Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a fully non-Gaussian version of the Hamiltonian Monte Carlo (HMC) sampling filter. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled using a HMC approach (or any other scheme capable of sampling multimodal densities in high-dimensional subspaces). The main filter developed herein is named "cluster HMC sampling filter" (ClHMC). A multi-chain version of the ClHMC filter, namely MC-ClHMC is also proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption in the HMC filtering paradigm.
['Ahmed Attia', 'Azam S. Zavar Moosavi', 'Adrian Sandu']
I am writing a research paper on a idea Cluster Sampling Filters for Non-Gaussian Data Assimilation
[{"from": "human", "value": "I am writing a research paper on a idea Cluster Sampling Filters for Non-Gaussian Data Assimilation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  presents a fully non-Gaussian version of the Hamiltonian Monte Carlo (HMC) sampling filter. The Gaussian prior assumption in the original HMC filter is relaxed. Specifically, a clustering step is introduced after the forecast phase of the filter, and the prior density function is estimated by fitting a Gaussian Mixture Model (GMM) to the prior ensemble. Using the data likelihood function, the posterior density is then formulated as a mixture density, and is sampled using a HMC approach (or any other scheme capable of sampling multimodal densities in high-dimensional subspaces). The main filter developed herein is named \"cluster HMC sampling filter\" (ClHMC). A multi-chain version of the ClHMC filter, namely MC-ClHMC is also proposed to guarantee that samples are taken from the vicinities of all probability modes of the formulated posterior. The new methodologies are tested using a quasi-geostrophic (QG) model with double-gyre wind forcing and bi-harmonic friction. Numerical results demonstrate the usefulness of using GMMs to relax the Gaussian prior assumption in the HMC filtering paradigm."}]