Dept of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur 741246, India.
The Institute of Mathematical Sciences-HBNI, CIT Campus, Taramani, Chennai 600113, India.
Sci Rep. 2017 Jan 31;7:41638. doi: 10.1038/srep41638.
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the Ornstein-Uhlenbeck process and can be observed directly in experiment. Here we present Bayesian methods for inferring the parameters of this process, the trap stiffness and the particle diffusion coefficient, that use exact likelihoods and sufficient statistics to arrive at simple expressions for the maximum a posteriori estimates. This obviates the need for Monte Carlo sampling and yields methods that are both fast and accurate. We apply these to experimental data and demonstrate their advantage over commonly used non-Bayesian fitting methods.
贝叶斯推断为估计在离散时间点观测到的随机过程的参数提供了一种有条理的方法。在光阱中受限的粒子的过阻尼布朗运动通常由 Ornstein-Uhlenbeck 过程建模，并且可以在实验中直接观察到。在这里，我们提出了贝叶斯方法来推断该过程的参数，即阱的刚度和粒子扩散系数，这些方法使用精确似然和充分统计量，得到了最大后验估计的简单表达式。这避免了需要蒙特卡罗采样，并产生了快速而准确的方法。我们将这些方法应用于实验数据，并证明了它们比常用的非贝叶斯拟合方法具有优势。
