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In today's modern era of Big data, computationally efficient and scalablemethods are needed to support timely insights and informed decision making. Onesuch method is sub-sampling, where a subset of the Big data is analysed andused as the basis for inference rather than considering the whole data set. Akey question when applying sub-sampling approaches is how to select aninformative subset based on the questions being asked of the data. A recentapproach for this has been proposed based on determining sub-samplingprobabilities for each data point, but a limitation of this approach is thatappropriate sub-sampling probabilities rely on an assumed model for the Bigdata. In this article, to overcome this limitation, we propose a model robustapproach where a set of models is considered, and the sub-samplingprobabilities are evaluated based on the weighted average of probabilities thatwould be obtained if each model was considered singularly. Theoretical supportfor such an approach is provided. Our model robust sub-sampling approach isapplied in a simulation study and in two real world applications whereperformance is compared to current sub-sampling practices. The results showthat our model robust approach outperforms alternative approaches.

A model robust sub-sampling approach for Generalised Linear Models in Big data settings