I could generate the necessary amount of random numbers in R and pass them in as data, although that would be less efficient due to serialization/deserialization of a large amount of data.

Is there a better way?

I understand the problem of the non-deterministic lp. What if the rng inside the model could be initialized with a fixed seed at the beginning of each leapfrog step? Then the lp would be deterministic and smooth.

The reason you canât use RNGs as part of the model definition is that Stan works by defining a differentiable log density. Using an RNG would break differentiablity as we canât differentiate through it. It also violates Bayesian information flow principles in the same way as âcutâ in BUGS did.

If you need to generate continuous ârandomâ variables, just define parameters and give them sampling distributioins. That will not be equivalent to just generating RNGs, but it will have the correct information flow properties where the context in which the parameter is used will feed information back into the parameter.

Using an RNG would break differentiablity as we canât differentiate through it.

I donât see why. If you used a constant seed, the random numbers would effectively be constants â youâd have no problem differentiating through them.

If you need to generate continuous ârandomâ variables, just define parameters and give them sampling distributioins.

This doesnât at all sound like what I need. Primarily because I want the numbers to be truly random and not be âoptimizedâ by stan to maximize the log probability. I suspect it would bias the result.

Not to mention all the efficiency concerns â I donât want stan to waste time by optimizing a huge array of random numbers, store them in memory, return them as the result etc.

To clarify, the model I am thinking about looks something like this:

model {
# simulate num_samples trajectories
for (i in 1:num_samples)
x = x0;
# for each trajectory, simulate num_steps steps
for (j in 1:num_steps) {
z = normal_rng(0, sigma);
x = update(x, z);
}
# see how well the end point of the trajectory matches our expectations
x ~ normal(x1, sigma);
}
}

Stan requires you to define a joint log density proportional to the posterior if you want to do full Bayesian inference. Then the information flows from the data to the parameters.

When you use RNGs in the model, that flow is cut.

If your sigma is a constant, then youâd be generating z at random and somehow using those to define a variable x (that is also defined in terms of x0).

Sampling doesnât optimize the log density, but the optimizer does.

Iâm also not sure what you mean by âtruly randomâ. Itâs that property that cuts the flow of information.

What youâre suggesting is often done for things like multiple imputation, where itâs too costly to jointly analyze. And itâs done using the cut operation in BUGS. But we donât support these things in Stan because theyâre not based on a model plus full Bayesian inference. Instead, itâs procedural.

Sampling doesnât optimize the log density, but the optimizer does.

Yes, at the moment Iâm mainly interested in ML/MAP.

What youâre suggesting is often done for things like multiple imputation, where itâs too costly to jointly analyze. [âŚ] But we donât support these things in Stan because theyâre not based on a model plus full Bayesian inference. Instead, itâs procedural.

Yes, it is multiple imputation in a way. Now I see what you were suggesting above when you told me to make it a parameter â thanks. But this amounts to a very different computational method. Iâd be curious to see how the two compare â but in order to compare them, Iâd still need to implement the original simulated likelihood, probably by passing in random numbers as part of the data.

We pass in a bunch of random numbers into Stan and we also give recipes to ensure convergence of results. The supplements contain the sources and I am happy to share them if this is useful.

I am very interested in reading your supplements of the source code, but I couldnât open it from the journal website. Do you mind sharing with me? Thanks!

Cool that someone is diving into this! I recall that the simulation example is straightforward. So start with that. I can dig up the code tomorrow and have a look in case you are still struggling. Note that I generated the random numbers within R if my memory serves me right.

EDIT: Now I remember, I passed in the chain_id into the stan program. The Stan model then selected out of a big array the sub-slice of random numbers which were all generated in R.

I checked the code of linear_baad.R and pkpd_baad.R, but I am not sure which lines of code did you refer to. I saw the chain id was fixed at 4 in both files.

I am using 4 chains at most. The random numbers are generated in the linear_baad.R script on line 161 (named xi). This is an array of length 4 over a matrix (as many chains I have) and in the stan program I am selecting the set of random numbers according to the CHAIN_ID which is handled within the sampling command. you can see that CHAIN_ID is varied as I am printing it when the Stan program starts.

Thank you so much! I was able to generate random numbers in R and then pass them into Stan as you suggested. But I still have a problem with selecting the set of random number according to the CHAIN_ID. I saw that in linear_baad.R line 161 you generated random numbers in R, and then passed into Stan in line 164-166. But I didnât understand how Stan knows which set of random numbers to use according to CHAIN_ID (in your linear_mvn_approx.stan line 82 and 142). I tried to run your code so that I could understand better, but it ran into an error âvalue for âpstream__â not found .â If you could provide me more explanations on this, that would be great!

The model I wrote is rather hard for the compiler and it can be that it does not compile at the moment. I would recommend you to use rstan 2.17 which is what I used at the time, I think.

The CHAIN_ID is generated on the fly from rstan and is passed as data to the Stan program. This is not supported by cmdstan, for example.

If you have to run this with a newer Stan version, then I can look into the matter and get it running again.

@serenejiang: Hi, Iâm working on something similar to this idea where I need to generate random quantity in model block. Could you please share the code in @wds15âs paper with me

Bob, would it be possible to use one different random number in each different iteration?

I am trying to implement a two-step estimator. Estimates from the first step become data for the second stage, but should not be influenced by the second step. The second step needs to account for the uncertainty in the estimates from the first step.

What I am doing so far is estimate the first step and store the chains. Then pass the mean and sd to the second step and use them to generate a parameter, but it seems the draws are still influenced by the likelihood of the second step.

This should be trivial to do in a single model, but we should probably start a new topic for it. Can you do so, while posting the code you have for the two separate models, then I should be able to advise on how to properly combine.