Ok I think I got it.
So it’s basically Gibbs sampling where a sample from the conditionnal distribution is generated using in your example one iteration of: Metropolis for parameter p and Binary Gibbs Metropolis for ni ? But of course the Metropolis/Binary Gibbs metropolis can refuse the proposed new parameter and no change for that parameter occured.
When the steps are automatically attributed to parameters, how do we know in which order does the two steps take place? Is it a random order at each iteration or a fixed one?