Missing documentation for results dictionary

[jacopok]

• UltraNest version: 3.6.4
• Python version: 3.11.0
• Operating System: Ubuntu 22.04

Description

I cannot seem to find any spot in the documentation where the meaning of all the various entries in the result dictionary (e.g. obtained by result = sampler.run() in the Basic usage tutorial). In the API documentation, all it says is "Yields: results (dict)"

Proposal

I'd be glad to contribute with a PR to add this reference! Here is what I think I got from the names and some guessing.

• niter (int): number of sampler iterations (not likelihood evaluations!)
• logz (float64): natural logarithm of the evidence $Z = \int p(d|\theta) p(\theta) \text{d}\theta$
• logzerr (float64): $1\sigma$ error on $\log Z$ (can be safely assumed to be Gaussian)
• logz_bs (float64): ?
• logz_single (float64): ?
• logzerr_tail (float64): ?
• logzerr_bs (float64): ?
• ess (float64): ?
• H (float64): information gained, i.e. relative entropy from posterior to prior $2^H = \int \log(p(\theta |d) / p(\theta)) p(\theta) \text{d}\theta$ (?)
• Herr (float64): (Gaussian) error on $H$ (?)
• posterior (dict): summary information on the posterior marginals - a dictionary of lists each with as many items as the fit parameters, indexed as $\theta_i$ in the following:
  • mean (list): expectation value of $\theta_i$
  • stdev (list): standard deviation of $\theta_i$
  • median (list): median of $\theta_i$
  • errlo (list): one-sigma lower quantile of the marginal for $\theta_i$, i.e. $15.8655$% quantile
  • errup (list): one-sigma upper quantile of the marginal for $\theta_i$, i.e. $84.1345$% quantile
  • information_gain_bits (list): information gain from the marginal prior on $\theta_i$ to the posterior
• weighted_samples (dict): weighted samples from the posterior, as computed during sampling, sorted by their log-likelihood value
  • upoints (ndarray): sample locations in the unit cube $[0, 1]^{d}$, where $d$ is the number of parameters - the shape is n_iter by $d$
  • points (ndarray): sample locations in the physical, user-provided space (same shape as upoints)
  • weights (ndarray): sample weights - shape n_iter, they add to 1
  • logw (ndarray): ?
  • bootstrapped_weights (ndarray): ?
  • logl (ndarray): log-likelihood values at the sample points (?)
• samples (ndarray): re-weighted posterior samples: distributed according to $p(\theta | d)$ - these points are not sorted, and can be assumed to have been randomly shuffled (?)
• maximum_likelihood (dict): summary information on the maximum likelihood value $\theta_{ML}$ found by the posterior exploration
  • logl (float64): value of the log-likelihood at $p(d | \theta_{ML})$
  • point (list): coordinates of $\theta_{ML}$ in the physical space
  • point_untransformed (list): coordinates of $\theta_{ML}$ in the unit cube
• ncall (int): total number of likelihood evaluations (accepted and not)
• paramnames (list): input parameter names
• logzerr_single (float64): (?)
• insertion_order_MWW_test (dict) (?)
  • independent_iterations (float)
  • converged (bool)

[JohannesBuchner]

Yes please. Some of it is documented at https://johannesbuchner.github.io/UltraNest/performance.html#output-files but it would be best to have it in the API docs.

[JohannesBuchner]

Hi @jacopok, would you be able to help out with a pull request? You'd need to add information here: https://github.com/JohannesBuchner/UltraNest/blob/master/ultranest/integrator.py#L2433

[jacopok]

Hi, sorry for disappearing! I meant to do this quickly but then other things took priority. I made a draft PR now, it's not complete yet since I had some trouble building the docs.

[jacopok]

Solved by #138