The general treatment of nuisance parameters can be broadly similar between frequentist and Bayesian approaches to theoretical statistics.
When this partition can be achieved it may be possible to complete a Bayesian analysis for the parameters of interest by determining their joint posterior distribution algebraically.
The partition allows frequentist theory to develop general estimation approaches in the presence of nuisance parameters.
Practical approaches to statistical analysis treat nuisance parameters somewhat differently in frequentist and Bayesian methodologies.
In Bayesian analysis, a generally applicable approach creates random samples from the joint posterior distribution of all the parameters: see Markov chain Monte Carlo.