贝叶斯方法与频率论方法的结合：不可识别性条件下的推理研究
Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability
摘要：
越来越复杂的应用涉及大型数据集与非线性和高维数学模型的组合。在这种情况下，统计推断是一个具有挑战性的问题，需要务实的方法，利用贝叶斯和频率论的方法。贝叶斯方法的优雅性在于实验数据和先验假设提供的信息内容对模型预测的后验概率分布的传播。然而，对于复杂的应用，实验数据和先验假设可能约束后验概率分布不够。在这些情况下，贝叶斯马尔可夫链蒙特卡罗抽样可能是不可行的。从频率论的观点来看，不充分的实验数据和先前的假设可以被解释为不可识别性。轮廓似然方法提供了检测和解决不可识别性的实验设计迭代。因此，它允许更好地约束后验概率分布，直到可以安全地使用马尔可夫链蒙特卡罗抽样。使用细胞生物学的应用程序，我们比较了这两种方法，并表明，这两种方法的连续应用，有利于模型预测的不确定性的现实评估。
英文摘要：
Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.
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