Inference of Interdependent Simulator Parameters in SBI

[hdahmou]

Hi,

I'm working on a problem involving simulator parameter inference that I think could be solved using the SBI framework.

Given a system of $N$ agents, each characterized by parameters $(\theta_{1, i}, \theta_{2, i})$ where $i \in \set{1, ..., N}$ drawn from half-normal distributions with unknown means and variances $\mu_1, \sigma_1, \mu_2, \sigma_2$. My goal is to infer the posterior distributions of these mean and variance parameters that could generate an observation. I believe that treating these parameters as independent is wrong given the natural dependency between the mean and variance of each parameter.

Any pointer on the best practices or methods within the SBI framework for this type of problem?

Thank you

[janfb]

Hi,

sorry for the delay in the response. As I understand it, you have two parameters, $\mu$ and $\sigma$ per agent, and $N$ agents.

What is the dimensionality $D$ of the simulated data? Do you generate multiple i.i.d. trials per agent?

If it is, say $D<10$ I think you could try solving this problem with neural likelihood estimation (NLE). You would use NLE to estimate the single trial likelihood for each agent and then perform MCMC to obtain posterior samples.
You could probably set up a hierarchical inference here as well, e.g., define a hyper prior on the parameters of the half-normal prior so that information across agents can be shared?

A different more brute force approach would be to directly apply neural posterior estimation (NPE). As input you take the data for all agents and you learn the $2*N$ dimensional posterior from that. Again, whether this is feasible strongly depends on $N$ and on $D$.

I hope this help! Let me know if anything is unclear.

[hdahmou]

Hi,

Thank you for your response.

I have a system of $N$ agents, each characterized by two parameters, $\theta_1$​ and $\theta_2$​. These parameters are independently drawn from two distinct half-normal distributions. My goal is to estimate the mean and standard deviation (std) for each of these distributions, resulting in four parameters in total. However, these parameters are not independent because the mean and std describe the properties of the same underlying distribution.

The data comprises multiple time series that are correlated and detail the interactions between these agents. I have managed to reduce the dimensionality to a $D \lt 10$.

Given that $N * D * 2 \gt 100$ (and the slow simulator) brute force would be infeasible. Instead, a hierarchical Bayesian inference approach can be the solution, do you have any example of how it can be implemented within the SBI toolbox?

[janfb]

Sorry, this was completely off my radar until now. No we don't have a tutorial on hierarchical inference with sbi. I will add this to the list of todos for updating the documentation during the upcoming hackathon.