We show that student learning can be accurately modeled using a mixture of learning curves, each of which specifies error probability as a function of time. This approach generalizes Knowledge Tracing [7], which can be viewed as a mixture model in which the learning curves are step functions. We show that this generality yields order-of-magnitude improvements in prediction accuracy on real data...

Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature as to whether such parametric assumptions are important or innocuous. In the context of generalized linear mixed models used to analyze clustered or longitu...

Many conventional statistical procedures are extremely sensitive to seemingly minor deviations from modeling assumptions. This problem is exacerbated in modern high-dimensional settings, where the problem dimension can grow with and possibly exceed the sample size. We consider the problem of robust estimation of sparse functionals, and provide a computationally and statistically efficient algor...

In this review, we first set out the general linear model (GLM) for the non technical reader, as a tool able to do both linear regression and ANOVA within the same flexible framework. We present a short history of its development in the fMRI community, and describe some interesting examples of its early use. We offer a few warnings, as the GLM relies on assumptions that may not hold in all situ...

We statistically analysed the chemical components present in waste water from mines in Galicia (NW Spain). These elements pose a risk to public health and the environment, most particularly in the event of a failure in the containment structure of a pond or dam. The statistical processing of the data, which started with an analysis of the typical contaminants present in mining ponds and dams, p...

A stochastic formulation of the Analytic Hierarchy Process (AHP) using an approach based on Bayesian categorical data models has been developed. However, in categorical data models it is known that the selection of the link function may have an impact on the model estimates. In particular, the selection of the probit link implies an assumption that model error terms are normally distributed and...

background: investigators frequently encounter continuous outcomes with plenty of values clumped at zero called semi-continuous outcomes. the gensini score, one of the most widely used scoring systems for expressing coronary angiographic results, is of this type. the aim of this study was to apply two statistical approaches based on the categorization and original scale of the gensini score to ...

In this paper we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is tted to accumulating data and we provide a uniied theory which explains the \independent increments" structure commonly seen in group sequential test statistics. Our theory covers normal linear models, including the case of correlated observations, and ...