Determining Effective Methods of Presenting Bayesian Problems to a General Audience

Abstract

The thesis presents six experiments designed to further understanding of effective methods of presenting Bayesian problems to a general audience. The fi rst four experiments (Part I) focus on general Bayesian reasoning. The nal two experiments (Part II) focus speci fcally on the legal domain. Experiment one compares two leading theories for Bayesian presentation: Macchi's (2000) `nested sets' approach, and Krynski and Tenenbaum's (2007) `causal' approach. It also uses a think aloud protocol, requiring thought-process recording during solution. A nested sets framing effect is found, but no causal framing effect. From the think aloud data, a fi ve-stage solution process (the `nested sets' process), modal among successful individuals, is found. In experiment two, Macchi's approach is tested on a problem with greater ecological validity. An increase in accuracy is still seen. Experiment two also fi nds that conversion of the problem to integers by participants is highly associated with accuracy. Experiment three confi rms the null causal fi nding of experiment one and fi nds that the think aloud protocol itself increases accuracy. Experiment four experimentally tests whether prompting problem conversion to integers, and prompting individuals to follow the nested sets process improve accuracy. No effect is found for conversion, but an effect is found for the nested sets process prompt. Experiment fi ve tested whether statistically untrained individuals can undertake accurate Bayesian reasoning of a legal case including necessary forensic error rates (Fenton et al., 2014). No single individual is found to provide the normative answer. Instead a range of heuristics are found. Building upon this, experiment six compares two approaches to presenting the Bayesian output of a legal case: the popular event tree diagram, and the Bayesian network diagram recommended by (Fenton et al., 2014). Without inclusion of false positives and negatives the event-tree diagram was rated more trust worthy and easy to understand than the Bayesian network diagram. However, including these error types, this pattern reversed.