beta_binom_post_plot.ipynb

Kernel: Unknown Kernel

import jax.numpy as jnp
import matplotlib.pyplot as plt

try:
    import probml_utils as pml
except ModuleNotFoundError:
    %pip install -qq git+https://github.com/probml/probml-utils.git
    import probml_utils as pml
from jax.scipy.stats import beta, bernoulli

# Points where we evaluate the pdf
x = jnp.linspace(0.001, 0.999, 100)


# Forms graph given the parameters of the prior, likelihood and posterior:
def make_graph(data, save_name):
    prior = beta.pdf(x, a=data["prior"]["a"], b=data["prior"]["b"])
    n_0 = data["likelihood"]["n_0"]
    n_1 = data["likelihood"]["n_1"]
    samples = jnp.concatenate([jnp.zeros(n_0), jnp.ones(n_1)])
    likelihood_function = jnp.vectorize(lambda p: jnp.exp(bernoulli.logpmf(samples, p).sum()))
    likelihood = likelihood_function(x)
    posterior = beta.pdf(x, a=data["posterior"]["a"], b=data["posterior"]["b"])

    fig, ax = plt.subplots()
    axt = ax.twinx()
    fig1 = ax.plot(
        x,
        prior,
        "k",
        label=f"prior Beta({data['prior']['a']}, {data['prior']['b']})",
        linewidth=2.0,
    )
    fig2 = axt.plot(x, likelihood, "r:", label=f"likelihood Bernoulli", linewidth=2.0)
    fig3 = ax.plot(
        x,
        posterior,
        "b-.",
        label=f"posterior Beta({data['posterior']['a']}, {data['posterior']['b']})",
        linewidth=2.0,
    )
    fig_list = fig1 + fig2 + fig3
    labels = [fig.get_label() for fig in fig_list]
    ax.legend(fig_list, labels, loc="upper left", shadow=True)
    axt.set_ylabel("Likelihood")
    ax.set_ylabel("Prior/Posterior")
    ax.set_title(f"$N_0$:{n_0}, $N_1$:{n_1}")
    pml.savefig(save_name)


data1 = {
    "prior": {"a": 1, "b": 1},
    "likelihood": {"n_0": 1, "n_1": 4},
    "posterior": {"a": 5, "b": 2},
}
make_graph(data1, "betaPostUninfSmallSample.pdf")

data2 = {
    "prior": {"a": 1, "b": 1},
    "likelihood": {"n_0": 10, "n_1": 40},
    "posterior": {"a": 41, "b": 11},
}
make_graph(data2, "betaPostUninfLargeSample.pdf")

data3 = {
    "prior": {"a": 2, "b": 2},
    "likelihood": {"n_0": 1, "n_1": 4},
    "posterior": {"a": 6, "b": 3},
}
make_graph(data3, "betaPostInfSmallSample.pdf")

data4 = {
    "prior": {"a": 2, "b": 2},
    "likelihood": {"n_0": 10, "n_1": 40},
    "posterior": {"a": 42, "b": 12},
}
make_graph(data4, "betaPostInfLargeSample.pdf")


plt.show()