Adaptive Kernel-density Independence Sampling based Monte Carlo Sampling (A-KISMCS) for inverse hydrological modelling

Markov chain Monte Carlo (MCMC) methods have been applied in many hydrologic studies to explore posterior parameter distributions within a Bayesian framework. Accurate estimation of posterior parameter distributions is key to reliably estimate marginal likelihood functions and hence to reliably estimate measures of Bayesian complexity. This paper introduces an alternative to well-known random walk based MCMC samplers. An Adaptive Kernel Density Independence Sampling based Monte Carlo Sampling (A-KISMCS) is proposed. A-KISMCS uses an independence sampler with Metropolis-Hastings (M-H) updates which ensures that candidate observations are drawn independently of the current state of a chain. This ensures efficient exploration of the target distribution. The bandwidth of the kernel density estimator is also adapted online in order to increase its accuracy and ensure fast convergence to a target distribution. The performance of A-KISMCS is tested on one several case studies, including synthetic and real world case studies of hydrological modelling and compared with Differential Evolution Adaptive Metropolis (DREAM-zs), which is fundamentally based on random walk sampling with differential evolution. Results show that while DREAM-zs converges to slightly sharper posterior densities, A-KISMCS is slightly more efficient in tracking the mode of the posteriors.