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Figure 5.2: Using PyMC3 to fit a Bayesian GLM linear regression model to simulated data
The key point here is that we do not receive a single point estimate for a regression line, i.e.
"a line of best fit", as in the frequentist case. Instead we receive a distribution of likely regression
lines.
We can plot these lines using a method of the glm library called plot_posterior_predictive.
The method takes a trace object and the number of lines to plot (samples).
Firstly we use the seaborn lmplot method, this time with the fit_reg parameter set to
False to stop the frequentist regression line being drawn. Then we plot 100 sampled posterior
predictive regression lines. Finally, we plot the "true" regression line using the original β 0 = 1
and β 1 = 2 parameters. The code snippet below produces such a plot:
..
..
if __name__ == "__main__":
..
..
# Plot a sample of posterior regression lines
sns.lmplot(x="x", y="y", data=df, size=10, fit_reg=False)
plt.xlim(0.0, 1.0)
plt.ylim(0.0, 4.0)
pm.glm.plot_posterior_predictive(trace, samples=100)
x = np.linspace(0, 1, N)
y = beta_0 + beta_1*x
plt.plot(x, y, label="True Regression Line", lw=3., c="green")
plt.legend(loc=0)