The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

The thriving developer community has a significant impact on the widespread use of R software. To better understand this community, we conducted a study analyzing all R packages available on CRAN. We identified the most popular topics of R packages by text mining the package descriptions. Additionally, using network centrality measures, we…

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their…

Meta-analyses of clinical trials targeting rare events face particular challenges when the data lack adequate numbers of events for all treatment arms. Especially when the number of studies is low, standard random-effects meta-analysis methods can lead to serious distortions because of such data sparsity. To overcome this, we suggest the use of…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

To compute the probability of having a disease, given a positive test result, is a standard probability problem. The sensitivity and specificity of the test must be given and the prevalence of the disease. We ask how a test-maker might determine the tradeoff between sensitivity and specificity. Adding hypothetical costs for detecting or failing to…

One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…

In this article, a Bayesian model selection approach is introduced that can select the best of a set of inequality and equality constrained hypotheses for contingency tables. The hypotheses are presented in terms of cell probabilities allowing researchers to test (in)equality constrained hypotheses in a format that is directly related to the data.…

Sharing user information between systems is an area of interest for every field involving personalization. Recommender Systems are more advanced in this aspect than Intelligent Tutoring Systems (ITSs) and Intelligent Learning Environments (ILEs). A reason for this is that the user models of Intelligent Tutoring Systems and Intelligent Learning…

A Bayesian approach for finding latent classes in data is discussed. The approach uses finite mixture models to describe the underlying structure in the data and demonstrate that the possibility of using full joint probability models raises interesting new prospects for exploratory data analysis. The concepts and methods discussed are illustrated…

During the last years, development of open learning environments that support effectively their users has been a challenge for the research community of educational technologies. The open interactive nature of these environments results in users experiencing difficulties in coping with the plethora of available functions, especially during their…