Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses randomly taking small steps within uncertain regions in the parameter space. We are the first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space where deterministic submanifolds are embedded and propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction. We study the characteristics of Chebyshev particles and embed them into sequential MCMC, a novel sampler with a high acceptance ratio that proposes only a few evaluations. We have achieved high performance from the experiments for parameter inference in a linear Gaussian state-space model with synthetic data and a non-linear stochastic volatility model with real-world data.

Markov链蒙特卡洛(MCMC)是推断隐藏马尔可夫模型的可行方法，但由于参数空间中蒙特卡洛采样器在不确定区域内随机采取小步骤，受维度诅咒的约束往往导致计算上的限制。我们首次将目标的后验分布视为样本在无限维欧几里得空间中的映射，其中嵌入了确定性子流形，并提出了一种通过最大化加权里捷极化量来离散化可矩阵流形的新准则。我们研究了Chebyshev粒子的特性，并将它们嵌入到连续的MCMC中，这是一种高接受率的新型采样器，只提出了少量评估。我们在合成数据的线性高斯状态空间模型和真实数据的非线性随机波动率模型的参数推断实验中取得了高性能。

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