We propose a Markov chain Monte Carlo-based deconvolution method designed to estimate the number of peaks in spectral data, along with the optimal parameters of each radial basis function. Assuming cases where the number of peaks is unknown, and a sweep simulation on all candidate models is computationally unrealistic, the proposed method efficiently searches over the probable candidates via trans-dimensional moves assisted by annealing effects from replica exchange Monte Carlo moves. Through simulation using synthetic data, the proposed method demonstrates its advantages over conventional sweep simulations, particularly in model selection problems. Application to a set of olivine reflectance spectral data with varying forsterite and fayalite mixture ratios reproduced results obtained from previous mineralogical research, indicating that our method is applicable to deconvolution on real data sets.

中文翻译：

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使用简单可逆跳跃动作的快速贝叶斯反卷积

我们提出了一种基于马尔可夫链蒙特卡罗的反卷积方法，旨在估计光谱数据中的峰数以及每个径向基函数的最佳参数。假设情况是未知的，并且所有候选模型的扫描模拟在计算上都不现实，则该方法通过副本交换蒙特卡洛运动的退火效应辅助的多维运动有效地搜索了可能的候选对象。通过使用合成数据进行仿真，该方法证明了其优于常规扫描仿真的优势，尤其是在模型选择问题上。将具有不同镁橄榄石和铁橄榄石混合比的橄榄石反射光谱数据应用到以前的矿物学研究中得出的结果，