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Model fitting is possibly the most extended problem in science. Classical approaches include the use of least-squares fitting procedures and maximum likelihood methods to estimate the value of the parameters in the model. However, in recent…
This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an…
Most Item Response Theory (IRT) models for dichotomous responses are based on probit or logit link functions which assume a symmetric relationship between the probability of a correct response and the latent traits of individuals submitted…
Accelerated life testing (ALT) is typically used to assess the reliability of material's lifetime under desired stress levels. Recent advances in material engineering have made a variety of material alternatives readily available. To…
Computerized Adaptive Testing (CAT) has proven effective for efficient LLM evaluation on multiple-choice benchmarks, but modern LLM evaluation increasingly relies on generation tasks where outputs are scored continuously rather than marked…
With the rapid advancement of intelligent education, Computerized Adaptive Testing (CAT) has attracted increasing attention by integrating educational psychology with deep learning technologies. Unlike traditional paper-and-pencil testing,…
Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's…
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
Computerized Adaptive Testing (CAT) measures an examinee's ability while adapting to their level. Both too many questions and too many hard questions can make a test frustrating. Are there some CAT algorithms which can be proven to be…
Adaptive online testing efficiently assesses examinee proficiency by dynamically adjusting the difficulty of test items based on their performance. To achieve this, items are selected so that their difficulty closely matches the test…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
Existing Computerized Adaptive Testing (CAT) frameworks typically select questions based on the predicted likelihood that the student will answer correctly. This design ignores information contained in students' open-ended responses,…
Interim assessment is frequently administered via computerized adaptive testing (CAT), offering direct support to teaching and learning. This study attempted to fill a vital knowledge gap about the nuanced landscape of examinees'…
In this article, we propose a novel probabilistic framework to improve the accuracy of a weighted majority voting algorithm. In order to assign higher weights to the classifiers which can correctly classify hard-to-classify instances, we…
Model evaluation is a critical component in supervised machine learning classification analyses. Traditional metrics do not currently incorporate case difficulty. This renders the classification results unbenchmarked for generalization.…
Item difficulty plays a crucial role in test performance, interpretability of scores, and equity for all test-takers, especially in large-scale assessments. Traditional approaches to item difficulty modeling rely on field testing and…
This paper considers multiple binary hypothesis tests with adaptive allocation of sensing resources from a shared budget over a small number of stages. A Bayesian formulation is provided for the multistage allocation problem of minimizing…
Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in…
Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing…
Traditional Item Response Theory models assume the distribution of the abilities of the population in study to be Gaussian. However, this may not always be a reasonable assumption, which motivates the development of more general models.…