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Title: Data integration using hierarchical Gaussian process models under shape constraints Authors:  Shuang Zhou - Arizona State University (United States) [presenting]
Abstract: Data integration has been a hot topic in real-world applications that combines data residing at different sources and extracts the shared information across sources. Hierarchical Bayesian models are a powerful tool for modelling grouped data by modelling the data and their interaction across the groups via hierarchies. We develop a method for data integration under multiple constraints using a hierarchical constrained regression with basis expansion approach. At the global level, we can incorporate multiple constraints simultaneously by finding a one-to-one mapping of the constraints on the coefficient space from the original function space under a suitable basis. At the group level, we integrate a multiplicative random effect into the sub-models with the knowledge of data annotation to estimate the group-wise unknown response deviation. We apply our model to the proton radius puzzle problem in nuclear physics, where the constraints come from the law of physics and the unknown experimental errors associate with the data sources. We recover both the global parameters and the group errors related to the sources in the synthetic data analysis and in the real application we provide reliable analyses to reconcile with the new results for the proton radius extraction.