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：模型误设定会给概率模型的实施带来重大挑战，这促使人们开发了一系列直接应对该问题的鲁棒方法。然而，是否需要采用这些更复杂的方法取决于模型是否真的被误设定，但目前缺乏通用的方法来回答这一问题。本文提出了一种此类方法。具体而言，我们针对复杂的复合检验问题提出了基于核的假设检验，其中我们关注的是数据是否来自某个参数族中的任意分布。我们的检验利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，包括参数模型的密度仅在归一化常数已知时成立的情况，或模型采用模拟器形式的情况。作为主要结果，我们证明能够在同一数据上（无需数据分割）同时估计参数并进行检验，同时维持正确的检验水平。我们的方法在一系列问题上得到了验证，包括检验非参数非归一化密度模型的拟合优度，以及生物细胞网络中难处理的生成模型拟合优度。