I am working on a project with Turing.jl using the Metropolis-Hastings (MH) algorithm. I’m interested in tracking the acceptance rate of the sampler in real-time and obtaining the final acceptance rate after the inference is complete.

While exploring the Turing.jl, I noticed that it offers functionality for tracking various diagnostics during sampling, and the documentation includes a TensorBoard showing the acceptance rate for HMC.

Could anyone provide insights or examples on how to use TuringCallbacks.jl to monitor the acceptance rate for MH in a similar way?

How to set up TuringCallbacks to track the acceptance rate during sampling with the MH algorithm?

How can I obtain the acceptance rate after the inference from the `chain`

?

Do I need to write an internal function for that? If it is, how it might be?

Thank you for your support!

Example code:

```
using Turing, TuringCallbacks
@model function demo(x)
s ~ InverseGamma(2, 3)
m ~ Normal(0, sqrt(s))
for i in eachindex(x)
x[i] ~ Normal(m, sqrt(s))
end
end
xs = randn(100) .+ 1;
model = demo(xs);
# Number of MCMC samples/steps
num_samples = 10_000
# Sampling algorithm to use
alg = MH()
# Create the callback
callback = TensorBoardCallback("tensorboard_logs/run")
# Sample
chain = sample(model, alg, num_samples; callback = callback)
...
```