To extend the proposed Bayesian approach to handle more complex nonlinear models like deep neural networks, several strategies can be employed. One approach is to incorporate Bayesian neural networks (BNNs), which can capture complex nonlinear relationships while providing uncertainty estimates. By defining appropriate prior distributions over the network weights and hyperparameters, the Bayesian framework can be extended to train and make predictions with deep neural networks. Additionally, techniques like variational inference or Markov Chain Monte Carlo (MCMC) sampling can be used to approximate the posterior distribution of the network weights, enabling uncertainty quantification in the predictions. Furthermore, hierarchical Bayesian models can be utilized to model the uncertainty at different levels of the neural network architecture, allowing for more robust and interpretable predictions.