Bayesian Optimal Experimental Design (BOED) is crucial for adaptive experimentation, where the goal is to maximise information gain about
parameters of interest through sequential decision-making. BOED's significance lies in its ability to optimise experimental processes, reducing
costs and time. However, traditional BOED methods assume the model is well-specified, which can lead to suboptimal designs and poor data
quality when the model is misspecified in real-world scenarios. Addressing this challenge is essential for making BOED robust and widely
applicable. This research aims to develop methodologies to mitigate these challenge