Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznań, Poland.
J Chem Phys. 2011 Feb 7;134(5):054112. doi: 10.1063/1.3544494.
In this work we explore the statistical properties of the maximum likelihood-based analysis of one-color photon arrival trajectories. This approach does not involve binning and, therefore, all of the information contained in an observed photon strajectory is used. We study the accuracy and precision of parameter estimates and the efficiency of the Akaike information criterion and the Bayesian information criterion (BIC) in selecting the true kinetic model. We focus on the low excitation regime where photon trajectories can be modeled as realizations of Markov modulated Poisson processes. The number of observed photons is the key parameter in determining model selection and parameter estimation. For example, the BIC can select the true three-state model from competing two-, three-, and four-state kinetic models even for relatively short trajectories made up of 2 × 10(3) photons. When the intensity levels are well-separated and 10(4) photons are observed, the two-state model parameters can be estimated with about 10% precision and those for a three-state model with about 20% precision.
在这项工作中，我们探索了基于最大似然的单色光子到达轨迹分析的统计特性。这种方法不涉及分箱，因此，所有观测到的光子轨迹中包含的信息都被利用了。我们研究了参数估计的准确性和精度，以及 Akaike 信息准则和贝叶斯信息准则 (BIC) 在选择真实动力学模型方面的效率。我们专注于低激发状态，其中光子轨迹可以被建模为马尔可夫调制泊松过程的实现。观测到的光子数量是决定模型选择和参数估计的关键参数。例如，即使对于由 2×10(3)个光子组成的相对较短的轨迹，BIC 也可以从竞争的二态、三态和四态动力学模型中选择真实的三态模型。当强度水平相差较大并且观测到 10(4)个光子时，二态模型的参数可以估计到约 10%的精度，而三态模型的参数可以估计到约 20%的精度。
