Stefania Mignani

Markov Chain Monte Carlo in Stastical Mechanics

The appearance of the article by N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller marked the birth of the Monte Carlo method for the study of statistical-mechanical systems and of a specific form of “importance sampling”—namely, Markov chain Monte Carlo. After nearly 40 years of statistical usage, this technique has had a profound impact on statistical theory, on both Bayesian and classical statistics. Markov chain Monte Carlo is used essentially to estimate integrals in high dimensions. This article addresses the accuracy of such estimation. Through computer experiments performed on the two-dimensional Ising model, we compare the most common method for error estimates in statistical mechanics. It appears that the moving-block bootstrap outperforms other methods based on subseries values when the number of observations is relatively small and the time correlation between successive configurations decays slowly. Moreover, the moving-block bootstrap enables estimates of the standard error to be made not only for the averages of directly obtained data but also for estimates derived from sophisticated numerical procedures.

An Item Response Theory Model for Student Ability Evaluation Using Computer-Automated Test Results

The aim of this paper is to evaluate the student learning about Computer Science subjects. A questionnaire based on ordinal scored items has been submitted to the students through a computer automated system. The data collected have been analyzed by using a latent variable model for ordinal data within the Item Response Theory framework. The scores obtained from the model allow to classify the students according to the reached competence.

Computer-Automated Testing: An Evaluation of Student Performance

In the last few years, the need for an automated way to assess people has increased quickly because of the growing request from both private and public structures. Many Learning Management Systems (LMS) have been developed in order to automatize the learning and assessment process. In most of the cases these systems don’t allow a quality content evaluation and an efficient ability estimation. In this paper we analyze the features of the Proportional Odd Model (POM), belonging to the Item Response Theory. The POM enables to translate an automatic test deliver in an efficient way in order to get an evaluation through either a summative or a formative way. The data have been collected in some undergraduate courses of Bologna University, by using test delivering and by authoring system developed in ASP and Java, respectively.

Statistics in the 150 years from Italian Unification. SIS 2011 Statistical Conference, Bologna, 8 - 10 June 2011. Book of Abstracts

Statistics in the 150 years from Italian Unification. SIS 2011 Statistical Conference, Bologna, 8 – 10 June 2011. Book of Abstracts