A1247
Title: An efficient Bayesian estimation of nonlinear hierarchical decision models
Authors: Emi Mise - University of Leicester (United Kingdom) [presenting]
Sanjit Dhami - University of Leicester (United Kingdom)
Ali al-Nowaihi - University of Leicester (United Kingdom)
James Cannam - University of Leicester (United Kingdom)
Abstract: For estimating decision models such as stochastic cumulative prospect theory (CPT), Bayesian hierarchical modelling is a popular choice. However, standard MCMC algorithms are computationally extremely inefficient or impossible to implement in practice. One, the natural parameters of the statistical model are complex nonlinear functions of the parameters of interest; and two, the dimension of the parameter space grows exponentially with the sample size. An efficient two-stage sampling algorithm is presented, which can cope with any number of parameters. This method is applied to sample the posterior densities of the parameters in two decision theories using experimental data obtained from 556 subjects: CPT and decision by sampling (DbS). The latter has garnered considerable interest but has yet to be tested on experimental data. It is shown that the proposed method works well for both CPT, whose parameters are all continuous and can be transformed to the entire real line, as well as for DbS, which contains a mix of continuous and discrete parameters. It is also demonstrated that DbS has some serious shortcomings despite its early promise.