# Sequential effects: A Bayesian analysis of prior bias on reaction time and behavioral choice

 Shunan Zhang University of California, San Diego He Huang University of California, San Diego Angela J. Yu University of California, San Diego

### Abstract

Human subjects exhibit sequential effects" in many psychological experiments, in which they respond more rapidly and accurately to a stimulus when it reinforces a local pattern in stimulus history, compared to when it violates such a pattern. This is often the case even if the local pattern arises by chance, such that stimulus history has no real predictive power, and therefore any behavioral adjustment based on these erroneous predictions essentially amounts to superstition. Earlier, we proposed a normative Bayesian learning model, the Dynamic Belief Model (DBM), to demonstrate that such behavior reflects the engagement of mechanisms that identify and adapt to changing patterns in the environment \cite{Yu2009}. In that earlier work, we assumed a monotonic relationship between prior bias and response time (bias {\it toward} a stimulus was assumed to result in faster reaction time when that was the actual stimulus; conversely, when the other stimulus was present, it was assumed to result in a slower response). Here, we present a more detailed and quantitative analysis of the relationship between prior bias and behavioral outcome, in terms of response time and choice accuracy. We also present novel behavioral data, along with a framework for jointly identifying subject-specific parameters of the trial-by-trial learning (Dynamic Belief Model, DBM) and within-trial sensory processing and decision-making (Drift-Diffusion Model, DDM) based on the behavioral data. Our results provide strong evidence for DBM, and reveal potential individual differences, in their differential beliefs about the timescale at which local patterns persist in sequential data.