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Abstract We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question‐level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi‐dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests. 

Abstract Spatially resolved transcriptomics technologies enable the measurement of transcriptome information while retaining the spatial context at the regional, cellular or sub-cellular level. While previous computational methods have relied on gene expression information alone for clustering single-cell populations, more recent methods have begun to leverage spatial location and histology information to improve cell clustering and cell-type identification. In this study, using seven semi-synthetic datasets with real spatial locations, simulated gene expression and histology images as well as ground truth cell-type labels, we evaluate 15 clustering methods based on clustering accuracy, robustness to data variation and input parameters, computational efficiency, and software usability. Our analysis demonstrates that even though incorporating the additional spatial and histology information leads to increased accuracy in some datasets, it does not consistently improve clustering compared with using only gene expression data. Our results indicate that for the clustering of spatial transcriptomics data, there are still opportunities to enhance the overall accuracy and robustness by improving information extraction and feature selection from spatial and histology data. 

Abstract We propose a Bayesian nonparametric clustering approach to study the spatial heterogeneity effect for functional data observed at spatially correlated locations. We consider a geographically weighted Chinese restaurant process equipped with a conditional autoregressive prior to capture fully the spatial correlation of function curves. To sample efficiently from our model, we customize a prior called Quadratic Gamma, which ensures conjugacy. We design a Markov chain Monte Carlo algorithm to infer simultaneously the posterior distributions of the number of groups and the grouping configurations. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated examples and a U.S. annual precipitation study.