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：模型误设定可能为概率模型的实施带来重大挑战，这促使了一系列直接解决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真的被误设定，而目前普遍缺乏回答此问题的通用方法。本文提出了一种这样的方法。具体而言，我们针对具有挑战性的复合检验问题提出了基于核的假设检验，该检验旨在判断数据是否来自某个参数族中的任意分布。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。该方法具有广泛的适用性，包括参数模型密度仅已知归一化常数的情况，或模型采用模拟器形式的情况。作为主要结论，我们证明能够在同一份数据上（无需数据分割）同时进行参数估计和假设检验，同时保持正确的检验水平。本文在一系列问题上展示了该方法的应用，包括对非参数未标准化密度模型的拟合优度检验，以及对生物细胞网络中难以处理的生成模型的检验。