Early noise introduces noise into the decision-making process at the time of stimulus encoding, as captured by encoding-decoding models of perception (Wei & Stocker, 2012). Recent work in visual perception has shown that priors can originate from our interactions with the natural environment (Girshick, Landy, & Simoncelli, 2011). The concept of a naturalistic prior has also been used to explain biases in numerosity judgements, where the prior follows a power law (Cheyette & Piantadosi, 2020). This conflicts with Bayesian models of numerosity perception where the prior is allowed to adapt to the context (Prat-Carrabin & Woodford, 2022). Here, we test the competing models of numerosity judgements by causally manipulating early noise and imposing biased priors. We find a relationship between signal precision and response predictability which is only predicted by Bayesian models with adaptive priors. Therefore, while naturalistic priors are plausible, they may only explain a subset of situations in which numerosity judgements are used, and models of numerosity judgement should allow priors to adapt to specific contexts.
