Extension to multiple summary statistics

[scheidan]

After some discussion Carlo and I came to the following, preliminary conclusions.

We get multiple distances (rho) from f_dist. We change the initialization as follows:

1. get n_particle prior samples and compute distances
2. learn the multivariate CDF of the distances -> this function maps a vector of summary distances to the scalar number u.
3. Choose epsilon_init (as epsilon_init relates now to u it shoud have an easy interpretation)
4. Keep sampling with acceptance probability exp(- u ./ epsilon_init) until we have n_particle samples.
5. (optional) relearn the multivariate CDF form the larger sample.

We need to think about:

• How to efficiently compute the multivariate cdf? See e.g. this old paper, this newer paper, or here. Ideally we find a an implementation for this.
• Should we use the empirical cdf (steps) or some kind of interpolation?

[scheidan]

The multivariate CDF is not a correct solution!