Nishio Mizuho, Ota Eiji, Matsuo Hidetoshi, Matsunaga Takaaki, Miyazaki Aki, Murakami Takamichi
Department of Radiology, Kobe University Graduate School of Medicine, Kobe, Japan.
Futaba Numerical Technologies, Iruma, Japan.
PeerJ Comput Sci. 2023 Oct 5;9:e1620. doi: 10.7717/peerj-cs.1620. eCollection 2023.
The purpose of this study is to compare two libraries dedicated to the Markov chain Monte Carlo method: pystan and numpyro. In the comparison, we mainly focused on the agreement of estimated latent parameters and the performance of sampling using the Markov chain Monte Carlo method in Bayesian item response theory (IRT).
Bayesian 1PL-IRT and 2PL-IRT were implemented with pystan and numpyro. Then, the Bayesian 1PL-IRT and 2PL-IRT were applied to two types of medical data obtained from a published article. The same prior distributions of latent parameters were used in both pystan and numpyro. Estimation results of latent parameters of 1PL-IRT and 2PL-IRT were compared between pystan and numpyro. Additionally, the computational cost of the Markov chain Monte Carlo method was compared between the two libraries. To evaluate the computational cost of IRT models, simulation data were generated from the medical data and numpyro.
For all the combinations of IRT types (1PL-IRT or 2PL-IRT) and medical data types, the mean and standard deviation of the estimated latent parameters were in good agreement between pystan and numpyro. In most cases, the sampling time using the Markov chain Monte Carlo method was shorter in numpyro than that in pystan. When the large-sized simulation data were used, numpyro with a graphics processing unit was useful for reducing the sampling time.
Numpyro and pystan were useful for applying the Bayesian 1PL-IRT and 2PL-IRT. Our results show that the two libraries yielded similar estimation result and that regarding to sampling time, the fastest libraries differed based on the dataset size.
本研究旨在比较两个专门用于马尔可夫链蒙特卡罗方法的库：pystan和numpyro。在比较中，我们主要关注估计的潜在参数的一致性以及贝叶斯项目反应理论（IRT）中使用马尔可夫链蒙特卡罗方法的采样性能。
使用pystan和numpyro实现贝叶斯1PL-IRT和2PL-IRT。然后，将贝叶斯1PL-IRT和2PL-IRT应用于从一篇已发表文章中获得的两种类型的医学数据。pystan和numpyro都使用相同的潜在参数先验分布。比较了pystan和numpyro之间1PL-IRT和2PL-IRT潜在参数的估计结果。此外，还比较了两个库之间马尔可夫链蒙特卡罗方法的计算成本。为了评估IRT模型的计算成本，从医学数据和numpyro生成了模拟数据。
对于IRT类型（1PL-IRT或2PL-IRT）和医学数据类型的所有组合，pystan和numpyro之间估计的潜在参数的均值和标准差一致性良好。在大多数情况下，numpyro中使用马尔可夫链蒙特卡罗方法的采样时间比pystan中的短。当使用大型模拟数据时，配备图形处理单元的numpyro有助于减少采样时间。
Numpyro和pystan对于应用贝叶斯1PL-IRT和2PL-IRT很有用。我们的结果表明，这两个库产生了相似的估计结果，并且在采样时间方面，最快的库因数据集大小而异。
