Ratcliff扩散决策模型首达时间密度的另一种近似
Another Approximation of the First-Passage Time Densities for the Ratcliff Diffusion Decision Model
摘要：
提出了一种新的方法来近似Ratcliff扩散决策模型（DDM）中的首次通过时间的概率密度函数（PDF）。我们使用$\texttt{R}$包$\texttt{Rcpp}$在$\texttt{C++}$中实现了这种近似方法，以利用更快的$\texttt{C++}$语言，同时保持$\texttt{R}$语言接口。除了我们的新的近似方法，我们还编译了所有已知的近似方法的DDM密度函数（固定和可变的漂移率），包括以前未使用的技术组合中发现的相关文献。我们将这些近似方法移植到$\texttt{C++}$中，并对其进行了优化，使其能够在这种新语言中运行。给定PDF近似值的可接受误差容限，我们对所有这些近似方法进行基准测试，以比较它们的速度，并与文献中常用的$\texttt{R}$函数进行比较。这些测试的结果表明，我们的新的近似方法不仅是数量级快于目前的标准，但它也比所有其他近似方法，即使在翻译和优化后，更快的$\texttt{C++}$语言。所有这些近似方法都捆绑在$\texttt{R}$统计计算语言的$\texttt{fddm}$包中;该包可通过CRAN获得，源代码可在GitHub上获得。
英文摘要：
We present a novel method for approximating the probability density function (PDF) of the first-passage times in the Ratcliff diffusion decision model (DDM). We implemented this approximation method in $\texttt{C++}$ using the $\texttt{R}$ package $\texttt{Rcpp}$ to utilize the faster $\texttt{C++}$ language while maintaining the $\texttt{R}$ language interface. In addition to our novel approximation method, we also compiled all known approximation methods for the DDM density function (with fixed and variable drift rate), including previously unused combinations of techniques found in the relevant literature. We ported these approximation methods to $\texttt{C++}$ and optimized them to run in this new language. Given an acceptable error tolerance in the value of the PDF approximation, we benchmarked all of these approximation methods to compare their speed against each other and also against commonly used $\texttt{R}$ functions from the literature. The results of these tests show that our novel approximation method is not only orders of magnitude faster than the current standards, but it is also faster than all of the other approximation methods available even after translation and optimization to the faster $\texttt{C++}$ language. All of these approximation methods are bundled in the $\texttt{fddm}$ package for the $\texttt{R}$ statistical computing language; this package is available via CRAN, and the source code is available on GitHub.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
