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Kernel Density Independence Sampling based Monte Carlo Scheme (KISMCS) for inverse hydrological modeling

Posterior sampling methods are increasingly being used to describe parameter and model predictive uncertainty in hydrologic modelling. This paper proposes an alternative to random walk chains (such as DREAM-zs). We propose a sampler based on independence chains with an embedded feature of standardized importance weights based on Kernel density estimates. A Markov Chain Monte Carlo sampling algorithm is proposed with Metropolis-Hastings (M-H) updates using an independence sampler. The independence sampler ensures that candidate observations are drawn independently of the current state of a chain, thereby ensuring efficient exploration of the target distribution. The M-H acceptance-rejection criterion is used to sample across 3 chains, which ensures that the chains are well mixed. Kernel density estimation on last 600 samples in a chain is used to calculate standardized importance weights within the independence sampler to ensure fast convergence of sampled points to the target distribution. Its performance is contrasted with a state of the art algorithm, Differential Evolution Adaptive Metropolis (DREAM-zs), based on a toy 10 dimensional bi-modal Gaussian mixture distribution and HYMOD model based synthetic and real world case studies. The comparison of KISMCS and DREAM-zs is done based on their convergence to ‘true’ posterior parameter distributions in case of synthetics case studies and their convergence to a stationary distribution in case of real world hydrological modeling case studies.