Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss new adaptive proposal strategies for sequential Monte Carlo algorithms—also known as particle filters—relying on new criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus,  show how the long-used coefficient of variation (suggested by [10]) of the ights can be used for estimating the chi-square distance beten the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis  obtain an auxiliary adjustment multiplier ight type for which this chi-square distance is minimal. Moreover,  establish an empirical estimate of linear complexity of the Kullback-Leibler divergence beten the involved distributions. Guided by these results,  discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example.
['Julien Cornebise', 'Eric Moulines', 'Jimmy Olsson']
I am writing a research paper on a idea Adaptive methods for sequential importance sampling with application to state space models
[{"from": "human", "value": "I am writing a research paper on a idea Adaptive methods for sequential importance sampling with application to state space models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss new adaptive proposal strategies for sequential Monte Carlo algorithms\u2014also known as particle filters\u2014relying on new criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is a major concern and can dramatically influence the quality of the estimates. Thus,  show how the long-used coefficient of variation (suggested by [10]) of the ights can be used for estimating the chi-square distance beten the target and instrumental distributions of the auxiliary particle filter. As a by-product of this analysis  obtain an auxiliary adjustment multiplier ight type for which this chi-square distance is minimal. Moreover,  establish an empirical estimate of linear complexity of the Kullback-Leibler divergence beten the involved distributions. Guided by these results,  discuss adaptive designing of the particle filter proposal distribution and illustrate the methods on a numerical example."}]