  Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of
complex statistical distributions, and while bypassing the cumbersome
requirement of a specific analytical expression for the target, this stochastic
exploration of an uncertain parameter space comes at the expense of a large
number of samples, and this computational complexity increases with parameter
dimensionality. Although at the exploration level, some methods are proposed to
accelerate the convergence of the algorithm, such as tempering, Hamiltonian
Monte Carlo, Rao-redwellization, and scalable methods for better performance,
it cannot avoid the stochastic nature of this exploration. We consider the
target distribution as a mapping where the infinite-dimensional Eulerian space
of the parameters consists of a number of deterministic submanifolds and
propose a generalized energy metric, termed weighted Riesz energy, where a
number of points is generated through pairwise interactions, to discretize
rectifiable submanifolds. We study the properties of the point, called Riesz
particle, and embed it into sequential MCMC, and we find that there will be
higher acceptance rates with fewer evaluations, we validate it through
experimental comparative analysis from a linear Gaussian state-space model with
synthetic data and a non-linear stochastic volatility model with real-world
data.
