Bayesian model averaging based deep learning forecasts of inpatient bed occupancy in mental health facilities

Mental health disorders affect over 15% of the global working-age population, contributing to an annual economic loss of approximately USD 1 trillion due to diminished productivity and increased healthcare expenditures. In India, the post-pandemic surge in hospitalizations has placed additional strain on mental health infrastructure, exacerbating an already significant treatment gap. Overcrowding and inadequate forecasting mechanisms have resulted in occupancy rates that exceed hospital capacity, underscoring the urgent need for predictive tools to support admission planning and resource allocation. This study introduces a novel forecasting framework that applies Bayesian Model Averaging (BMA) with Zellner's g-prior used here for the first time alongside deep learning models for predicting weekly bed occupancy at India's second-largest mental health hospital. Time series data from 2008 to 2024 were used to train six models: Time Delay Neural Networks (TDNN), Recurrent Neural Networks (RNN), Gated Recurrent Units (GRU), Long Short-Term Memory (LSTM), Bidirectional LSTM (BiLSTM), and Bidirectional GRU (BiGRU). Model performance was optimized using random search (RS) and grid search (GS) hyperparameter tuning, allowing the framework to account for model uncertainty while improving predictive accuracy and consistency. Among all models, BiLSTM with GS tuning and BMA-GS model showed the best forecasting performance for bed-occupancy, achieving 98.06% accuracy (MAPE: 1.939%) and effectively capturing weekly fluctuations within ±13 beds. In contrast, RS-tuned models yielded higher errors (MAPE: 2.331%). Moreover, the average credible interval width decreased from 16.34 under BMA-RS to 13.28 with BMA-GS, indicating improved forecast precision and reliability. This study demonstrates that embedding Bayesian statistics specifically BMA with Zellner's g-prior into deep learning architectures offers a robust and scalable solution for forecasting hospital bed occupancy. The proposed framework enhances predictive accuracy and reliability, supporting data-driven planning for hospital administrators and policymakers. It aligns with the objectives of India's National Mental Health Programme (NMHP) and Sustainable Development Goal 3, advancing equitable and efficient access to mental healthcare.