Variational Bayes Equations in ar1_binary_mab

[ahmadkhanloo]

Dear Dr. Chris Mathys,

I was examining the tapas_hgf_ar1_binary_mab function, which implements the HGF for multi-armed bandit scenarios with binary outcomes. I noticed that the variational Bayes update equations in this implementation differ from those in your 2014 paper, "Uncertainty in perception and the Hierarchical Gaussian Filter".
Specifically, the differences are reflected in the parameters, particularly with the ar1 component introducing autoregression in the dynamics of the second level, characterized by ϕ and m, unlike tapas_hgf_binary_mab, which uses a single drift parameter p.

Could you please guide me to the reference or paper where these updated equations, particularly for the ar1 extension, are derived?

[chmathys]

Dear @ahmadkhanloo,

We have never made a particular paper dedicated to the derivation of these update equations. In any case, they follow from the procedure set out in Mathys et al. (2011) and explained further in Mathys et al. (2014). The most comprehensive exposition of this is my PhD thesis. The only difference to the standard derivation is in the prediction step (calculating muhat), cf. Eq. B5 in Mathys et al. (2014).