Variational Inference for Bayesian MIDAS Regression

We develop a Coordinate Ascent Variational Inference (CAVI) algorithm for Bayesian Mixed Data Sampling (MIDAS) regression with linear weight parameterizations. The model separates impact coeffcients from weighting function parameters through a normalization constraint, creating a bilinear structure that renders generic Hamiltonian Monte Carlo samplers unreliable while preserving conditional conjugacy exploitable by CAVI. Each variational update admits a closed-form solution: Gaussian for regression coefficients and weight parameters, Inverse-Gamma for the error variance. The algorithm propagates uncertainty across blocks through second moments, distinguishing it from naive plug-in approximations. In a Monte Carlo study spanning 21 data-generating configurations with up to 50 predictors, CAVI produces posterior means nearly identical to a block Gibbs sampler benchmark while achieving speedups of 107x to 1,772x (Table 9). Generic automatic differentiation VI (ADVI), by contrast, produces bias 714 times larger while being orders of magnitude slower, confirming the value of model-specific derivations. Weight function parameters maintain excellent calibration (coverage above 92%) across all configurations. Impact coefficient credible intervals exhibit the underdispersion characteristic of mean-field approximations, with coverage declining from 89% to 55% as the number of predictors grows a documented trade-off between speed and interval calibration that structured variational methods can address. An empirical application to realized volatility forecasting on S&P 500 daily returns cofirms that CAVI and Gibbs sampling yield virtually identical point forecasts, with CAVI completing each monthly estimation in under 10 milliseconds.

Potential-energy gating for robust state estimation in bistable stochastic systems

We introduce potential-energy gating, a method for robust state estimation in systems governed by double-well stochastic dynamics. The observation noise covariance of a Bayesian filter is modulated by the local value of a known or assumed potential energy function: observations are trusted when the state is near a potential minimum and progressively discounted as it approaches the barrier separating metastable wells. This physics-based mechanism differs from statistical robust filters, which treat all state-space regions identically, and from constrained filters, which bound states rather than modulating observation trust. The approach is especially relevant in non-ergodic or data-scarce settings where only a single realization is available and statistical methods alone cannot learn the noise structure. We implement gating within Extended, Unscented, Ensemble, and Adaptive Kalman filters and particle filters, requiring only two additional hyperparameters. Monte Carlo benchmarks (100 replications) on a Ginzburg-Landau double-well with 10% outlier contamination show 57-80% RMSE improvement over the standard Extended Kalman Filter, all statistically significant (p < 10^{-15}, Wilcoxon test). A naive topological baseline using only well positions achieves 57%, confirming that the continuous energy landscape adds ~21 percentage points. The method is robust to misspecification: even with 50% parameter errors, improvement never falls below 47%. Comparing externally forced and spontaneous Kramers-type transitions, gating retains 68% improvement under noise-induced transitions whereas the naive baseline degrades to 30%. As an empirical illustration, we apply the framework to Dansgaard-Oeschger events in the NGRIP delta-18O ice-core record, estimating asymmetry gamma = -0.109 (bootstrap 95% CI: [-0.220, -0.011]) and showing that outlier fraction explains 91% of the variance in filter improvement.

Time Series Foundation Models for Energy Load Forecasting on Consumer Hardware: A Multi-Dimensional Zero-Shot Benchmark

Time Series Foundation Models (TSFMs) have introduced zero-shot prediction capabilities that bypass the need for task-specific training. Whether these capabilities translate to mission-critical applications such as electricity demand forecasting--where accuracy, calibration, and robustness directly affect grid operations--remains an open question. We present a multi-dimensional benchmark evaluating four TSFMs (Chronos-Bolt, Chronos-2, Moirai-2, and TinyTimeMixer) alongside Prophet as an industry-standard baseline and two statistical references (SARIMA and Seasonal Naive), using ERCOT hourly load data from 2020 to 2024. All experiments run on consumer-grade hardware (AMD Ryzen 7, 16GB RAM, no GPU). The evaluation spans four axes: (1) context length sensitivity from 24 to 2048 hours, (2) probabilistic forecast calibration, (3) robustness under distribution shifts including COVID-19 lockdowns and Winter Storm Uri, and (4) prescriptive analytics for operational decision support. The top-performing foundation models achieve MASE values near 0.31 at long context lengths (C = 2048h, day-ahead horizon), a 47% reduction over the Seasonal Naive baseline. The inclusion of Prophet exposes a structural advantage of pre-trained models: Prophet fails when the fitting window is shorter than its seasonality period (MASE > 74 at 24-hour context), while TSFMs maintain stable accuracy even with minimal context because they recognise temporal patterns learned during pre-training rather than estimating them from scratch. Calibration varies substantially across models--Chronos-2 produces well-calibrated prediction intervals (95% empirical coverage at 90% nominal level) while both Moirai-2 and Prophet exhibit overconfidence (~70% coverage). We provide practical model selection guidelines and release the complete benchmark framework for reproducibility.