Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models.
Fast and accurate Monte Carlo sampling of first-passage times from Wiener diffusion models.
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DOI：
10.1038/srep20490
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发表时间：
2016-02-11
影响因子：
4.6
通讯作者：
Drugowitsch J
中科院分区：
文献类型：
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作者：
Drugowitsch J
我们提出了一种新的，快速的方法从维纳扩散模型绘制边界交叉样本。扩散模型广泛应用于二选一决策中的模型选择和反应时间。这些模型的样本可以用来模拟他们预测的选择和反应时间。反过来，这些样本可以用来调整模型的参数，以匹配从人类和其他动物观察到的行为。通常，此类样本是通过以离散时间步长模拟随机微分方程来提取的，这很慢，并且会导致反应时间估计的偏差。相反，我们的方法有助于已知的首次通过时间密度的表达式，这会导致无偏的，精确的样本和在典型情况下的速度增加一百到一千倍。在其最基本的形式，它仅限于扩散模型的对称边界和非泄漏的积累，但我们的方法可以扩展到也处理非对称边界或近似泄漏的积累。
We present a new, fast approach for drawing boundary crossing samples from Wiener diffusion models. Diffusion models are widely applied to model choices and reaction times in two-choice decisions. Samples from these models can be used to simulate the choices and reaction times they predict. These samples, in turn, can be utilized to adjust the models’ parameters to match observed behavior from humans and other animals. Usually, such samples are drawn by simulating a stochastic differential equation in discrete time steps, which is slow and leads to biases in the reaction time estimates. Our method, instead, facilitates known expressions for first-passage time densities, which results in unbiased, exact samples and a hundred to thousand-fold speed increase in typical situations. In its most basic form it is restricted to diffusion models with symmetric boundaries and non-leaky accumulation, but our approach can be extended to also handle asymmetric boundaries or to approximate leaky accumulation.