<p>The Bayesian Attention with Input Reliability Scaling (BARS), a probabilistic framework for robust cost escalation prediction in construction projects, where data quality often varies significantly due to heterogeneous sources. Traditional attention mechanisms in transformers or LSTMs rely on deterministic weight assignments, which can overemphasize noisy or unreliable features; our method addresses this limitation by reformulating attention weights as random variables governed by posterior distributions inferred from input noise and model uncertainty. The core innovation lies in dynamically adjusting attention weights based on a composite reliability score, which quantifies both input noise through signal-to-noise ratios and model uncertainty via Monte Carlo dropout entropy, thereby prioritizing stable and informative temporal patterns. Furthermore, the framework integrates seamlessly with conventional architectures through a hierarchical transformer design, featuring a reliability estimation subnetwork and a Bayesian multi-head attention layer that samples weights from a Dirichlet distribution. Experiments demonstrate that BARS enhances prediction accuracy under noisy conditions while maintaining computational efficiency. The proposed method not only improves cost forecasting robustness but also provides interpretable reliability flags for preprocessing modules, making it particularly valuable for real-world construction projects with inconsistent data quality. This work bridges the gap between probabilistic deep learning and practical cost escalation analysis, offering a scalable solution for AI-driven decision-making in infrastructure management.</p>