Computationally efficient Bayesian unit-level random neural network modelling of survey data under informative sampling for small area estimation

Abstract The topic of neural networks has seen a surge of interest in recent years. However, one of the main challenges with these approaches is quantification of uncertainty. The use of random weight models offer a potential solution. In addition to uncertainty quantification, these models are extremely computationally efficient as they do not require optimisation through stochastic gradient descent. We show how this approach can be used to account for informative sampling of survey data through the use of a pseudo-likelihood. We illustrate the effectiveness of this methodology through simulation and data application involving American National Election Studies data.