Fig. 4: The hierarchical particle filter model.
From: Computational processes of simultaneous learning of stochasticity and volatility in humans
a Structure of the (generative) model: the observation (e.g., the bag) on trial \(t\), \({o}_{t}\), is generated based on a hidden cause, \({x}_{t}\), (e.g., the bird) plus some independent noise (e.g., wind) whose variance is given by the stochasticity, \({s}_{t}\). The hidden cause itself depends on its value on the previous trial plus some noise whose variance is given by the volatility, \({v}_{t}\). Both volatility and stochasticity are generated noisily based on their value on the previous trial. The learner should infer value of the hidden cause, volatility and stochasticity based on observations. b, c Mean learning rate by the model across participants as a function of the two experimental factors (n = 223). Mean and standard error of mean are plotted in (b). Individual data-points for the two main effects as well as their median are plotted in (c). d, e Dynamics of the stochasticity signal estimated by the model. f, g Dynamics of the volatility signal estimated by the model. Mean and standard error of mean are plotted in (d–g).
