This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent. In the case of separable tests, we demonstrate the mathematical causes of paradoxical results, develop a computationally feasible means to check whether they can occur in any given test, and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them.

Bayesian statistics offers a normative description for how a person should combine their original beliefs (i.e., their priors) in light of new evidence (i.e., the likelihood). Previous research suggests that people tend to under-weight both their prior (base rate neglect) and the likelihood (conservatism), although this varies by individual and situation. Yet this work generally elicits people’s knowledge as single point estimates (e.g., x has a 5% probability of occurring) rather than as a full distribution. Here we demonstrate the utility of eliciting and fitting full distributions when studying these questions. Across three experiments, we found substantial variation in the extent to which people showed base rate neglect and conservatism, which our method allowed us to measure for the first time simultaneously at the level of the individual. While most people tended to disregard the base rate, they did so less when the prior was made explicit. Although many individuals were conservative, there was no apparent systematic relationship between base rate neglect and conservatism within each individual. We suggest that this method shows great potential for studying human probabilistic reasoning.

Arachnoid cysts are benign cysts occurring in the intra-arachnoid space and containing cerebrospinal fluid. They constitute approximately 1 per cent of all intracranial masses. They are uncommon in the posterior cranial fossa. Common presenting symptoms include headaches, seizures, focal neurologic signs and vague dizziness. Magnetic resonance imaging is the preferred method of investigation, and the treatment for symptomatic cysts is generally surgical drainage.

We report the unusual presentation of a young patient with a posterior fossa arachnoid cyst that manifested in the form of isolated unilateral sensorineural hearing loss. The patient underwent posterior fossa craniotomy and marsupialization of the cyst. To our knowledge, posterior fossa arachnoid cyst presenting with isolated hearing loss alone has not been reported in the English literature. A review of the literature pertaining to posterior fossa arachnoid cysts, including the clinical features, diagnosis and management, is also presented.