Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS).  provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution.  further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.
['Yizhe Zhang', 'Xiangyu Wang', 'Changyou Chen', 'Ricardo Henao', 'Kai Fan', 'Lawrence Carin']
I am writing a research paper on a idea Towards Unifying Hamiltonian Monte Carlo and Slice Sampling
[{"from": "human", "value": "I am writing a research paper on a idea Towards Unifying Hamiltonian Monte Carlo and Slice Sampling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS).  provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution.  further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications."}]