The mean for the Poisson distribution is parameterized by the sum of
feature promiscuity (number of SecMs g connected to a feature) μf
, interactor promiscuity (number of SecPs with a feature finteracting with a SecM) μg , the interaction synergy sf,g and an
intercept variable. The feature promiscuity μfquantifies the probability of a feature f to partake in an
interaction with any secMs. Likewise, the interactor promiscuityμg measures the tendency for a secM g to
interact with any features. The coefficient of interest, the interaction
synergy s f,g between f and g ,
quantifying the degree to which f and g interact more than
by random chance, quantifies the degree to which f and g interact more
than by random chance. In previous work, this approach has correctly
estimated epistasis intensity
(Shen et al., 2017). To
better regularize the promiscuities, their Bayesian priors are all
normally distributed around 0, with their variances parameterized by the
hyper priors 𝜎f , 𝜎g and
𝜎s which follow an exponential distribution. The
intercept ɑ is parameterized by a standard normal distribution.
We used the rethinking R package
(McElreath, 2020) to
construct the model and sample the coefficients.