PyMC, the first model

PyMC is at 6.3.2, released on 8 September 2026. The 6.0.0 release shipped on 13 May 2026 and it was a breaking one: PyMC 6 is built on PyTensor 3.0, the default compute backend switched to numba, and if nutpie is installed it is the default NUTS sampler, tuning for 400 steps where PyMC's own NUTS tunes for 1000. It requires Python 3.12 or later. The install that gets you the default sampler is pip install pymc[nutpie].

ArviZ is at 1.3.0 and is no longer one library. It is three, arviz-base for data and converters, arviz-stats for diagnostics, arviz-plots for plotting, all reached through the same import arviz as az. The result container changed with it: arviz.InferenceData no longer exists and what pm.sample() returns is an xarray.DataTree. Existing netCDF and zarr files still load, because az.from_netcdf now wraps open_datatree, and a group is reached as dt["posterior"].dataset.

• PyTensor 3.0. The tensor library PyMC 6 compiles your model with. Its default backend is numba; pytensor.config.linker = "cvm" reverts to the old one.
• nutpie. The NUTS sampler PyMC 6 hands the work to when it is installed. 400 tuning steps by default against 1000 for PyMC's own NUTS.
• xarray.DataTree. The container a sample call returns. Groups such as the posterior are reached as dt["posterior"].dataset. It replaced InferenceData.
• arviz-base, arviz-stats, arviz-plots. The three libraries that make up ArviZ 1.3.0. You do not import them separately for ordinary work; import arviz as az reaches all three.
• PlotCollection. What every ArviZ 1.x plot returns. Not axes.
• prob. The renamed hdi_prob. The interval level argument on summaries and plots.
• stats.ci_prob and stats.ci_kind. The two rcParams that set the default interval: 0.89 and "eti". They were 0.94 and HDI.
• Equal-tailed interval. The 5.5 and 94.5 percent quantiles of the posterior draws. Every interval in these sessions is one, and every page says so.

Three of the changes in the 6.0.0 release notes touch every model. The compute backend is numba, through PyTensor 3.0; you can revert to the previous one with pytensor.config.linker = "cvm", and you will want to know that line exists the first time a compile surprises you. The sampler is nutpie whenever it is installed, which is why the install line is pip install pymc[nutpie] rather than plain pymc. And nutpie tunes for 400 steps by default where PyMC's own NUTS tunes for 1000, so a run on the new default is doing less warm-up than the same run a year ago, which is precisely why session 4's diagnostics are read every time rather than trusted once.

Two smaller changes bite specific lines. sample_prior_predictive lost its deprecated samples argument, so a notebook that asks for a particular number of prior draws by that name stops at that line. sample_posterior_predictive gained sample_vars and freeze_vars, which session 8 uses. Several functions were also removed from the root namespace. None of this is exotic; it is the ordinary churn of a tool at a major version, and the fix is to write the model for the tool you have rather than the one the notebook remembers.

What pm.sample() hands back is an xarray.DataTree. It holds groups, and the one you want most nights is the posterior, reached as dt["posterior"].dataset: an xarray dataset with a chain dimension and a draw dimension, which is exactly the shape session 4 said a set of chains has. The diagnostics are written for that shape. az.rhat(dt) and az.ess(dt, sample_dims=["chain", "draw"]) take the tree directly, and after import arviz_stats the same effective sample size is one accessor away as dt.azstats.ess().

The old container, arviz.InferenceData, is gone from the tool, but the files it wrote are not stranded. az.from_netcdf now wraps open_datatree, so a result saved last year opens as a DataTree this year. The thing that does not survive the move is code that reaches into the old container by its old attributes. The honest rule for a migration is to load the file, look at the tree, and rewrite the reads.

The rename everyone notices is hdi_prob to prob. The change that matters is in the defaults behind it. Two rcParams now govern every summary interval: stats.ci_prob is 0.89, where it was 0.94, and stats.ci_kind is "eti", an equal-tailed interval, where it was HDI. The migration guide's reason for the level: "Using 0.89 produces intervals with lower variability, leading to more stable summaries." So a summary table produced today, with no arguments, reports an 89 percent interval cut at the 5.5 and 94.5 percent quantiles of the draws. The same call in 2023 reported a 94 percent highest-density interval.

That is not a cosmetic difference. A third party, the CoursIA repo in its issue #15592, documented two notebooks whose intervals silently became equal-tailed on upgrade while the prose beside them still said HDI. The code ran, the numbers changed, the words did not. Every interval in these sessions is therefore stated as what it is, an 89 percent equal-tailed interval, and the sentence you write for anyone else should carry both the level and the kind. If you need a different interval, pass prob and say so in the text; if you take the default, say that too. What you may not do is leave the reader to assume.

Six moves, always in this order. Model: inside with pm.Model(), a pm.Beta for the rate with the flat Beta(1, 1) of session 2, two pseudo-observations, and a pm.Binomial with n=900 and observed=127. Prior predictive: pm.sample_prior_predictive() before touching the data, to see what counts out of 900 the prior alone considers plausible; under a flat prior that is every count from 0 to 900 equally, which is what "flat" means and why session 2 counts it as worth only two pseudo-observations. Sample: pm.sample(), which goes to nutpie if it is installed. Diagnose: az.rhat(dt) and az.ess(dt, sample_dims=["chain", "draw"]), read the way session 4 taught, before anything is reported. Summarise: az.summary(dt), one row for the rate. Plot: az.plot_dist, the picture of the posterior.

The number you are checking against is 0.142, the flat-prior posterior mean at Westfield that session 1 got with a + 127 and b + 773. If the summary row says something else, the model is wrong, not the arithmetic. That is the whole reason to run the tool on a case whose answer you already hold: the first model is a test of the tooling, and only after it passes does the tool get to tell you anything you did not already know.

The row az.summary(dt) prints for the rate has three kinds of column, and all of them are statements about the posterior draws. Location and spread: the posterior mean, which at Westfield under the flat prior is 0.142, and the spread of the draws around it. The interval: two columns giving the ends of the default interval, which in ArviZ 1.3.0 is 89 percent equal-tailed, the 5.5 and 94.5 percent quantiles of the draws. Read them as session 3 taught: an 89 percent probability, given this prior and these 900 vouchers, that the rate sits between them. The diagnostics: effective sample size and R-hat, the session 4 checks, telling you how much to trust the columns to their left.

What the row does not contain is anything from the other tradition. There is no confidence interval on it and no p-value, and the interval columns must not be read as either; learn-statistics-with-phoebe owns those words and the procedures behind them. The credible interval is the sentence everybody thinks a confidence interval is, and the summary row is where that sentence's two numbers come from. Say the level and say the kind: "0.142, with an 89 percent equal-tailed interval." Both halves are defaults, and defaults change.

Three words tell you a notebook predates the tool: pymc3, InferenceData, hdi_prob. Any one of them is enough. The first is a dead import and will not run. The second names a container that no longer exists. The third names an argument that was renamed, and its presence means every interval in the notebook was cut under the old default, a 94 percent HDI, so none of its reported intervals matches what the current tool prints for the same model. McElreath's own 2024 course page still lists "Python with PyMC3"; do not copy that either.

The fix is not to patch the three lines. It is to rerun the model on the current tool, read the new summary, and rewrite every sentence that quoted an interval, because the level and the kind both changed. A notebook whose code was patched and whose prose was not is exactly the case the CoursIA issue documented: correct-looking output under a description that is no longer true of it. If you are handed such a notebook, the two-line reply is "this predates PyMC 6 and ArviZ 1; the intervals need recutting and restating before anyone quotes them."