# Why Reversible jump mcmc has only one step increase/ decrease?

I was applying reversible jump MCMC for joint estimation of model order and parameter estimation. I've a conceptual question in my mind. First of all, the algorithm has 3 steps, namely the birth, death and update. In birth and death steps, the model order is either increased or decreased by 1.

I've seen some papers where after each iteration, a hyper parameter ($$\Lambda$$) is updated based on a MH step and that again is used as the Possion distribution parameter for the model order in the next iteration. In short, the model order on every iteration is adaptively chosen and then the birth/ death moves are considered again. This makes it converge faster.

This made me think the following. Instead of increasing/ deceasing the model order by 1, why not do the following.

1. Randomly choose an order based on the Poisson distribution. Based on the current model order, add or remove parameters and compute the a MH step and accept one of the orders.
2. Update step
3. Repeat

1 and 2 can be performed based on a uniform random draw is less/ greater than a threshold.

The parameter of the Poisson can be used as a hyper parameter nicely here.

It’s more like a joint estimation but with arbitrary steps.

Is it popular? Or, is it very stupid of me to think an approach like this. I’m sure the authors thought very carefully about the increase/ decrease by only 1 in the RJMCMC.

• Increasing/decreasing by one is nothing special. The RJMCMC algorithm allows for proposed moves between arbitrary pairs of models. For instance, in Bayesian Core, we detail a RJMCMC for $AR(k)$ models where the proposed moves are between $k$ and $k\pm 1, k\pm 2$. Choosing an order with a Poisson proposal is thus perfectly legit. Sep 23 at 6:35