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Mediation analysis aims to assess if, and how, a certain exposure influences an outcome of interest through intermediate variables. This problem has recently gained a surge of attention due to the tremendous need for such analyses in scientific fields. Testing for the mediation effect (ME) is greatly challenged by the fact that the underlying null hypothesis (i.e. the absence of MEs) is composite. Most existing mediation tests are overly conservative and thus underpowered. To overcome this significant methodological hurdle, we develop an adaptive bootstrap testing framework that can accommodate different types of composite null hypotheses in the mediation pathway analysis. Applied to the product of coefficients test and the joint significance test, our adaptive testing procedures provide type I error control under the composite null, resulting in much improved statistical power compared to existing tests. Both theoretical properties and numerical examples of the proposed methodology are discussed.

In this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice.

After graphene was first exfoliated in 2004, research worldwide has focused on discovering and exploiting its distinctive electronic, mechanical, and structural properties. Application of the efficacious methodology used to fabricate graphene, mechanical exfoliation followed by optical microscopy inspection, to other analogous bulk materials has resulted in many more two-dimensional (2D) atomic crystals. Despite their fascinating physical properties, manual identification of 2D atomic crystals has the clear drawback of low-throughput and hence is impractical for any scale-up applications of 2D samples. To combat this, recent integration of high-performance machine-learning techniques, usually deep learning algorithms because of their impressive object recognition abilities, with optical microscopy have been used to accelerate and automate this traditional flake identification process. However, deep learning methods require immense datasets and rely on uninterpretable and complicated algorithms for predictions. Conversely, tree-based machine-learning algorithms represent highly transparent and accessible models. We investigate these tree-based algorithms, with features that mimic color contrast, for automating the manual inspection process of exfoliated 2D materials (e.g., MoSe₂). We examine their performance in comparison to ResNet, a famous Convolutional Neural Network (CNN), in terms of accuracy and the physical nature of their decision-making process. We find that the decision trees, gradient boosted decision trees, and random forests utilize physical aspects of the images to successfully identify 2D atomic crystals without suffering from extreme overfitting and high training dataset demands. We also employ a post-hoc study that identifies the sub-regions CNNs rely on for classification and find that they regularly utilize physically insignificant image attributes when correctly identifying thin materials.