ArviZ Quickstart¶

import arviz as az
import numpy as np

ArviZ style sheets¶

# ArviZ ships with style sheets!
az.style.use("arviz-darkgrid")

Feel free to check the examples of style sheets here.

Get started with plotting¶

ArviZ is designed to be used with libraries like PyStan and PyMC3, but works fine with raw NumPy arrays.

az.plot_posterior(np.random.randn(100_000));

Plotting a dictionary of arrays, ArviZ will interpret each key as the name of a different random variable. Each row of an array is treated as an independent series of draws from the variable, called a chain. Below, we have 10 chains of 50 draws, each for four different distributions.

size = (10, 50)
az.plot_forest(
    {
        "normal": np.random.randn(*size),
        "gumbel": np.random.gumbel(size=size),
        "student t": np.random.standard_t(df=6, size=size),
        "exponential": np.random.exponential(size=size),
    }
);

ArviZ rcParams¶

You may have noticed that for both plot_posterior() and plot_forest(), the Highest Density Interval (HDI) is 94%, which you may find weird at first. This particular value is a friendly reminder of the arbitrary nature of choosing any single value without further justification, including common values like 95%, 50% and even our own default, 94%. ArviZ includes default values for a few parameters, you can access them with az.rcParams. To change the default HDI value to let’s say 90% you can do:

az.rcParams['stats.hdi_prob'] = 0.90

import pymc3 as pm

J = 8
y = np.array([28.0, 8.0, -3.0, 7.0, -1.0, 1.0, 18.0, 12.0])
sigma = np.array([15.0, 10.0, 16.0, 11.0, 9.0, 11.0, 10.0, 18.0])
schools = np.array(
    [
        "Choate",
        "Deerfield",
        "Phillips Andover",
        "Phillips Exeter",
        "Hotchkiss",
        "Lawrenceville",
        "St. Paul's",
        "Mt. Hermon",
    ]
)

with pm.Model() as centered_eight:
    mu = pm.Normal("mu", mu=0, sd=5)
    tau = pm.HalfCauchy("tau", beta=5)
    theta = pm.Normal("theta", mu=mu, sd=tau, shape=J)
    obs = pm.Normal("obs", mu=theta, sd=sigma, observed=y)

    # This pattern is useful in PyMC3
    prior = pm.sample_prior_predictive()
    centered_eight_trace = pm.sample()
    posterior_predictive = pm.sample_posterior_predictive(centered_eight_trace)

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (2 chains in 2 jobs)
NUTS: [theta, tau, mu]

100.00% [2000/2000 00:09<00:00 Sampling 2 chains, 28 divergences]

There were 8 divergences after tuning. Increase `target_accept` or reparameterize.
There were 20 divergences after tuning. Increase `target_accept` or reparameterize.
The acceptance probability does not match the target. It is 0.7010749464965044, but should be close to 0.8. Try to increase the number of tuning steps.
The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.
The estimated number of effective samples is smaller than 200 for some parameters.

100.00% [1000/1000 00:01<00:00]

Most ArviZ functions work fine with trace objects from PyMC3:

az.plot_autocorr(centered_eight_trace, var_names=["mu", "tau"]);

/Users/percy/anaconda3/envs/arviz/lib/python3.6/site-packages/arviz/data/io_pymc3.py:89: FutureWarning: Using `from_pymc3` without the model will be deprecated in a future release. Not using the model will return less accurate and less useful results. Make sure you use the model argument or call from_pymc3 within a model context.
  FutureWarning,

Convert to InferenceData¶

For much more powerful querying, analysis and plotting, we can use built-in ArviZ utilities to convert PyMC3 objects to xarray datasets. Note we are also giving some information about labelling.

ArviZ is built to work with InferenceData. The more groups it has access to, the more powerful analyses it can perform. You can check the InferenceData structure specification here. Given below is a plot of the trace, which is common in PyMC3 workflows. Don’t forget to note the intelligent labels.

data = az.from_pymc3(
    trace=centered_eight_trace,
    prior=prior,
    posterior_predictive=posterior_predictive,
    model=centered_eight,
    coords={"school": schools},
    dims={"theta": ["school"], "obs": ["school"]},
)
data

arviz.InferenceData

posterior

posterior_predictive
log_likelihood

sample_stats

prior

prior_predictive
observed_data

az.plot_trace(data);

Installation guide

Introduction to xarray, InferenceData, and netCDF for ArviZ

ArviZ Quickstart¶

ArviZ style sheets¶

Get started with plotting¶

ArviZ rcParams¶

Convert to InferenceData¶

Plotting with PyStan objects¶