Personalized Risk Calculations with a Generative Bayesian Model: Am I Fast Enough to React in Time?

Abstract

We present a Bayesian modeling and decision procedure to answer the question of whether the reaction speed of a single individual is slower and thus more risky than the speed of a randomly selected individual in a reference population. The behavioral domain under investigation is simple reaction times (SRTs). To do this, we need to consider aspects of Bayesian cognitive modeling, psychometric measurement, person-centered risk calculation, and coding with the experimental, Turing-complete, functional, probabilistic programming language WebPPL. We pursue several goals: First, we lean on the new and paradoxical metaphor of a cautious gunslinger. We think that a whole range of risky situations can be embedded into this metaphor. Second, the above described gunslinger metaphor can be mapped to the framework of Bayesian decision strategies. We want to show by way of example that within this framework the research question ‘transfer the locus of longitudinal control’ in Partial Autonomous Driver Assistant Systems (PADAS) can be tackled. Third, evidence-based priors for our generative Bayesian models are obtained by reuse of meta-analytical results. For demonstration purposes we reuse reaction-time interval estimates of Card, Moran, and Newell’s (CMN’s) meta-analysis, the Model Human Processor (MHP). Fourth, the modification of priors to posterior probability distributions is weighted by a likelihood function, which is used to consider the SRT data from a single subject as evidence and to measure how plausibly alternative prior hypotheses generate these data. Fifth, we want to demonstrate the expressiveness and usefulness of WebPPL in computing posterior distributions and personal probabilities of risk.