Leveraging Bayesian Analytics for Real-Time Uncertainty Management and Predictive Risk Intelligence

Modern financial systems operate under persistent uncertainty, rapid data flows, and strict regulatory expectations around model risk. Traditional point-estimate approaches of ten fail to capture parameter uncertainty, regime shifts, and tail behaviour, which can lead to underestimation of risk during stressed periods. This dissertation develops a unified Bayesian analytics framework for real-time uncertainty management and predictive risk intelligence across three core domains: market volatility forecasting, transaction-level fraud detection, and compliance-oriented risk monitoring. First, a Dynamic Linear Model (DLM) for daily S&P 500 volatility is constructed in a state-space setting and estimated with Bayesian methods. The model produces calibrated predictive distributions and achieves competitive or superior performance to GARCH and LSTM baselines in terms of root mean squared error, continuous ranked probability score, and predictive interval coverage. One-step-ahead Value-at-Risk (VaR) forecasts derived from the posterior predictive distribution attain empirical exceedance rates close to the nominal level even during the COVID-19 stress period, demonstrating robust tail-risk quantification. Second, fraud detection is evaluated on a highly imbalanced credit card transaction dataset using two uncertainty-aware classifiers: a hierarchical Bayesian logistic regression model and a compact Bayesian neural network implemented via Monte Carlo dropout. The Bayesian models improve minority-class detection quality at low false positive operating points relative to isolation forest and tree-based baselines, while also producing probabilistic outputs that support threshold setting, investigator prioritisation, and model-risk governance through interpretable posterior summaries. Third, a hierarchical Beta state-space model is proposed for latent compliance risk monitoring using proxy indicators. Posterior trajectories for baseline risk and sensitivity parameters adapt to changing market conditions and highlight periods of elevated latent risk, offering an interpretable early-warning signal even in the absence of fully labelled regulatory outcomes. Together, these components illustrate how a single Bayesian toolkit can deliver calibrated, interpretable, and real-time risk estimates across multiple financial use cases. The thesis also outlines a GPU-enabled microservice architecture for deploying the models at scale, linking methodological contributions to practical implementation in contemporary FinTech environments.

• Supervision