A Bayesian Analysis of a Multiple Choice Test

In a multiple choice test, examinees gain points based on how many correct responses they got. However, in this traditional grading, it is assumed that questions in the test are replications of each other. We apply an item response theory model to estimate students' abilities characterized by item's feature in a midterm test. Our Bayesian logistic Item response theory model studies the relation between the probability of getting a correct response and the three parameters. One parameter measures the student's ability and the other two measure an item's difficulty and its discriminatory feature. In this model the ability and the discrimination parameters are not identifiable. To address this issue, we construct a hierarchical Bayesian model to nullify the effects of non-identifiability. A Gibbs sampler is used to make inference and to obtain posterior distributions of the three parameters. For a ""nonparametric"" approach, we implement the item response theory model using a Dirichlet process mixture model. This new approach enables us to grade and cluster students based on their ""ability"" automatically. Although Dirichlet process mixture model has very good clustering property, it suffers from expensive and complicated computations. A slice sampling algorithm has been proposed to accommodate this issue. We apply our methodology to a real dataset obtained on a multiple choice test from WPI’s Applied Statistics I (Spring 2012) that illustrates how a student's ability relates to the observed scores

China the anomaly : Hannah Arendt, totalitarianism and the PRC

During the autumn of 1949, Hannah Arendt completed the manuscript of The Origins of Totalitarianism. On 1 October of the same year, the People’s Republic of China was founded under the leadership of Mao Zedong. This article documents Arendt’s claim in 1949 that the prospects of totalitarianism in China were ‘frighteningly good’, and yet her ambivalent judgment, on the eve of the Cultural Revolution, about the totalitarian character of the Maoist regime. Despite being the premier theorist of totalitarian formations, Arendt’s interest in China was half-hearted and her analysis often wildly inaccurate. The concern of this paper, however, is less with the veracity of her remarks, than with a counterfactual question. If Arendt had known what we know now, would she have considered Maoist China to be a totalitarian regime? Put another way: to what extent is our modern picture of Mao’s regime consistent with Arendt’s depiction of the Soviet Union under Stalin or Germany under Hitler? While Arendt got many of her facts wrong, her theory of totalitarianism — as shapeless, febrile, voracious of human flesh, and endlessly turbulent — was in good measure applicable to Mao’s regime, even though she failed to recognize it

Experiments of keV negative ions transmitted through straight and tapered glass capillaries: tilt angle dependence

In this study, experiments are performed to study the transmission of 15 keV C− ions through straight and tapered borosilicate glass capillaries. The tilt angle is varied from 0° to 0.8°. In a straight capillary, the transmitted ions produced only one spot on the detector, and its intensity declined with increasing tilt angle. In this case, almost 98% of the transmitted particles maintained their initial charge. However, in the tapered capillary, the transmitted particles formed a different pattern composed of a core and a halo. The negative ion fractions of the core and the halo were 97.5% and 42.5% at a 0° tilt angle, respectively. Therefore, the particles formed the halo by scattering after colliding with the inner surface of the capillary, and most of them were neutralized. As the tilt angle increased, the intensity and negative ion fraction of the transmitted particles declined, and the halo gradually became quite asymmetric. These results indicate that the scattering process plays a role in the transmission