Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more involved methods are required will depend on whether the model is really misspecified, and there is a lack of generally applicable methods to answer this question. In this paper, we propose one such method. More precisely, we propose kernel-based hypothesis tests for the challenging composite testing problem, where we are interested in whether the data comes from any distribution in some parametric family. Our tests make use of minimum distance estimators based on the maximum mean discrepancy and the kernel Stein discrepancy. They are widely applicable, including whenever the density of the parametric model is known up to normalisation constant, or if the model takes the form of a simulator. As our main result, we show that we are able to estimate the parameter and conduct our test on the same data (without data splitting), while maintaining a correct test level. Our approach is illustrated on a range of problems, including testing for goodness-of-fit of an unnormalised non-parametric density model, and an intractable generative model of a biological cellular network.

翻译：模型误设会给概率模型的实现带来重大挑战，这促使了一系列直接应对该问题的鲁棒方法的发展。然而，是否需要采用这些更为复杂的方法取决于模型是否确实存在误设，而目前缺乏通用的方法来回答这一问题。在本文中，我们提出了一种这样的方法。具体而言，针对具有挑战性的复合检验问题（即我们关注数据是否来自某个参数族中的任意分布），我们提出了基于核的假设检验。我们的检验采用了基于最大均值差异和核斯坦差异的最小距离估计量。这些方法具有广泛的适用性，包括在参数模型的密度仅归一化常数已知、或模型以模拟器形式存在的情况下。作为主要结果，我们证明能够在不进行数据分割的情况下，使用同一数据集同时完成参数估计和假设检验，同时保持正确的检验水平。我们的方法在一系列问题上得到了验证，包括对未归一化的非参数密度模型进行拟合优度检验，以及对一个棘手的生物细胞网络生成模型进行检验。