CoCalc -- ttest_bambi.ipynb

GitHub Repository: probml/pyprobml
Path: blob/master/notebooks/book2/03/ttest_bambi.ipynb
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Kernel: base

Perform one sample Bayesian t-test on some toy data. Code is from

https://github.com/bambinos/bambi/blob/main/docs/notebooks/t-test.ipynb

In [1]:

try:
    from probml_utils import savefig, latexify
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    from probml_utils import savefig, latexify

In [9]:

import os

# For making figures in the book
# os.environ["FIG_DIR"] = "/Users/kpmurphy/github/bookv2/figures"
# os.environ["LATEXIFY"] = "1"
# latexify(fig_height=1.5)

Out[9]:

/opt/anaconda3/lib/python3.8/site-packages/probml_utils/plotting.py:25: UserWarning: LATEXIFY environment variable not set, not latexifying
  warnings.warn("LATEXIFY environment variable not set, not latexifying")

In [2]:


try:
    import bambi
except ModuleNotFoundError:
    %pip uninstall -y numba numpy resampy librosa kapre # hack for public colab (h/t Ravin Kumar)
    %pip install git+https://github.com/bambinos/bambi.git
    #%pip install bambi
    import bambi

Out[2]:

WARNING (pytensor.configdefaults): g++ not detected!  PyTensor will be unable to compile C-implementations and will default to Python. Performance may be severely degraded. To remove this warning, set PyTensor flags cxx to an empty string.
<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject
WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.

In [26]:

import arviz as az
import bambi as bmb
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

In [4]:

az.style.use("arviz-darkgrid")
np.random.seed(1234)

In [6]:

a = np.random.normal(6, 2.5, 160)
b = np.random.normal(8, 2, 120)
df = pd.DataFrame({"Group": ["a"] * 160 + ["b"] * 120, "Val": np.hstack([a, b])})

df.head()

Out[6]:

In [11]:

az.plot_violin({"a": a, "b": b})
savefig("ttest_bambi_violin")

Out[11]:

/opt/anaconda3/lib/python3.8/site-packages/arviz/plots/backends/matplotlib/violinplot.py:64: UserWarning: This figure was using a layout engine that is incompatible with subplots_adjust and/or tight_layout; not calling subplots_adjust.
  fig.subplots_adjust(wspace=0)

saving image to /Users/kpmurphy/github/bookv2/figures/ttest_bambi_violin.pdf
Figure size: [13.8  4.6]

In [25]:

ndx = df["Group"] == "a"
data_a = df[ndx]["Val"]
data_a

Out[25]:

     4.773791
     5.063908
     0.006240
     9.852575
     6.157711
         ...    
   9.893494
   4.516609
   5.574279
  10.181567
   4.648000
Name: Val, Length: 160, dtype: float64

In [28]:

sns.boxplot(y="Val", x="Group", data=df)
savefig("ttest_bambi_boxplot")
plt.show()

Out[28]:

saving image to /Users/kpmurphy/github/bookv2/figures/ttest_bambi_boxplot.pdf
Figure size: [6. 4.]

In [12]:

# We fit a model with no intercept (by specifying 0 in the formula)
# Thus  beta[g] corresponds to group g for g in {A,B}

model_2 = bmb.Model("Val ~ 0 + Group", df)
results_2 = model_2.fit()

Out[12]:

Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [Group, Val_sigma]

Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 57 seconds.

In [13]:

model_2

Out[13]:

Formula: Val ~ 0 + Group
Family name: Gaussian
Link: identity
Observations: 280
Priors:
  Common-level effects
    Group ~ Normal(mu: [0. 0.], sigma: [11.6292 11.6292])

  Auxiliary parameters
    sigma ~ HalfStudentT(nu: 4, sigma: 2.302)
------
* To see a plot of the priors call the .plot_priors() method.
* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()

In [14]:

az.plot_trace(results_2, kind="rank_vlines");

Out[14]:

In [19]:

post_group = results_2.posterior["Group"]
diff = post_group.sel(Group_dim="b") - post_group.sel(Group_dim="a")
az.plot_posterior(diff, hdi_prob=0.95)
savefig("ttest_bambi_post_diff")

Out[19]:

saving image to /Users/kpmurphy/github/bookv2/figures/ttest_bambi_post_diff.pdf
Figure size: [6. 4.]

In [20]:

post_group = results_2.posterior["Group"]
az.plot_posterior(post_group.sel(Group_dim="a"), hdi_prob=0.95)
savefig("ttest_bambi_post_a")

az.plot_posterior(post_group.sel(Group_dim="b"), hdi_prob=0.95)
savefig("ttest_bambi_post_b")

Out[20]:

saving image to /Users/kpmurphy/github/bookv2/figures/ttest_bambi_post_a.pdf
Figure size: [6. 4.]
saving image to /Users/kpmurphy/github/bookv2/figures/ttest_bambi_post_b.pdf
Figure size: [6. 4.]

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