5. Post Analysis

The output of an inference scheme is a Journal (:py:class:abcpy.output.Journal) which holds all the necessary results and convenient methods to do the post analysis.

For example, one can easily access the sampled parameters and corresponding weights using:

print(journal.get_parameters())
print(journal.get_weights())

The output of get_parameters() is a Python dictionary. The keys for this dictionary are the names you specified for the parameters. The corresponding values are the marginal posterior samples of that parameter. Here is a short example of what you would specify, and what would be the output in the end:

a = Normal([[1],[0.1]], name='parameter_1')
b = MultivariateNormal([[1,1],[[0.1,0],[0,0.1]]], name='parameter_2')

If one defined a model with these two parameters as inputs and n_sample=2, the following would be the output of journal.get_parameters():

{'parameter_1' : [[0.95],[0.97]], 'parameter_2': [[0.98,1.03],[1.06,0.92]]}

These are samples at the final step of ABC algorithm. If you want samples from the earlier steps you can get a Python dictionary for that step by using:

journal.get_parameters(step_number)

Since this is a dictionary, you can also access the values for each step as:

journal.get_parameters(step_number)["name"]

For the post analysis basic functions are provided:

# do post analysis
print(journal.posterior_mean())
print(journal.posterior_cov())

Also, to ensure reproducibility, every journal stores the parameters of the algorithm that created it:

print(journal.configuration)

Finally, you can plot the inferred posterior distribution of the parameters in the following way:

journal.plot_posterior_distr(path_to_save="posterior.png")

The above line plots the posterior distribution for all the parameters and stores it in posterior.png; if you instead want to plot it for some parameters only, you can use the parameters_to_show argument; in addition, the ranges_parameters argument can be used to provide a dictionary specifying the limits for the axis in the plots:

journal.plot_posterior_distr(parameters_to_show='parameter_1',
                             ranges_parameters={'parameter_1': [0,2]})

For journals generated with sequential algorithms, we provide a way to check the convergence by plotting the estimated Effective Sample Size (ESS) at each iteration, as well as an estimate of the Wasserstein distance between the empirical distributions defined by the samples and weights at subsequent iterations:

journal.plot_ESS()
journal.Wass_convergence_plot()

And certainly, a journal can easily be saved to and loaded from disk:

journal.save("experiments.jnl")
new_journal = Journal.fromFile('experiments.jnl')