Faculty of Engineering Science, Kansai University, Japan.
Faculty of Engineering Science, Kansai University, Japan.
Neural Netw. 2019 Oct;118:159-166. doi: 10.1016/j.neunet.2019.05.004. Epub 2019 May 15.
Nagata et al. proposed a parameter estimation method using Markov chain Monte Carlo (MCMC) for the spectral deconvolution of observed data. However, a systematic error occurs when the parameters to be estimated are close. In this paper, we first clarify that the exchange symmetry of parameters, which is essentially included in the spectral deconvolution problem, causes the systematic error. In particular, we show that estimation from a single data set is inherently difficult because the posterior distribution becomes unimodal or multimodal depending on the data set when the parameters to be estimated are close. Second, we alleviate the problem to the case of using multiple data sets and propose an extension of the exchange Monte Carlo method to low temperatures. This extension corresponds to bridging the gap between posterior mean (PM) estimation and maximum a posteriori (MAP) estimation. The above alleviation and bridging achieve a good estimation even when the parameters are close.
永田等人提出了一种使用马尔可夫链蒙特卡罗（MCMC）的参数估计方法，用于对观测数据进行光谱解卷积。然而，当要估计的参数接近时，会出现系统误差。在本文中，我们首先阐明，参数的交换对称性，这在本质上包含在光谱解卷积问题中，导致了系统误差。特别是，我们表明，当要估计的参数接近时，由于数据集的不同，后验分布会变成单峰或多峰，因此从单个数据集进行估计本质上是困难的。其次，我们将问题减轻到使用多个数据集的情况，并提出了一种将交换蒙特卡罗方法扩展到低温的方法。这种扩展对应于在后验均值（PM）估计和最大后验（MAP）估计之间架起桥梁。即使参数接近，上述缓解和桥接也可以实现良好的估计。
