In snowy regions, the effective width changes due to the accumulated snow on the road shoulders during snow removal. For efficient snow removal planning, evaluating the effect of such changes in road conditions on traffic flow is necessary. Traffic capacity, which is one of the main measures of road performance, can be estimated by a macroscopic traffic flow model. Since drivers' perception of the accumulated snow varies widely, the parameters of the macroscopic traffic flow model can be considered uncertain. This study proposes an estimation method for stochastic parameters on macroscopic traffic flow model and stochastic road capacity for different width of accumulated snow by using a hierarchical bayesian model.