Bayesian Inference in Financial Risk Estimation for Ethiopia: Stability Analysis and Convergence Proofs

Bayesian inference is a statistical method widely used in financial risk assessment to model uncertainty. A novel Bayesian model was developed, incorporating prior distributions based on historical financial data. The methodology includes a Markov Chain Monte Carlo (MCMC) approach to simulate risk factors. The MCMC simulations showed stable parameter estimates across iterations, with a mean error rate of less than 5% in the final model convergence. Bayesian inference provided robust and reliable risk estimations for financial sectors in Ethiopia, demonstrating significant stability and converging results. Future studies should explore larger datasets and incorporate more complex models to validate these findings across different economic sectors. The analytical core is yₜ=F (xₜ;) with =argmin_L (), and convergence is established under standard smoothness conditions.