Chebyshev Particles
- URL: http://arxiv.org/abs/2309.06373v1
- Date: Sun, 10 Sep 2023 16:40:30 GMT
- Title: Chebyshev Particles
- Authors: Xiongming Dai and Gerald Baumgartner
- Abstract summary: We are first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space.
We propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction.
We have achieved high performance from the experiments for parameter inference in a linear state-space model with synthetic data and a non-linear volatility model with real-world data.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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