Multi-stage process modeling using Gaussian Processes

In multi-stage processes, dependence on noisy observations of the intermediates is a problem to overcome to predict the outputs accurately. This requires a Multi-Stage Gaussian Process (MSGP)- a modeling idea to incorporate such intermediate observations, considering various observation likelihoods effectively.
The MSGP may further boost predictive performance by indirectly observing the multi-stage process by adopting Directed Acyclic Graph (DAG) architecture and Variational Inference (VI) methods. Such a model would use the prior information and increase the accuracy of inference, making Bayesian optimization and prediction effective in situations where one can hardly make direct observations.