When scores are used to make decisions about respondents, it is of interest to estimate classification accuracy (CA), the probability of making a correct decision, and classification consistency (CC), the probability of making the same decision across two parallel administrations of the measure. Model-based estimates of CA and CC computed from the…

Large-scale education data are collected via complex sampling designs that incorporate clustering and unequal probability of selection. Multilevel models are often utilized to account for clustering effects. The probability weighted approach (PWA) has been frequently used to deal with the unequal probability of selection. In this study, we examine…

Cluster sampling is common in survey practice, and the corresponding inference has been predominantly design-based. We develop a Bayesian framework for cluster sampling and account for the design effect in the outcome modeling. We consider a two-stage cluster sampling design where the clusters are first selected with probability proportional to…

Given the necessity to bridge the gap between what happened and what is likely to happen, this paper aims to explore how to apply Bayesian inference to cost-effectiveness analysis so as to capture the uncertainty of a ratio-type efficiency measure. The first part of the paper summarizes the characteristics of the evaluation data that are commonly…

How do people make rich inferences from such sparse data? Recent research has explored this inferential ability by investigating probabilistic reasoning in infancy. For example, 8- and 11-month-old infants can make inferences from samples to populations and vice versa (Denison & Xu, 2010a; Xu & Denison, 2009; Xu & Garcia, 2008a). The…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

Recently, researchers have investigated differences in decision making based on description and experience. We address the issue of when experience-based judgments of probability are more accurate than are those based on description. If description is well understood ("transparent") and experience is misleading ("wicked"), it…

Examines the question of how large a sample must be in order to produce empirical Bayes estimates which are preferable to other commonly used estimates, such as proportion correct observed score. (Author/RC)

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute…

A Bayesian Model II approach to the estimation of proportions in m groups is extended to obtain posterior marginal distributions for the proportions. The approach is extended to allow greater use of prior information than previously and the specification of this prior information is discussed. (Author/RC)

Several Bayesian approaches to the simultaneous estimation of the means of k binomial populations are discussed. This has particular applicability to criterion-referenced or mastery testing. (Author/JKS)

The empirical Bayes modeling approach--latent ability random sampling in the item response theory (IRT) context--to the IRT modeling of psychological tests is described. Under the usual empirical Bayes unidimensional IRT modeling approach, the posterior distribution of examinee ability given test response is approximately normal for a long test.…

This paper describes a study, now in progress, of new methods for representing the sampling variability of Mantel-Haenszel differential item functioning (DIF) results, based on the system for categorizing the severity of DIF that is now in place at the Educational Testing Service. The methods, which involve a Bayesian elaboration of procedures…

A linear classification rule (used with equal covariance matrices) was contrasted with a quadratic rule (used with unequal covariance matrices) for accuracy of internal and external classification. The comparisons were made for seven situations which resulted from combining three data conditions (equal and unequal covariance matrices, minimal and…