Empirical Priors in Polytomous Computerized Adaptive Tests: Risks and Rewards in Clinical Settings

The use of empirical prior information about participants has been shown to substantially improve the efficiency of computerized adaptive tests (CATs) in educational settings. However, it is unclear how these results translate to clinical settings, where small item banks with highly informative polytomous items often lead to very short CATs. We explored the risks and rewards of using prior information in CAT in two simulation studies, rooted in applied clinical examples. In the first simulation, prior precision and bias in the prior location were manipulated independently. Our results show that a precise personalized prior can meaningfully increase CAT efficiency. However, this reward comes with the potential risk of overconfidence in wrong empirical information (i.e., using a precise severely biased prior), which can lead to unnecessarily long tests, or severely biased estimates. The latter risk can be mitigated by setting a minimum number of items that are to be administered during the CAT, or by setting a less precise prior; be it at the expense of canceling out any efficiency gains. The second simulation, with more realistic bias and precision combinations in the empirical prior, places the prevalence of the potential risks in context. With similar estimation bias, an empirical prior reduced CAT test length, compared to a standard normal prior, in 68% of cases, by a median of 20%; while test length increased in only 3% of cases. The use of prior information in CAT seems to be a feasible and simple method to reduce test burden for patients and clinical practitioners alike.     

Peat Bogs,Sperm, and Family Values: Teaching Naturalism Charitably

Introductory courses dealing with sex, gender and sexuality often assign excerpts from Thomas Aquinas as an exemplar of the naturalist view. Given that most novice students tend to side against such naturalism uncritically, they need to be exposed to a more charitable account of the biological considerations motivating a stance like Aquinas.’ With that in mind, this article presents accessible arguments aimed at restoring deliberative balance in the classroom.     

On Adjoint and Brain Functors

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate parts (left and right representations of heteromorphisms). Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory and is focused on the interpretation and application of the mathematical concepts.