Step one is to load some data. Rather than going through a whole modelling workflow, we’ll just take one of the example MCMC outputs that arviz provides via the function load_arviz_data.
This particular MCMC output has to do with measurements of soil radioactivity in the USA. You can read more about it here.
-
+
import arviz as azimport numpy as np # numpy is for numerical programmingimport xarray as xr # xarray is for manipulating n dimensional tables; arviz uses it a lot!
@@ -5181,8 +5181,8 @@
For example, if you click on the dropdown arrows above you will see that the group posterior contains a variable called a_county that has three dimensions called chain, draw and County. There are 85 counties and the first one is labelled 'AITKIN'.
The function az.summary lets us look at some useful summary statistics, including \(\hat{R}\), divergent transitions and MCSE.
The variable lp, which you can find in the group sample_stats is the model’s total log probability density. It’s not very meaningful on its own, but is useful for judging overall convergence. diverging counts the number of divergent transitions.
/Users/tedgro/repos/biosustain/bayesian_statistics_for_computational_biology/.venv/lib/python3.12/site-packages/arviz/stats/diagnostics.py:592: RuntimeWarning: invalid value encountered in scalar divide
@@ -8275,7 +8275,7 @@
Example
In this case there were no post-warmup diverging transitions, and the \(\hat{R}\) statistic for the lp variable is pretty close to 1: great!
Sometimes it’s useful to summarise individual parameters. This can be done by pointing az.summary at the group where the parameters of interest live. In this case the group is called posterior.
Now we can start evaluating the model. First we check to see whether replicated measurements from the model’s posterior predictive distribution broadly agree with the observed measurements, using the arviz function plot_lm:
