Sequential classification on partially ordered sets
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In this article, a general theorem on the asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set.Abstract:
Summary. A general theorem on the asymptotically optimal sequential selection of experiments is presented and applied to a Bayesian classification problem when the parameter space is a finite partially ordered set. The main results include establishing conditions under which the posterior probability of the true state converges to 1 almost surely and determining optimal rates of convergence. Properties of a class of experiment selection rules are explored.read more
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Data analytic methods for latent partially ordered classification models
TL;DR: A general framework is presented for data analysis of latent finite partially ordered classification models and it is demonstrated that sequential analytic methods can dramatically reduce the amount of testing that is needed to make accurate classifications.
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Test Construction for Cognitive Diagnosis
TL;DR: In this article, a general CDM index based on Kullback-Leibler information is proposed to measure how informative an item is for the classification of examinees, and the effectiveness of the index is examined for items calibrated using the deterministic input noisy gate model and the reparameterized unified model by implementing a simple heuristic to construct a test from an item bank.
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Patterns of Diagnosed Mathematical Content and Process Skills in TIMSS-R Across a Sample of 20 Countries
TL;DR: Interestingly, success in geometry was found to be highly associated with logical reasoning and other important mathematical thinking skills across the sampled countries.
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When Cognitive Diagnosis Meets Computerized Adaptive Testing: CD-CAT
TL;DR: This paper showcases the application of the optimal sequential selection methodology in item selection of CAT that is built upon cognitive diagnostic models, and proposes two new heuristics that are compared against the randomized item selection method and the two heuristic investigated in Xu et al. (2003).
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An Overview of Recent Developments in Cognitive Diagnostic Computer Adaptive Assessments.
TL;DR: In this article, the authors provide practitioners and researchers with an introduction to and overview of recent developments in cognitive diagnostic computer adaptive assessments, which aim to diagnose examinees' mastery status of a group of discretely defined skills or attributes, thereby providing them with detailed information regarding their specific strengths and weaknesses.
References
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Book
Introduction to lattices and order
TL;DR: The Stone Representation Theorem for Boolean algebras and its application to lattices in algebra can be found in this article, where the structure of finite distributive lattices and finite Boolean algebraic structures are discussed.
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