  Baxterisation is a procedure which constructs solutions of the Yang-Baxter
equation from algebra representations. A recent paper arXiv:2004.05035 provides
Baxterisation formulas for a fused Hecke algebra. In this paper, we provide a
stochastic version of Baxterisation for the fused Hecke algebra, which yields
stochastic solutions to the Yang-Baxter equation. The coefficients in the
Baxterisation formula previously appeared as the $q$-Hahn weights. This results
in new formulas for the weights of the stochastic higher-spin vertex model.
