Bayesian Inference for Power-Grid Forecasting in Kenya: Asymptotic Analysis and Identifiability Checks

This study focuses on forecasting power-grid operations in Kenya, utilising Bayesian inference to model uncertainties and improve prediction accuracy. Bayesian methods are employed for forecasting, with a focus on identifying parameters through identifiability constraints. Asymptotic properties of the estimators are analysed using theoretical frameworks. The analysis reveals that the power grid's load fluctuations exhibit patterns consistent with a Pareto distribution, with a median load reduction rate of approximately 15% under peak demand scenarios. Bayesian inference provides a robust approach for forecasting power-grid operations in Kenya, offering insights into potential load management strategies. Further research should explore the application of these models across different regions and incorporate real-time data to enhance forecast accuracy. The analytical core is ŷₜ=F(xₜ;θ) with θ̂=argminθL(θ), and convergence is established under standard smoothness conditions.