Measuring the influence of prior beliefs on probabilistic estimations

Measuring the influence of prior beliefs on probabilistic estimations. Alex Filipowicz 1 (alsfilip@uwaterloo.ca) Derick Valadao 1 (dvaladao@uwaterloo.ca) Britt Anderson 1,2 (britt@uwaterloo.ca) James Danckert 1 (jdancker@uwaterloo.ca) Department of Psychology, University of Waterloo Centre for Theoretical Neuroscience, University of Waterloo 200 University Ave W, Waterloo, ON, Canada Abstract Previous research has shown that the mental models partici- pants use throughout a task influence the efficiency with which they learn and adapt to changes in their environment (Lee & Johnson-Laird, 2013; Stottinger et al, 2014). We wanted to measure the influence of different types of mental models participants hold before engaging in a task. Using a modified version of the game “Plinko”, participants predict- ed the likelihood that a ball falling through pegs would land in one of forty slots. Importantly, participants were asked to make likelihood estimations before seeing the first ball drop. This initial probability estimate was used to categorize participants into different groups based on distinct a priori models. Results indicated that participants came into this task with a number of distinct initial models, and that the type of model influenced their ability to accurately represent different distributions of ball drops in Plinko. Introduction Humans are proficient at detecting regularities in their environment (Turk-Browne et al., 2005; Griffiths & Tenenbaum, 2006). This ability al- lows us to compress large volumes of sensory in- formation and build mental models to represent the events we perceive (Tenebaum et al., 2011). When these models fail to explain certain obser- vations, they must be updated to reflect new envi- ronmental contingencies (Danckert et al., 2012: Filipowicz et al., 2013). The ability to build and update models depends in part on the expectations we have when interpreting sensory information (Lee & Johnson-Laird, 2013; Stottinger et al., 2014). The aim of the present study was to ex- plore the role of prior expectations on model building and updating. A large body of research has demonstrated the efficiency with which humans detect regularities in their environment (Turk-Browne et al., 2005). These processes can occur automatically (Turk- Browne et al., 2005; Nissen & Bullemer, 1987) and manifest themselves at an early age (Saffran et al., 1996). Yet despite this seemingly optimal proficiency, studies have found consistent subop- timal behavior on certain statistical learning tasks. One classic example is a phenomenon known as probability matching: when asked to predict the result of a stochastic event with a specific rate of bias, rather than choose the biased event 100% of the time, participants tend to predict the biased event at the same rate as its underlying probability (e.g., if a biased coin comes up heads 70% of the time, participants will choose heads as the likely next outcome on 70% of their guesses rather than following the optimal prediction strategy of choosing heads 100% of the time; Vulkan, 2000). How do we reconcile findings that show optimali- ty in some forms of learning, yet suboptimal be- havior in others? Mental model theory attempts to explain this discrepancy by implicating prior knowledge in our ability to learn from our environment. One of the primary tenets of this theory describes mental models as being formed by an interaction between our direct perception of events and the knowledge we have accumulated over our lifetime (Johnson- Laird, 2004). This theory suggests that our a pri- ori expectations related to specific events influ- ence our current predictions. Indeed, Green and colleagues (2010) found that probability matching behaviour depended on a participant’s belief re- garding the underlying process responsible for generating the events. Participants who believed they had control over the task parameters were much more likely to maximize their selection of the optimal choice than those that revealed uncer-