$. Our second result settles the minimax lower bound for KSD estimation on general domains.

Agnideep Aich, Ashit Baran Aich, Dipak C. Jain

We propose Temporal Conformal Prediction (TCP), a distribution-free framework for constructing well-calibrated prediction intervals in nonstationary time series. TCP couples a modern quantile forecaster with a split-conformal calibration layer on a rolling window and, in its TCP-RM variant, augments the conformal threshold with a single online Robbins-Monro (RM) offset to steer coverage toward a target level in real time. We benchmark TCP against GARCH, Historical Simulation, and a rolling Quantile Regression (QR) baseline across equities (S&P 500), cryptocurrency (Bitcoin), and commodities (Gold). Three results are consistent across assets. First, rolling QR yields the sharpest intervals but is materially under-calibrated (e.g., S&P 500: 83.2% vs. 95% target). Second, TCP (and TCP-RM) achieves near-nominal coverage across assets, with intervals that are wider than Historical Simulation in this evaluation (e.g., S&P 500: 5.21 vs. 5.06). Third, the RM update changes calibration and width only marginally at our default hyperparameters. Crisis-window visualizations around March 2020 show TCP/TCP-RM expanding and then contracting their interval bands promptly as volatility spikes and recedes, with red dots marking days where realized returns fall outside the reported 95% interval (miscoverage). A sensitivity study confirms robustness to window size and step-size choices. Overall, TCP provides a practical, theoretically grounded solution to calibrated uncertainty quantification under distribution shift, bridging statistical inference and machine learning for risk forecasting.