A partially identified model, where the parameters can not be uniquely identified, often arises during statistical analysis. While researchers frequently use Bayesian inference to analyze the models, when Bayesian inference with an off-the-shelf MCMC sampling algorithm is applied to a partially identified model, the computational performance can be poor. It is found that using importance sampling with transparent reparameterization (TP) is one remedy. This method is preferable since the model is known to be rendered as identified with respect to the new parameterization, and at the same time, it may allow faster, i.i.d. Monte Carlo sampling by using conjugate convenience priors. In this paper, we explain the importance sampling method with the TP and a pseudo-TP. We introduce the pseudo-TP, an alternative to TP, since finding a TP is sometimes difficult. Then, we test the methods' performance in some scenarios and compare it to the performance of the off-the-shelf MCMC method - Gibbs sampling - applied in the original parameterization. While the importance sampling with TP (ISTP) shows generally better results than off-the-shelf MCMC methods, as seen in the compute time and trace plots, it is also seen that finding a TP which is necessary for the method may not be easy. On the other hand, the pseudo-TP method shows a mixed result and room for improvement since it relies on an approximation, which may not be adequate for a given model and dataset.

翻译：部分可识别模型——即参数无法被唯一识别的模型——在统计分析中经常出现。尽管研究者常使用贝叶斯推断来分析此类模型，但当采用现成的MCMC采样算法对部分可识别模型进行贝叶斯推断时，其计算性能往往不佳。研究发现，采用透明重参数化（TP）的重要性采样是一种有效的改进方法。该方法的优势在于，已知模型在新参数化下可转化为可识别模型，同时通过使用共轭便利先验，可能实现更快速的独立同分布蒙特卡洛采样。本文阐述了结合TP及伪TP的重要性采样方法。我们引入伪TP作为TP的替代方案，因为寻找TP有时较为困难。随后，我们在若干场景中测试了这些方法的性能，并将其与应用于原始参数化的现成MCMC方法——吉布斯采样——进行对比。虽然TP重要性采样（ISTP）在计算时间和轨迹图方面总体表现优于现成MCMC方法，但研究也发现，寻找该方法所需的TP可能并不容易。另一方面，伪TP方法由于依赖近似处理，其结果具有不稳定性且存在改进空间，因为这种近似可能不适用于特定模型和数据集。