Posterior probability distributions

[BoburaII]

I’m executing NPrun on a dataset containing 250 subjects. By default, after convergence, Bayesian posterior parameter distributions are generated only for the first 100 subjects.
I’d like to modify the run to ensure that posterior distributions are generated for all subjects. I appreciate clarification on how this could be achieved.

[mhovd]

I think the best approach is to run the model, and then run it again with zero cycles on a partition of your data limited to 100 subjects at the time. It is very important that you update the error model to use the final gamma/lambda when you do your zero-cycle run, to ensure that the likelihoods are the same.

We are close to releasing a new version of Pmetrics where there is no such limitation, and will give you the Bayesian posterior parameter distributions for all subjects, with no upper limit on the number of subjects.

Please let me know if you need any assistance.

[BoburaII]

Thank you for suggesting this workaround—very helpful! with this approach, I notice that the posterior distributions for the partitioned data would end up in separate run output folders. What would be the best way to merge and simulate from the distribution of posteriors for all subjects?

For a given run output, I'm using the implementation below to simulate from posteriors:

run2$sim(limits = NA,
                predInt = c(0, 24, 2),
                usePost = T,
                combine = T,
                nsim = 1000)

Would you recommend aggregating the outputs before or after simulations?

[mhovd]

Unfortunately, the "easiest" way is to perform simulation on each run containing your partitioned data. I would recommend aggregating the outputs after the simulation.

This will be much simplified with the next release of Pmetrics when there is no limit on the number of subjects you can calculate the posterior probabilities for, or perform simulation on. While it is too early for an official beta release, we do have a working prototype that you can access if you have any pressing needs for larger scale simulation. Let me know if that is the case, and I can help setting you up with the new version.

On that note, in my experience I found no drastic differences when simulating from the posteriors as opposed to the population parameter densities, so that could be an alternative solution for you that doesn't require multiple runs. For a "perfect" model and data, the sum of the posterior distributions are exactly the population parameter distributions.

[BoburaII]

Thank you for the detailed response. I appreciate you pointing out that this issue is addressed in the upcoming Pmetrics release – I’ll be sure to lookout for it.

I agree with your observation about the similarity between simulations from posterior distributions and those based on population parameter distributions. Simulating from the population parameter distributions is generally preferable and more efficient, especially when population model bias and imprecision are minimized.

[mhovd]

Hi again - with the latest release of Pmetrics 3.0, we provide posterior probabilities for all subjects.

We have updated the documentation for Pmetrics, which is available at https://lapkb.github.io/Pmetrics/
A more in-depth introduction to Pmetrics can be found at https://lapkb.github.io/PM_tutorial