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We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. We evaluate our model via a series of simulations as well as apply it to an English assessment data. 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.

In a boundary layer ingestion (BLI) propulsion system, the compressor rotor operates under the condition of a severe inflow distortion because the boundary layers on the surface of aircraft have been ingested. In this situation, the low-momentum fluid would inevitably raise the blade load and aggravate the local aerodynamic losses, thus severely deteriorating the compressor overall aerodynamic performance. The paper has applied a sweep optimization design based on surrogate model and genetic algorithm to a transonic axial-flow compressor at the condition of total pressure distorted inflow. The optimization objective is to improve the compressor efficiency. The sweep design has been implemented through controlling the shape of the blade stacking line and the time-saving steady numerical simulations are mainly utilized in the optimization process. Then, the full-annulus unsteady CFD calculations have been conducted for validating the optimized design and further analyzing the flow mechanisms of performance improvements. The computational results show that the inflow distortion has led to non-uniform distributions of the tip leakage loss and the hub flow separation loss along the circumferential direction. It is found that the rotor blade has suffered from the highest tip leakage losses and hub separation losses during the blade leaving the distorted region. After rotor sweep optimization, both tip leakage and hub separation losses have been notably reduced along the full circumferential direction. Moreover, for different pitchwise locations, the optimized rotor sweep design has achieved more aerodynamic performance improvements in the process of the rotor blade leaving the distorted region than those in the processes of the rotor blade moving out of, moving towards and entering the distorted region. Overall, the optimized design performs better than the baseline design in terms of adiabatic efficiency in the entire operating range. In the meanwhile, the total pressure ratio has been maintained. Specifically, an approximately 0.5% increment of efficiency has been achieved by the optimized design at the optimization point. For this paper, the major purpose is to offer useful guidelines for fan/compressor design strategy to achieve high aerodynamic performances under distorted inflow working condition.

We study the spatial heterogeneity effect on regional COVID-19 pandemic timing and severity by analyzing the COVID-19 growth rate curves in the United States. We propose a geographically detailed functional data grouping method equipped with a functional conditional autoregressive (CAR) prior to fully capture the spatial correlation in the pandemic curves. The spatial homogeneity pattern can then be detected by a geographically weighted Chinese restaurant process prior which allows both locally spatially contiguous groups and globally discontiguous groups. We design an efficient Markov chain Monte Carlo (MCMC) algorithm to simultaneously infer the posterior distributions of the number of groups and the grouping configuration of spatial functional data. The superior numerical performance of the proposed method over competing methods is demonstrated using simulated studies and an application to COVID-19 state-level and county-level data study in the United States., Comment: 33 pages, 4 figures, 2 tables

Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.