Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: As a key sampling scheme in Markov chain Monte Carlo (MCMC) methods, Gibbs sampling is widely used in various research fields due to its elegant univariate conditional sampling, especially in tacking with multidimensional sampling systems. , a Gibbs-based sampler named as symmetric Metropolis-within-Gibbs (SMWG) algorithm is proposed for lattice Gaussian sampling. By adopting a symmetric Metropolis-Hastings (MH) step into the Gibbs update,  show the Markov chain arising from it is geometrically ergodic, which converges exponentially fast to the stationary distribution. Moreover, by optimizing its symmetric proposal distribution, the convergence efficiency can be further enhanced.
['Zheng Wang', 'Cong Ling']
I am writing a research paper on a idea Symmetric Metropolis-within-Gibbs algorithm for lattice Gaussian sampling
[{"from": "human", "value": "I am writing a research paper on a idea Symmetric Metropolis-within-Gibbs algorithm for lattice Gaussian sampling"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: As a key sampling scheme in Markov chain Monte Carlo (MCMC) methods, Gibbs sampling is widely used in various research fields due to its elegant univariate conditional sampling, especially in tacking with multidimensional sampling systems. , a Gibbs-based sampler named as symmetric Metropolis-within-Gibbs (SMWG) algorithm is proposed for lattice Gaussian sampling. By adopting a symmetric Metropolis-Hastings (MH) step into the Gibbs update,  show the Markov chain arising from it is geometrically ergodic, which converges exponentially fast to the stationary distribution. Moreover, by optimizing its symmetric proposal distribution, the convergence efficiency can be further enhanced."}]