ABSTRACT
This chapter provides an overview of assessment and the central challenges that may be advantageously addressed by adopting a Bayesian perspective. In psychometrics, it presents knowledge representations found in quantitative methods, including Bays' theorem and other mathematical equations, graphical models, and graphical representations of data. The evidence-centered design (ECD) provides a framework for working through the many details, relationships, and pieces of machinery that make an operational assessment, including the psychometric models. ECD is also prescriptive in the sense that it provides a set of guiding principles for the design of assessment, the aim of which is to articulate how the assessment can be used to make warranted inferences. In educational assessment, we employ a probability model to quantify how likely certain behaviors on tasks are, given the student's proficiencies. The terminology of ECD reflects its origins in educational assessment, but the notions may be interpreted more broadly.
