In this paper, we present a flexible approach to estimating parametric cumulative Prospect Theory using Hierarchical Bayesian methods. Bayesian methods allow us to include prior knowledge in estimation and heterogeneity in individual responses. The model employs a generalised parametric specification of the value function allowing each individual to be risk-seeking in low-stakes mixed prospects. In addition, it includes parameters accounting for varying levels of model noise across domains (gain, loss, and mixed) and several aspects of lottery design that can influence respondent behaviour. Our results indicate that enhancing value function flexibility leads to improved model performance. Our analysis reveals that choices within the gain domain tend to be more predictable. This implies that respondents find tasks in the gain domain cognitively less challenging in comparison to making choices within the loss and mixed domains.
